# 3-D temperature distribution beneath the Mid-Norwegian continental margin (the Vøring and Møre basins)

3-D temperature distribution beneath the Mid-Norwegian continental margin (the Vøring and Møre... SUMMARY A 3-D thermal model of the Møre and Vøring segments of the Mid-Norwegian continental margin and adjacent areas of the continent has been calculated in a recent 3-D lithospheric and potential field model. The thermal model correlates well with the main tectonic units of the study area, showing a clear increase of the temperatures towards the oceanic domain where the lithosphere-asthenosphere boundary is still shallow at the present day. This long-wavelength thermal effect prevails over other thermal and semi-regional disturbances observed within the model area. In addition, the blanketing effect of the thick sedimentary infill in the Vøring Basin causes the modelled temperatures to be highest within this basin where the sedimentary infill is thickest. On the other hand, the Møre Basin is characterised by slightly lower temperatures and the modelled temperatures are even lower within the Trøndelag Platform, less affected by crustal thinning. A comparison between the modelled and measured temperatures indicates that there is a good correlation between the borehole measurements and the results of our simulations. However, some large residual misfits between the measured and the modelled temperatures in some of the boreholes indicate that a purely conductive thermal field within the Mid-Norwegian continental margin can be locally disrupted by fluid flow circulation (convection and/or advection). A clearly distinguished zone of increased radiogenic heat production has been traced through the Cretaceous and Cenozoic sedimentary intervals suggesting a possible source-to-sink correlation between the clastic material and the eroded rocks. This radiogenic pattern of the sedimentary rocks may also indicate a differentiation of the eroded clastics by grain size during their transportation. Heat flow, Atlantic Ocean, Europe, Numerical modelling, Continental margins: divergent, Heat generation and transport 1 INTRODUCTION Understanding the temperature distribution at different depths within a continental rifted margin is a challenging topic especially around the ambiguous continental-ocean transition (Clerc et al.2015). Located between Fennoscandia and the Norwegian-Greenland Sea, the Mid-Norwegian passive volcanic (and rifted) margin is not an exception (Fig. 1). Figure 1. View largeDownload slide Overview map of northwestern Europe (bathymetry and topography from the Norwegian Mapping Authority), showing location of the detailed 3-D thermal model (orange frame) and the large, low-resolution, 3-D thermal model (magenta dashed frame). Figure 1. View largeDownload slide Overview map of northwestern Europe (bathymetry and topography from the Norwegian Mapping Authority), showing location of the detailed 3-D thermal model (orange frame) and the large, low-resolution, 3-D thermal model (magenta dashed frame). The Mid-Norwegian continental margin comprises three tectonically different segments, such as the Lofoten-Vesterålen margin segment in the northeast and the Møre and Vøring segments in the southwest. The pre-breakup tectonic history of the study area was dominated by the Caledonian Orogeny (Roberts & Gee 1985; Gee et al.2008), structural features of which are still easily observed within western Scandinavia in terms of several tectonic sheets or nappes, overthrusted onto the Precambrian Fennoscandian Shield (e.g. Sigmond 2002; Gee et al.2017). The Caledonian orogen collapsed during a Devonian extensional event coeval with the formation of several Devonian basins (Fossen 2010). Later on, several Late Palaeozoic and Mesozoic extensional events led to the formation of Permo-Jurassic sub-basins within the Trøndelag Platform, as well as the deposition of thick Cretaceous sedimentary sequences along major and ‘superextended’ Cretaceous sag basins observed offshore Norway (Fig. 2; Blystad et al.1995; Doré et al.1999; Brekke 2000; Mosar et al.2002; Gernigon et al.2003; Scheck-Wenderoth et al.2007; Faleide et al.2008; Lundin & Doré 2011). The final stage of the Mid-Norwegian margin culminated in the early Cenozoic when continental breakup initiated the formation of a relatively young oceanic lithosphere between Laurentia and Baltica (Talwani & Eldholm 1977; Srivastava & Tapscott 1986; Brekke 2000; Skogseid et al.2000; Olesen et al.2007; Faleide et al.2008; Gaina et al.2009; Gernigon et al.2015a). Figure 2. View largeDownload slide Tectonic configuration of the Mid-Norwegian continental margin (simplified after Blystad et al.1995) with location of the large and detailed 3-D structural models. The bold black lines indicate the location of the three selected vertical slices through the model. Figure 2. View largeDownload slide Tectonic configuration of the Mid-Norwegian continental margin (simplified after Blystad et al.1995) with location of the large and detailed 3-D structural models. The bold black lines indicate the location of the three selected vertical slices through the model. Since the first oil discoveries on the Norwegian continental shelf in the 1960s–1970s, the structure of the Mid-Norwegian margin has been intensively investigated by both the oil and gas industry and academia, providing a large amount of borehole and reflection/refraction seismic data which are sufficient to constrain basin-scale 3-D structural and crustal models within the study area (Torne et al.2003; Ebbing et al.2006; Scheck-Wenderoth et al.2007; Maystrenko & Scheck-Wenderoth 2009; Reynisson 2010; Reynisson et al.2010; Maystrenko et al.2018). In addition, several attempts were already made to model the 2-D/3-D thermal state of the Mid-Norwegian margin (e.g. Fernandez et al. 2004, 2005; Gernigon et al.2006; Pascal & Ebbing 2007; Scheck-Wenderoth & Maystrenko 2008; Wangen et al.2008; Ebbing et al.2009; Rüpke et al. 2013), showing that detailed knowledge about the configuration and physical properties of the sedimentary cover, crystalline crust and uppermost mantle is a major and primary constraint for obtaining a consistent thermal structure of the deep parts of the continental margin. In addition, several heat-flow studies have been performed within the Mid-Norwegian margin (Sundvor et al.1989, 2000; Ritter et al.2004; Pascal & Midttømme 2006; Slagstad et al.2009; Pascal 2015) and the adjacent mainland (e.g. Slagstad et al.2009; Pascal 2015). In this paper, the most recent 3-D structural model by Maystrenko et al. (2018) has been used as a structural background for a new 3-D thermal modelling study within the Mid-Norwegian margin. The main aim of this study was to understand and simulate the conductive thermal regime beneath the Mid-Norwegian continental margin and adjacent areas. The background 3-D model from Maystrenko et al. (2018) is based on the most recently published/released structural data and has been validated by the 3-D density and magnetic modelling. It represents the most up-to-date data-based approximation of the Mid-Norwegian continental margin and its crustal configuration. The 3-D structural/crustal model has been accordingly transformed into a present-day 3-D thermal model by means of a full 3-D thermal modelling calculation. The method and results of this 3-D conductive thermal modelling are presented in this contribution, revealing the present-day temperature distribution and pattern of the subsurface within the Møre and Vøring segments of the Mid-Norwegian continental margin. This approach helps to test and better understand the present-day nature and composition of the basement rocks that are expected to occur underneath the sedimentary basins of the Norwegian shelf. 2 METHODOLOGY The 3-D temperature distribution within the structurally complex 3-D model of the Mid-Norwegian continental margin and adjacent mainland has been calculated using the commercial software package COMSOL Multiphysics. COMSOL Multiphysics is a finite-element analysis software package often used for a variety of physical processes. During the 3-D thermal modelling, the Heat Transfer Module was considered to simulate the stationary and time-dependent heat transfer in solid materials by heat conduction, which is considered to be the dominant mechanism of heat transfer at the regional scale within the subsurface of the investigated area. These calculations have been performed based on physical principles of the conductive 3-D thermal field by solving the heat equation (1):   \begin{eqnarray} \rho {C_{\rm{p}}}(\partial T/\partial t) &=& \nabla \cdot (k\nabla T) + Q \end{eqnarray} (1)where ρ is the density [kg m−3], Cp is the specific heat capacity [J kg−1 K−1], T is the temperature [K], k is the thermal conductivity [W m−1 K−1], ∇T is the temperature gradient [K m−1], t is the time [s], Q is the internal heat production (radioactive heat production) [W m−3], ∂T/∂t denotes the change of temperature with time, and ∇ is the operator giving the spatial variation in temperature. Consequently, the solution of the heat equation (1) is sensitive to the values of the thermal properties (specific heat capacity, thermal conductivity and radiogenic heat production) and density as well as the thermal boundary conditions. During the thermal simulation, the heat flux q [W m−2] has been calculated according to Fourier's law of heat conduction (2):   $$q = - k\nabla T$$ (2)where k is the thermal conductivity [W m−1 K−1] and ∇T is the temperature gradient [K m−1]. The thermal modelling has been performed in 3-D which is a suitable approach taking into consideration the rather complex geometry of the Mid-Norwegian continental margin and adjacent areas. The lateral boundaries are closed to heat transfer, assuming that the temperature gradient is zero across the thermally insulated lateral boundaries. The time-dependent temperatures at the seafloor and at the Earth’s surface (Fig. 3a) have been set as the upper thermal boundary condition, whereas the base of the lithosphere (Fig. 3b) has been taken as a lower thermal boundary, assuming that the lower thermal boundary corresponds to the ‘conventional’ 1300 °C isotherm (e.g. Turcotte & Schubert 2002). The importance of the lower thermal boundary configuration within the continent-ocean transition has been previously examined by Scheck-Wenderoth & Maystrenko (2008), indicating that lithospheric thickness from seismology, according to Zhang & Lay (1999), is a suitable and first-order assumption for 3-D thermal modelling. The depth to the lithosphere–asthenosphere boundary beneath the oceanic crustal domain has been obtained based on the age of the oceanic lithosphere (Müller et al.2008) and Love and Rayleigh wave-phase velocity empirical relations in Zhang & Lay (1999), reflecting a gradual cooling of the oceanic lithosphere after the continental breakup. The base of the lithosphere beneath the continent has been taken from Gradmann et al. (2013). Finally, an almost linear interpolation has been applied in order to fill the data gaps between the oceanic and the continental domains. Figure 3. View largeDownload slide (a) Present-day upper thermal boundary: annual average air temperatures during 1961–1990 for Norway (Tveito et al.2000) and Sweden (Raab & Vedin 1995). Average sea-bottom temperature, derived from Ottersen (2009); ICES (2012) and Korablev et al. (2014). (b) Depth to the present-day lower thermal boundary (represented by the 1300 °C isotherm at the lithosphere-asthenosphere boundary). COB, continent-ocean boundary (from Gernigon et al.2015a); JMC, Jan Mayen Corridor; JMFZ, Jan Mayen Fracture Zone; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. Figure 3. View largeDownload slide (a) Present-day upper thermal boundary: annual average air temperatures during 1961–1990 for Norway (Tveito et al.2000) and Sweden (Raab & Vedin 1995). Average sea-bottom temperature, derived from Ottersen (2009); ICES (2012) and Korablev et al. (2014). (b) Depth to the present-day lower thermal boundary (represented by the 1300 °C isotherm at the lithosphere-asthenosphere boundary). COB, continent-ocean boundary (from Gernigon et al.2015a); JMC, Jan Mayen Corridor; JMFZ, Jan Mayen Fracture Zone; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. The present-day temperature at the Earth’s surface (Fig. 3a) is represented by the annual average air temperatures of the region during the period 1961–1990 provided by the Norwegian Meteorological Institute (Tveito et al.2000) and the National Atlas of Sweden (Raab & Vedin 1995). The temperature at the seafloor (Fig. 3a) has been inferred from published values of bottom temperatures within the Norwegian Sea (Ottersen 2009; Korablev et al.2014), being set to be dependent on the bathymetry (Table 1) with a slight decrease of temperature towards the northeast (Fig. 3a). In addition, published seasonal values of average sea-bottom temperatures within the North Sea during 1997–2002 (ICES 2012) have been used to cross-check the sea-bottom temperatures within the northernmost part of the North Sea. Table 1. Present-day average annual temperature at the seafloor of the Norwegian Sea. Bathymetry (m)  100  300  500  600  700  750  800  850 and deeper  Temperature (°C)  7  6  5  4  3  2  1  0  Bathymetry (m)  100  300  500  600  700  750  800  850 and deeper  Temperature (°C)  7  6  5  4  3  2  1  0  View Large The 3-D thermal modelling also takes into account the detailed palaeoclimatic changes of the surface temperature during the last 228 000 yr before present (BP). During this time interval, the study area was affected by glaciations during the Saalian glacial period with interruptions during the Eemian interglacial period (220 000–118 000 yr BP) and the Weichselian glacial period (∼110 000–10 000 yr BP; Fig. 4), as well as by the Holocene interglacial period (10 000 yr BP to present day). The palaeotemperatures during the last 8000 yr (Table 2) are represented by almost 0.4 °C below the present-day average air temperature during the Little Ice Age (Nesje et al.2008; Mann et al.2009; Fig. 5a) and by 1 °C above the present-day average air temperature during the Holocene Climate Optimum (e.g. Seppä et al.2009; Fig. 5b). Palaeotemperature at 8000 yr BP (Fig. 5c) has been set to be 1 °C below the present-day surface temperature (Davis et al.2003; Fig. 3a). Figure 4. View largeDownload slide Ice cover during the Weichselian glaciation (after Olsen et al.2013). The detailed 3-D model is defined by the orange frame and the large-scale structural model by the magenta dashed frame. JMC, Jan Mayen Corridor; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. Figure 4. View largeDownload slide Ice cover during the Weichselian glaciation (after Olsen et al.2013). The detailed 3-D model is defined by the orange frame and the large-scale structural model by the magenta dashed frame. JMC, Jan Mayen Corridor; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. Figure 5. View largeDownload slide Annual average palaeotemperatures at the Earth’s surface and the sea bottom during the Weichselian glaciation. JMC, Jan Mayen Corridor; MB, Møre Basin; SM, Scandes Mountains; TP, Trøndelag Platform; VB, Vøring Basin. Figure 5. View largeDownload slide Annual average palaeotemperatures at the Earth’s surface and the sea bottom during the Weichselian glaciation. JMC, Jan Mayen Corridor; MB, Møre Basin; SM, Scandes Mountains; TP, Trøndelag Platform; VB, Vøring Basin. Table 2. Difference between palaeotemperatures and the present-day temperature for the last 8000 yr. Time, years before present BP  0 Present day  400 Little Ice Age  7500 Holocene Optimum  8000  Temperature difference in relation to present day (°C)  0  −0.4  +1  −1  Time, years before present BP  0 Present day  400 Little Ice Age  7500 Holocene Optimum  8000  Temperature difference in relation to present day (°C)  0  −0.4  +1  −1  View Large To reconstruct the palaeoclimatic thermal conditions at the Earth's surface within the Mid-Norwegian continental margin and surrounding areas, a model showing the spatio-temporal variations of the ice cover within Scandinavia during the Weichselian glacial period has been used according to a set of maps published in Olsen et al. (2013). The spatial distribution of the ice cover through time is reproduced in Fig. 4, showing the position of the large-scale and detailed 3-D structural models. According to these data (Olsen et al.2013; Fig. 4), the continent within the study area was almost continuously covered by a variably shaped Weichselian ice cover which could have reached up to 3 km thickness during the Last Glacial Maximum (Siegert et al.2001). The same palaeoclimatic scenario was also applied for the Saalian glacial/Eemian interglacial period (220 000–118 000 yr BP), taking into account that palaeoclimatic conditions were relatively similar during the Weichselian glacial/Holocene interglacial and the Saalian glacial/Eemian interglacial periods (Andersen & Borns 1994; Slagstad et al.2009). When the study area was glaciated, a temperature of −0.5 °C has been set at the Earth’s surface beneath the ice cover as previously used and discussed by Slagstad et al. (2009). A near-melting point temperature of −0.5 °C is in agreement with published estimations of the subglacial thermal regime beneath the large polar ice sheets in Antarctica, which is presumably a comparable analogue to the ice sheets developed during the Quaternary glacial cycles in northern Europe. The main features of the Antarctic subglacial conditions have been discussed by Pattyn (2010) who has shown that the mean basal temperature of the ice is in the range of −1 to 0 °C for the greater part of Antarctica. Besides, an airborne radar survey detected approximately 100 lakes under the Antarctic ice cap (Price et al.2002), the largest of which, Lake Vostok, has already been drilled (Jones 2012; Lake Vostok Drilling Project 2014). Palaeotemperature at the seafloor during the glacial periods was set as 0 °C which is in agreement with reconstructed temperature anomalies for the Norwegian Sea during the period 12 000–23 000 yr BP (Eldevik et al.2014). According to Eldevik et al. (2014), the palaeotemperatures were 6–7 °C less than the present-day temperatures within the Norwegian Sea. Palaeotemperatures have been taken from Schmittner et al. (2011) who modelled the annual mean surface temperatures during the Last Glacial Maximum. The estimated temperatures from Schmittner et al. (2011) are similar to other estimations of the surface temperatures during the Last Glacial Maximum (e.g. Otto-Bliesner et al.2006; Bartlein et al.1998; Hofer et al.2012; Ziemen et al.2012), showing that the near-surface air temperature difference could be about −20 °C lower compared to the pre-industrial period (present day before the Industrial Revolution). However, this estimation is only valid for the Last Glacial Maximum when the air temperatures were at their lowest estimation during the Weichselian glaciation. In order to consider this fact, temperatures lower than −11 °C from Schmittner et al. (2011) have been reduced slightly by 1–4 °C to become more similar to the modelled mean annual temperatures for the Younger Dryas (Renssen & Isarin 1998) when the palaeoclimate was warmer. Consequently, the reduced palaeotemperatures from Schmittner et al. (2011) have been considered at the Earth’s surface where the ice cover was absent. Temperatures along the marginal parts of the ice sheet are unknown in detail. For that reason, these temperatures have been obtained by a simple interpolation between −0.5 °C beneath the internal parts of the ice cover and the derived temperature over the remaining land areas. The reconstruction of the annual average palaeotemperatures at the sea bottom and the Earth’s surface demonstrates that the detailed 3-D model area was mostly characterised by much lower palaeotemperatures during the Weichselian glaciation compared to the present day (cf. Figs 3a and 5). In particular, the surface temperature could be locally less than −15 °C over the continent where the ice cover was absent or very thin. These sub-zero temperatures imply the persistence of permanently frozen ground during the glacial periods. From a theoretical point of view, the palaeopermafrost could have reached a depth of more than 1–2 km (e.g. Dobinski 2011). The global palaeo sea level was 80–120 m lower than the present-day one during the Weichselian glaciation (e.g. Hasenclever et al.2017). Moreover, the glacial erosion of the sedimentary cover could have been quite significant locally especially near the coastline that is marked by the presence of an erosional unconformity and the deposition of the relatively thick and youngest part of the Naust Formation (sequence T; e.g. Ottesen et al.2009; Montelli et al.2017). Therefore, the present-day bathymetry does not necessarily reflect the one that existed during Weichselian time. Due to the above-mentioned uncertainties, a zone showing a gradual transition of temperatures from the mainland conditions towards the sea has been included into the palaeotemperature scenario for the whole of the Weichselian glacial period (Fig. 5), covering the present-day 120 m bathymetry and a deeper one parallel to the coast. In general, a more complex palaeoclimatic scenario could apply for time intervals when some parts of the Mid-Norwegian continental margin were free of ice and seawater. However, more precise and regional-scale positions of the palaeo-shorelines within the study area are not yet available. We cannot exclude the possibility that a real temperature near the coastline within the areas with shallow bathymetry may differ from the temperatures which have been obtained during the thermal simulations of the uppermost levels of our 3-D model. In addition, the influence of the early Cenozoic continental breakup has been roughly taken into account during the 3-D thermal modelling. Two scenarios for the lithosphere-asthenosphere boundaries have been considered: (1) almost immediately after the continental breakup, around 55 Ma ago (Fig. 6a), and (2) almost at the end of the deposition of the Brygge Formation (23 Ma ago; Fig. 6b). These two time-periods (55 Ma and 23 Ma) provide an opportunity to simulate the effect of the increased geothermal gradient due to continental breakup in the early Cenozoic and the subsequent cooling of the oceanic lithosphere during the rest of the Cenozoic. However, it is worth noting that the position of the base of the lithosphere at the end of the Palaeocene is not known in detail especially if the controversial icelandic plume, alternatively small-scale convection and/or asthenospheric plumbing, was involved (or not) during the processes of breakup of the volcanic margin (e.g. Geoffroy 2005; Gernigon et al.2006). On the other hand, most numerical models predict a relatively shallow position of the 1300 °C isotherm within the present-day axis of the oceanic spreading centre beneath the mid-oceanic ridges (e.g. Chen & Lin 2004). In this study, the depth position of the lithosphere-asthenosphere boundary at the end of the Palaeocene has been tentatively set to be around 15 km deep beneath the present-day oceanic domain, representing the new accreted lithosphere there. According to seismic models for 0 Ma oceanic lithosphere by Zhang & Lay (1999), the chosen depth position of the lithosphere-asthenosphere boundary at the end of the Palaeocene could vary in the range of ±5 km if two average models for the Atlantic Ocean and three other oceans (Atlantic, Pacific and Indian oceans) are considered. Moreover, the present-day depth position of the base of the lithosphere, which is deeper than 85–95 km, has been kept constant beneath the mainland and over a large part of the continental margin. The depth to the lithosphere-asthenosphere boundary between the oceanic domain and the more than 85–95 km-deep continental lithosphere has been obtained by linear interpolation, assuming that the adjacent continental lithosphere has also been thinned in the vicinity of the oceanic domain (Fig. 6a). The lithosphere-asthenosphere boundary for the early Miocene (Fig. 6b) has been calculated as a half of the difference between the present-day base of the lithosphere (Fig. 3a) and the base after the continental breakup in the earliest Eocene (Fig. 6a) within the oceanic domain and the adjacent continental part. However, there are definitely large inherent uncertainties in these palaeo-depth estimations of the palaeobase of the lithosphere (Fig. 6). Figure 6. View largeDownload slide Estimated depth of the lithosphere–asthenosphere boundary corresponding to the 1300 °C isotherm after the continental breakup 55 Ma ago (a) and near the end of the Brygge interval 23 Ma ago (b). COB, continent–ocean boundary (from Gernigon et al.2015a); JMC, Jan Mayen Corridor; JMFZ, Jan Mayen Fracture Zone; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. Figure 6. View largeDownload slide Estimated depth of the lithosphere–asthenosphere boundary corresponding to the 1300 °C isotherm after the continental breakup 55 Ma ago (a) and near the end of the Brygge interval 23 Ma ago (b). COB, continent–ocean boundary (from Gernigon et al.2015a); JMC, Jan Mayen Corridor; JMFZ, Jan Mayen Fracture Zone; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. The next factor involving the thermal disturbance of the study area related to the syn-breakup magmatism is represented by the lower-crustal underplating, middle- to upper-crustal dykes and surface volcanic activity. The problem is that magmatic activity can locally increase the geothermal gradient, but the process itself is very complex and requires more detailed investigations which are outside the scope of the present study. Moreover, the real nature of the so-called underplating and its thermal implication is still under discussion (e.g. Fjeldskaar et al.2003; Gernigon et al.2006; Wangen et al.2011). For that reason, the influence of the syn-breakup magmatism has been mainly neglected in the present study. In addition to the above-mentioned factors, an influence of the post-breakup deposition of the Kai-Naust (middle Miocene-Pleistocene) and Brygge (Eocene-lower Miocene) formations (layers 2 and 3, respectively; Figs 7a and b) has been roughly included into the 3-D thermal modelling. This helps in considering the transient perturbations in the near-surface thermal regime as a result of the post-Palaeocene sedimentation. The Cenozoic palaeoclimatic scenario only reflects a gradual decrease of the palaeotemperature from 19 °C 55 Ma ago to present-day temperature at the mainland surface (e.g. Zachos et al.2001; Eldrett et al.2009). A temperature variation from 4 °C 18 Ma ago to 0 °C at the present-day seafloor within the deep sea was also considered (e.g. Hansen et al.2013). Palaeotemperature between the mainland and the deep sea has been obtained by interpolation of temperatures from the deep sea and the mainland. Figure 7. View largeDownload slide Thicknesses of the Cenozoic sedimentary rocks showing (a) the Kai-Naust formations (middle Miocene–Pleistocene; layer 2), (b) the Brygge Formation (Eocene-lower Miocene; layer 3) and (c) the Palaeocene (Base Tertiary Unconformity-top Palaeocene; layer 4). Thicknesses of the Cretaceous sedimentary rocks are represented by (d) the Upper Cretaceous (near top Cenomanian-Base Tertiary Unconformity; layer 6) and (e) the Lower Cretaceous (base Cretaceous unconformity-near top Cenomanian; layer 7). (f) Thickness of pre-Cretaceous sedimentary rocks. JMC, Jan Mayen Corridor; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. Figure 7. View largeDownload slide Thicknesses of the Cenozoic sedimentary rocks showing (a) the Kai-Naust formations (middle Miocene–Pleistocene; layer 2), (b) the Brygge Formation (Eocene-lower Miocene; layer 3) and (c) the Palaeocene (Base Tertiary Unconformity-top Palaeocene; layer 4). Thicknesses of the Cretaceous sedimentary rocks are represented by (d) the Upper Cretaceous (near top Cenomanian-Base Tertiary Unconformity; layer 6) and (e) the Lower Cretaceous (base Cretaceous unconformity-near top Cenomanian; layer 7). (f) Thickness of pre-Cretaceous sedimentary rocks. JMC, Jan Mayen Corridor; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. The thermal modelling workflow includes: A steady-state calculation of the 3-D conductive thermal field after the continental breakup 55 Ma ago. The lower thermal boundary (1300 °C) has been set to the inferred lithosphere-asthenosphere boundary at 55 Ma ago (Fig. 6a), whereas the top of Palaeocene deposits has been used as an upper thermal boundary. Top of the older rocks has been taken as the upper thermal boundary in places where the Palaeocene is absent. The Brygge and Kai-Naust formations (Eocene-Pleistocene interval) have been excluded from calculations. The porosity of the pre-breakup sedimentary rocks has been adjusted to shallower depth conditions compared to the present-day ones by subtraction of the thickness of the post-breakup sedimentary package (e.g. Brygge and Kai-Naust formations; Eocene-Pleistocene interval) from the present-day depths and correction of the present-day deep seafloor position. Accordingly, the porosity-dependent thermal conductivities and densities of the sedimentary cover have been adjusted to shallower depths. A time-dependent (transient) calculation of the 3-D conductive thermal field from 55 Ma ago to the end of Brygge interval in the early Miocene 18 Ma ago. The modelled 3-D temperature distribution from step (1) has been used as the initial temperature condition at the beginning of the time-dependent calculations (55 Ma ago). The lower thermal boundary (1300 °C) has been set to the lithosphere-asthenosphere boundary inferred for the late Brygge interval (23 Ma ago; Fig. 6b), whereas the top of the Brygge Formation (Eocene-lower Miocene) has been used as the upper thermal boundary. Top of the older rocks has been taken as the upper thermal boundary in places where the Brygge (Eocene-lower Miocene) Formation is absent. The Kai-Naust formations (middle Miocene-Pleistocene interval) have been excluded from the calculations. Porosity of the pre-breakup and Brygge (Eocene-lower Miocene) sedimentary rocks has been adjusted to new depth conditions by subtraction of the thickness of the Kai-Naust (middle Miocene-Pleistocene) formation from the present-day depths and correction of the present-day deep seafloor position. Therefore, due to technical simplifications, only the full thickness of the Brygge Formation has been considered during this step and does not consider any gradual infilling of the sedimentary basin. The final step includes a time-dependent (transient) calculation of the 3-D conductive thermal field from 18 Ma ago to the present day. The final modelled 3-D temperature distribution from step (2) has been used as the initial temperature condition at the beginning of the time-dependent calculations (18 Ma ago). The lower thermal boundary (1300 °C) has been set to the present-day lithosphere-asthenosphere boundary (Fig. 3b), whereas the seafloor offshore and Earth's surface onshore have been considered as the upper thermal boundary. Porosity has been estimated according to the present-day depths. During all steps, temperatures at the upper thermal boundary have been set to be time-dependent according to Tables 1–3 and Fig. 5. Table 3. Palaeotemperatures during the Cenozoic (based on Zachos et al.2001; Ravelo et al. 2004; Pekar et al.2006; Rise et al.2006; Eldrett et al.2009; Ehlers et al.2011; Hansen et al.2013; Inglis et al.2017). No.  Time, Ma ago  Mainland temperature (°C)  Deep sea temperature (°C)  1  55  19  –  2  45  15  9  3  34  11  4  4  25  12.5  6  5  18  11.5  5  6  5  7  2  7  3.6  +3 °C to present-day temperature  0  8  0.45  present-day temperature  present-day temperature  9  0.35  the same as glacial maximum 27 000 years ago in Fig. 5  the same as glacial maximum 27 000 yr ago in Fig. 5  10  0.228  present-day temperature  present-day temperature  11  0.220–0.118  the same as 0.110–0.0105 Ma ago  the same as 0.110–0.0105 Ma ago  12  0.110–0.0105  Fig. 5  Fig. 5  No.  Time, Ma ago  Mainland temperature (°C)  Deep sea temperature (°C)  1  55  19  –  2  45  15  9  3  34  11  4  4  25  12.5  6  5  18  11.5  5  6  5  7  2  7  3.6  +3 °C to present-day temperature  0  8  0.45  present-day temperature  present-day temperature  9  0.35  the same as glacial maximum 27 000 years ago in Fig. 5  the same as glacial maximum 27 000 yr ago in Fig. 5  10  0.228  present-day temperature  present-day temperature  11  0.220–0.118  the same as 0.110–0.0105 Ma ago  the same as 0.110–0.0105 Ma ago  12  0.110–0.0105  Fig. 5  Fig. 5  View Large 3 DATABASE Bathymetry and topography for the investigated area have been taken from the Norwegian Mapping Authority. The altitude of the Scandes mountains is more than 2100 m and depth to the seafloor is locally more than −2200 m, showing more than 4 km difference in relief between the Mid-Norwegian continental margin and the surrounding areas (Fig. 1). This large difference is one of the key factors which control the distribution of the subsurface temperature at the shallow levels of the 3-D model. It is important to note that the 3-D thermal modelling has been performed within a smaller area already covered by the large-scale 3-D structural model further described in detail in Maystrenko et al. (2018). This has been done in order to consider the long wavelengths and regional thermal influence between the oceanic and the continental lithospheric domains which are not completely covered by the NE-SW-oriented and detailed 3-D model described in this study (Figs 1 and 2). Use of the large 3-D model makes it possible to consider as much as possible the thermal effects of the lithosphere-asthenosphere boundary and Moho positions from the ocean (shallow) towards the Fennoscandian Shield (deep). The detailed 3-D thermal modelling has been restricted to the detailed 3-D model, whereas the larger model has been used only to consider the large-scale thermal influence. The sedimentary cover of the detailed 3-D model is described in detail in Masytrenko et al. (2018). This background model is characterised by six structural layers (Fig. 7): the Kai-Naust (base Kai-sea floor; middle Miocene-Pleistocene) (layer 2), the Brygge Formation (top Palaeocene-base Kai; Eocene-lower Miocene) (layer 3), the Palaeocene units (base Tertiary unconformity-top Palaeocene) (layer 4), Upper Cretaceous unit (near top Cenomanian-base Tertiary unconformity) (layer 6), the Lower Cretaceous unit (base Cretaceous unconformity-near top Cenomanian) (layer 7) and the pre-Cretaceous unit (Jurassic, Triassic and older sedimentary rocks) (layer 8). It is important to mention that the Kai-Naust, Brygge and Palaeocene correspond to the Nordland, Hordaland and Rogaland groups (Dalland et al.1988), respectively, whereas the Shetland and Cromer Knoll groups are not correlated exactly with the Upper Cretaceous and the Lower Cretaceous in some regions of the study area. The maps for the Brygge-Naust (Eocene-Pleistocene) interval (Figs 7a and b) have been derived based on data from Rise et al. (2005, 2010) Eidvin et al. (2007), Dowdeswell et al. (2010), and Ottesen et al. (2012), whereas maps for the Palaeocene and Cretaceous (Figs 7c–e) have been taken from Gernigon (NGU unpublished data). The thickness of the pre-Cretaceous (Fig. 7f) has been calculated as the difference between the base of the Cretaceous-Cenozoic sedimentary rocks and the top of the crystalline basement (Maystrenko et al., 2018). Configuration of the crystalline crust (Fig. 8) is an outcome of the combined 3-D density/magnetic modelling (Maystrenko et al., 2018) with use of the most recent geophysical data set mainly represented by the deep seismic profiles (Mjelde et al. 1997, 2001, 2002, 2003, 2005, 2009; Raum 2000, Raum et al.2002, 2006; Breivik et al. 2006, 2009, 2011; Kvarven et al. 2014, 2016), including structural data from Maystrenko & Scheck-Wenderoth (2009); Ebbing & Olesen (2010); Nirrengarten et al. (2014) and Gernigon et al. (2015b). Figure 8. View largeDownload slide Thicknesses: (a) the oceanic layer 2AB and upper crustal high-density rocks (layers 5 and 9, respectively), (b) the low-density upper-crustal layer (layer 10), (c) the regional upper-crustal layer (layer 11), (d) the middle crust (layer 12), (e) the lower crust including the high-density intracrustal layer (layers 13 and 14, respectively) and (f) the deep high-density lower-crustal layer (layer 15). JMC, Jan Mayen Corridor; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. Figure 8. View largeDownload slide Thicknesses: (a) the oceanic layer 2AB and upper crustal high-density rocks (layers 5 and 9, respectively), (b) the low-density upper-crustal layer (layer 10), (c) the regional upper-crustal layer (layer 11), (d) the middle crust (layer 12), (e) the lower crust including the high-density intracrustal layer (layers 13 and 14, respectively) and (f) the deep high-density lower-crustal layer (layer 15). JMC, Jan Mayen Corridor; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. The top of the crystalline basement (Maystrenko et al., 2018) is relatively complex (Fig. 9a), demonstrating that the Vøring and Møre basins are characterised by a very deeply located basement, whereas the Trøndelag Platform shows moderate basement depths that progressively shallow and crop out towards the coastline. The Moho topography (Maystrenko et al., 2018) used in this study shows that the crust-mantle boundary is deeply located beneath the Norwegian mainland and is much shallower beneath the Mid-Norwegian continental margin and the oceanic part of the model (Fig. 9b). Figure 9. View largeDownload slide Depth to the base of the sedimentary cover (top of the crystalline basement) (a) and Moho topography (b) beneath the study area. COB, continent-ocean boundary (from Gernigon et al.2015a); JMC, Jan Mayen Corridor; JMFZ, Jan Mayen Fracture Zone; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. Figure 9. View largeDownload slide Depth to the base of the sedimentary cover (top of the crystalline basement) (a) and Moho topography (b) beneath the study area. COB, continent-ocean boundary (from Gernigon et al.2015a); JMC, Jan Mayen Corridor; JMFZ, Jan Mayen Fracture Zone; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. 4 THERMAL PROPERTIES Prior to the 3-D thermal modelling, thermal properties represented by specific heat capacity, thermal conductivity and radiogenic heat production have been assigned for each layer of the 3-D model (Table 4). Table 4. Thermal properties of the layers of the 3-D structural model used during the 3-D thermal modelling (lithology of sediments is derived from Bell et al. (2014) and from NPD (2014)). No.  Layer of the 3-D structural model  Dominant lithology  Specific heat capacity Cp (J kg−1 K−1)  Thermal conductivity of the matrix kr (W m−1 K−1)  Radiogenic heat production S (μW m−3)  2  Kai and Naust (middle Miocene-Pleistocene)  92% shale, 8% sandstone  1180  2.3  0.5–1.5  3  Brygge (Eocene-lower Miocene)  98% shale, 2% sandstone  1180  2.2  0.47–1.5  4  Palaeocene  80% shale, 20% sandstone  1180  3.0  0.6–1.39  5  Oceanic layer 2AB  basalts and tuffs  880  1.8  0.4  6  Upper Cretaceous  95% shale, 5% sandstone  1180  2.5  0.7–1.68  7  Lower Cretaceous  92% shale, 3% sandstone, 5% limestone  1180  2.4  0.81–1.83  8  Pre-Cretaceous  80% shale, 20% sandstone  1180  3.3  0.8–1.64  9  Upper-crustal high-density crystalline rocks  gabbro to anorthositic rocks, metamorphic rocks  880  2.9  0.4  10  Low-density upper-crustal body  metasediments or granite  880  3.0  0.4–2.2  11  Upper-crustal regional layer  granite and gneiss  880  3.2  1.5 (0.9–2.5)  12  Middle crust  granitoids and/or gneiss  950  3.1  0.9 (0.4–2.5)  13  Lower crust  metamorphic rocks  1050  3.0  0.32  14  High-density intracrustal layer  mafic granulites, gabbros  1050  3.0  0.32  15  High-density Lower-crustal layer  gabbros, high-grade metamorphic rocks  1100  2.8 and 3.2  0.2  16  Lithospheric upper mantle  peridotite  1200  4.79  0.03  No.  Layer of the 3-D structural model  Dominant lithology  Specific heat capacity Cp (J kg−1 K−1)  Thermal conductivity of the matrix kr (W m−1 K−1)  Radiogenic heat production S (μW m−3)  2  Kai and Naust (middle Miocene-Pleistocene)  92% shale, 8% sandstone  1180  2.3  0.5–1.5  3  Brygge (Eocene-lower Miocene)  98% shale, 2% sandstone  1180  2.2  0.47–1.5  4  Palaeocene  80% shale, 20% sandstone  1180  3.0  0.6–1.39  5  Oceanic layer 2AB  basalts and tuffs  880  1.8  0.4  6  Upper Cretaceous  95% shale, 5% sandstone  1180  2.5  0.7–1.68  7  Lower Cretaceous  92% shale, 3% sandstone, 5% limestone  1180  2.4  0.81–1.83  8  Pre-Cretaceous  80% shale, 20% sandstone  1180  3.3  0.8–1.64  9  Upper-crustal high-density crystalline rocks  gabbro to anorthositic rocks, metamorphic rocks  880  2.9  0.4  10  Low-density upper-crustal body  metasediments or granite  880  3.0  0.4–2.2  11  Upper-crustal regional layer  granite and gneiss  880  3.2  1.5 (0.9–2.5)  12  Middle crust  granitoids and/or gneiss  950  3.1  0.9 (0.4–2.5)  13  Lower crust  metamorphic rocks  1050  3.0  0.32  14  High-density intracrustal layer  mafic granulites, gabbros  1050  3.0  0.32  15  High-density Lower-crustal layer  gabbros, high-grade metamorphic rocks  1100  2.8 and 3.2  0.2  16  Lithospheric upper mantle  peridotite  1200  4.79  0.03  View Large The thermal conductivities for the sedimentary rocks have been mostly derived from the previous estimations of the matrix thermal conductivity within boreholes of the northern Viking Graben (Brigaud et al.1992), the Mid-Norwegian continental margin and adjacent areas (Eldholm et al.2005; Pascal & Midttømme 2006; Pascal 2015), and other unconsolidated sampled sedimentary rocks from the Vøring Basin (Midttømme et al.1995). The obtained thermal conductivities of sedimentary rocks have been cross-validated with (1) the measured thermal conductivities from the North Sea boreholes (Evans 1977), (2) laboratory measurements of rock samples showing similar lithology (Čermak & Rybach 1982a; Clauser 2011) and (3) a comprehensive overview of different thermal conductivity values of sedimentary rocks (Midttømme & Roaldset 1999). The thermal conductivity of basalts (layer 5) has been set to be 1.8 W m−1 K−1 on average according to Balling et al. (2006) who measured thermal conductivity of basalts and tuffs for a depth interval of more than 3 km in the Lopra-1/1A borehole on the Faroe Islands, located south of the study area. Thermal conductivities of the upper crystalline crustal rocks have been set to be in the range of appropriate rock-sample measurements from within the Norwegian mainland (e.g. Olesen et al.1993; Slagstad et al.2009; Maystrenko et al.2015b). The mentioned thermal conductivities of the sedimentary infill, basalts and upper-crustal rocks have been supplemented with published values for the deeper crystalline crust and the lithospheric mantle (Čermak & Rybach 1982a; Wollenberg & Smith 1987; Hofmeister 1999; Artemieva et al.2006; Scheck-Wenderoth & Maystrenko 2008, 2013; Maystrenko et al.2014). The thermal conductivities of rocks have been set to be dependent on temperature. This has been done in order to consider a significant change in the thermal conductivities of sedimentary rocks as a result of increasing temperature and decreasing porosity of the sedimentary rocks with depth. Temperature-dependent values of the thermal conductivities for the uppermost crystalline crust have been calculated according to the empirical equation (3) from Sass et al. (1992):   $$k\left( T \right) = {k_{\rm{o}}}/\left( {1.007 + T\left( {0.036 - 0.0072/{k_{\rm{o}}}} \right)} \right)$$ (3)where k(T) is the thermal conductivity [W m−1 K−1] at temperature T in [°C], k(0) is the thermal conductivity [W m−1 K−1] at 0 °C and T is the temperature [°C]. The empirical equation (4) from Vosteen & Schellschmidt (2003) has been used to calculate the temperature-dependent thermal conductivities for the rest of the crystalline crust where the temperature is higher than 300 °C:   $$k\left( T \right) = {k_{\rm{o}}}/\left( {0.99 + T\left( {a - b/{k_{\rm{o}}}} \right)} \right)$$ (4)where k(T) is the thermal conductivity of crystalline rocks [W m−1 K−1] at temperature T in [K], ko is the thermal conductivity [W m−1 K−1] at 0 °C, T is the temperature [K], a and b are constants: a = 0.0030 ± 0.0015 and b = 0.0042 ± 0.0006. To define the temperature- and pressure-dependent thermal conductivities within the lithospheric mantle, the empirical equations (5) and (6) from Hofmeister (1999) have been taken:   \begin{eqnarray} k\left( {T,P} \right) &=& {k_r}{\left( {298/T} \right)^a}\exp [ - (4\gamma + 1/3)\alpha \left( {T - 298} \right)]\nonumber \\ &&\times \,\left( {1 + K{'_{\rm{o}}}P/{K_{\rm{o}}}} \right) + {k_{{\rm{rad}}}} \end{eqnarray} (5)  \begin{eqnarray} {k_{\rm{rad}}} &=& 4.7 ( \,{0.01753 - 0.00010365T} \nonumber\\ &&+\, {2.2451{T^2}/{{10}^7} - 3.407{T^3}/{{10}^{11}}} ) \end{eqnarray} (6)where k(T, P) is thermal conductivity [W m−1 K−1] at temperature T in [K] and under pressure P in [Pa], kr is the thermal conductivity [W m−1 K−1] at room temperature, γ is Grueneisen parameter (γ = 1 to 1.4), a is the phonon fitting parameter (a = 0.25 to 0.45), α is the volume coefficient of thermal expansion as a function of temperature, Ko is the bulk modulus [Pa] (Ko = 261 GPA), K΄o is the pressure derivative of the bulk modulus (K΄o = 5) and krad is the radiative component of the thermal conductivity, enhanced according to van den Berg et al. (2001). In addition, the empirical equation (4) has been used to calculate the temperature-dependent thermal conductivities for the solid material (porous matrix) of the sedimentary cover. In this case, constants a and b vary within the following range: a = 0.0034 ± 0.0006 and b = 0.0039 ± 0.0014. In addition, the thermal conductivity of the sedimentary rocks has also been set to be dependent on compaction by introducing the equivalent thermal conductivity. The thermal conductivity of the solid–fluid system keq is the so-called equivalent thermal conductivity and can be inferred by use of this equation:   $${k_{{\rm{eq}}}} = {\theta _{\rm{s}}}{k_{\rm{s}}} + {\theta _{\rm{f}}}{k_{\rm{f}}}$$ (7)where ks is the thermal conductivity of the solid material (porous matrix) and kf is the thermal conductivity of the fluid (water in the case of the present study), θs is the solid material's volume fraction, which is related to the volume fraction of the fluid θf as in the following:   $${\theta _{\rm{s}}} + {\theta _{\rm{f}}} = 1$$ (8) The thermal conductivity of the fluid in the pores of sedimentary rocks has been taken as the temperature-dependent thermal conductivity of water based on the thermodynamic properties of water and steam according to the International Association for Properties of Water and Steam Industrial Formulation 1997 (Wagner & Kretzschmar 2008). The volume fraction of the fluid θf is represented by porosity (Φ) which is assumed to decrease with depth according to eq. (9):   $$\Phi = 1 - \rho \left( z \right)/{\rho _{\rm{m}}}$$ (9)where Φ is the porosity, ρ(z) is depth-dependent density [kg m−3] which is specified for each layer according to exponential functions of increasing densities with depth from Maystrenko et al. (2018), z is depth [m], and ρm is matrix density [kg m−3] assumed to be the same (2700 kg m−3 on average) for all sedimentary layers due to uncertainties in defining the lithological composition. It is important to note that the densities of the rocks comprising the sedimentary cover have been locally reduced within the Jan Mayen Corridor compared to the rest of the study area. This has been done in accordance with the previous results of the 3-D density analysis (Maystrenko et al., 2018). Within the Jan Mayen Corridor, the calculated thermal conductivities have been accordingly reduced due to the very low degree of compaction within the uppermost sedimentary rocks (Maystrenko et al., 2018). In contrast, porosities of the crystalline rocks have been neglected during the 3-D thermal modelling because these rocks have, in general, extremely low porosities compared to the sedimentary rocks. For instance, according to the porosity measurements of crystalline rocks in Sweden (Tullborg & Larson 2006), porosities of crystalline rocks vary from 1.5 per cent at relatively shallow levels to 0.98 per cent in the deep crust. Densities of the crystalline rocks have been set based on the 3-D density modelling (Maystrenko et al., 2018). The assigned values of the specific heat capacity have also been set to be constant during the 3-D thermal modelling (Table 4) and have been derived mainly from values published in Clauser (2011). For the specific heat capacity of rock matrix, the dependence on temperature has been considered in terms of significant changes by assigning the average values for the layers at different temperature intervals, depending on the depth of the layer. These temperature-dependent average values of the specific heat capacity have been derived from the literature based on laboratory measurements at different temperature conditions (e.g. Čermak & Rybach 1982a; Afonso et al.2005; Clauser 2011). We used radiogenic heat productions of the upper and middle-crustal layers mostly derived from average values calculated from airborne gamma spectrometry surveys and/or based on average heat production for geological units in Norway according to rock-sample measurements (e.g. Slagstad 2008; Slagstad et al.2009; Slagstad & Lauritsen 2013). The values of radiogenic heat production for the lower-crustal layers and the lithospheric mantle have been considered to be constant (Table 4). In the case of the radiogenic heat production, there is no accurate mathematical way to predict the content of radiogenic elements within the deep-crustal layers. The radiogenic heat production is mostly dependent on the specific lithological composition of the layer rather than on depth, pressure and/or temperature. A decreasing content of the radiogenic elements with depth is generally observed. Accordingly, the average constant values of the radiogenic heat production rely on published values for the assumed lithological composition of each layer (Čermak & Rybach 1982b; Scheck-Wenderoth & Maystrenko 2008; Vila et al.2010). In order to obtain a reasonable fit between the observed and modelled temperatures in the available boreholes offshore, lateral and realistic variations of the radiogenic heat production have been applied for the low-density upper-crustal body (layer 10; Fig. 8b), upper-crustal regional layer (layer 11; Fig. 8c) and middle crust (layer 12; Fig. 8d). On the other hand, alternative explanations for local changes of the measured temperature should not be excluded and could also be explained by enforced fluid flow (convection and/or advection), significant variations in thermal conductivities, structural uncertainties and/or limited horizontal resolution of the 3-D model. However, these additional reasons require supplementary structural data, extra sampling material and further simulation of more complex physical processes (e.g. fluid flow). Absence of reliable data and difficulties in such a regional 3-D modelling approach do not allow us to test theses various aspects at this stage. The observed variations in the radiogenic heat production of the crystalline rocks on the mainland (e.g. Slagstad 2008; Pascal & Rudlang 2016) provide a possibility for assuming that a similar situation could also apply within the crystalline rocks offshore. Meanwhile, we consider that variable radiogenic heat production within the crystalline crust is the most reasonable and easiest applicable procedure for the 3-D thermal modelling. Several testing models including different values of the radiogenic heat production have been generated and validated to obtain a reasonable fit between the modelled and measured temperatures in the available boreholes. These assumptions also consider the result of the 3-D potential field modelling described in the companion paper of Maystrenko et al. (2018). In particular, the low-density upper-crustal body (layer 10) has been subdivided into two blocks with different radiogenic heat production (Fig. 10a). The southwesternmost part of this layer has been assigned a radiogenic heat production of 2.2 μW m−3. In contrast, the rest of this layer has been given a lower value of radiogenic heat production (0.4 μW m−3), implying possible lithological changes within this layer towards the northeast. The crustal block with the increased radiogenic heat production can most likely represent granitic rocks whereas the block with the reduced radiogenic heat production can possibly represent metasedimentary rocks. Figure 10. View largeDownload slide Radiogenic heat production of (a) the low-density upper-crustal layer, (b) the regional upper-crustal layer and (c) the middle crust. FH, Frøya High; JMC, Jan Mayen Corridor; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. Figure 10. View largeDownload slide Radiogenic heat production of (a) the low-density upper-crustal layer, (b) the regional upper-crustal layer and (c) the middle crust. FH, Frøya High; JMC, Jan Mayen Corridor; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. The upper-crustal regional layer (layer 11) is characterised by a relatively complex pattern of the assigned values of radiogenic heat production (Fig. 10b). Different blocks with increased or decreased values of radiogenic heat production match the basement configuration deduced from the 3-D magnetic modelling (Maystrenko et al., 2018). The block with increased radiogenic heat production within the northeastern part of the detailed 3-D model area is most likely related and/or similar to the granitoid rocks of the Transscandinavian Igneous Belt (Åhäll & Larson 2000). Based on more than 500 samples (Slagstad et al.2008), these Precambrian granitoids show a median heat production of 2.57 μW m−3. In the case of the present study, a lower value of 2.2 μW m−3 compared to the median heat production (Slagstad et al.2008) has been assigned to similar rocks. This lower value of the radiogenic heat production has been chosen to represent a possible decrease of radiogenic heat production with depth as observed within the Transscandinavian Igneous Belt onshore. To the west of the Transscandinavian Igneous Belt, a second block with anomalous magnetic susceptibility has been set with the same increased value of radiogenic heat production of 2.2 μW m−3. This block can also be associated with the Transscandinavian Igneous Belt and is possibly covered by relatively thick, upper-crustal, high-density crystalline rocks (layer 9) associated with younger and shallower Caledonian nappes (cf. Figs 8a and c and 10b). The two blocks within the southeastern corner of the detailed 3-D study area (Fig. 10b) are probably related to granitoids which are in general characterised by relatively high contents of radiogenic elements. Such basement rocks may explain the increased values of radiogenic heat production towards the south from the study area (e.g. Killeen & Heier 1975; Wilson et al.1977; Slagstad & Lauritsen 2013). The Frøya High and the neighbouring areas also have prominent and characteristic magnetic signatures and the upper-crustal blocks have been subdivided into three blocks (Fig. 10b): two blocks with increased radiogenic heat production (2.2 μW m−3) and one block in between with a lower heat production (1.2 μW m−3). Farther north, a small and speculative crustal block with an increased radiogenic heat production (2.5 μW m−3) has been set up within the northern part of the Trøndelag Platform (Fig. 10b) in order to raise the modelled temperatures. However, this upper-crustal block is not reflected in any specific gravity or magnetic anomalies and there is a possibility that the increased measured temperatures in that area are simply the local result of different processes. The transition zone from the Trøndelag Platform to the Vøring Basin is characterised by the presence of the hypothetical zone with relatively low values of radiogenic heat production in the necking zone, ranging from 0.9 to 1.1 μW m−3. In addition, a small crustal block with increased radiogenic heat production (2.2 μW m−3) has been included into the regional upper-crustal layer in the northwestern corner of the model area and a small block with decreased radiogenic heat production (1.0 μW m−3) has been set up within the southern part of the Møre Basin (Fig. 10b). A differentiation of the middle crust (layer 12) in terms of the radiogenic heat production was also considered in places where either a decreased or increased heat production has been assigned to the previously described layer (layer 11, cf. Figs 10b and c). Consequently, the block with increased values of radiogenic heat production (2.5 μW m−3) has been hypothetically distinguished within the northern part of the Trøndelag Platform and could represent potential Precambrian granitoids. The crustal blocks with the lowest heat production (0.4-0.6 μW m−3) are located at the transition between the Trøndelag Platform to the Vøring Basin and in the vicinity of the Frøya High (Fig. 10c). These crustal blocks are most likely gneisses derived from metamorphosed sedimentary rocks with low contents of radiogenic elements. The need to include middle-crustal blocks with a variable radiogenic heat production is partially related to the fact that the regional upper-crustal layer is locally too thin to reduce the misfit between the measured and the modelled temperatures. In the Møre and Vøring basin, the crystalline crust is indeed relatively thin and strongly attenuated but not necessary enough to develop large zones of mantle exhumation before breakup (e.g. Nirrengarten et al. 2014; Gernigon et al. 2015b; Maystrenko et al., 2018). On the other hand, the sedimentary cover is extremely thick in that area as well as in the Trøndelag Platform. Therefore, radiogenic heat production of sedimentary rocks could play an important role as an additional heat source. For instance, heat production varies from approximately 0.07 μW m−3 to about 2.21 μW m−3 in the Gulf of Mexico (McKenna & Sharp 1998) and has an average range of 0.4–2.1 μW m−3 in the Northeast German Basin (Norden & Förster 2006). In the present study, all sedimentary layers of the 3-D model have been assigned with variable radiogenic heat production values based on the results of gamma-ray logging in the selected boreholes, one of which is shown in Fig. 11. These boreholes have been chosen to cover the whole model area, giving a large range of values which are assumed to be representative of the thermal properties of the sedimentary rocks in the vicinity of each well. Figure 11. View largeDownload slide Plot showing stratigraphy, measured total natural gamma and derived radiogenic heat production for one of the boreholes (borehole 6406/12-2) used to calculate the radiogenic heat production of sedimentary cover (stratigraphy and gamma-ray log are from NPD 2014). Figure 11. View largeDownload slide Plot showing stratigraphy, measured total natural gamma and derived radiogenic heat production for one of the boreholes (borehole 6406/12-2) used to calculate the radiogenic heat production of sedimentary cover (stratigraphy and gamma-ray log are from NPD 2014). In order to obtain values of the radiogenic heat production for sedimentary rocks, natural gamma-ray logs have been collected from the NPD web site and were ultimately digitised (Fig. 11). The empirical relationship between total natural gamma and radiogenic heat production (10) from Bücker & Rybach (1996) has been applied to calculate the radiogenic heat production of the sedimentary infill in the selected boreholes (Figs 11 and 12; Table 5).   $$S = 0.0158\left( {{\rm{GR}} - 0.8} \right)$$ (10)where S is the radiogenic heat production (μW m−3) and GR is the total gamma (API units). The results of the calculation represent scaling values of the radiogenic heat production rather than precise ones. The empirical relationship (10) has been derived by Bücker & Rybach (1996) for the range of total natural gamma of 0–350 API. Values of the total natural gamma obtained for the sedimentary rocks of the Mid-Norwegian margin are mainly in the range 0–150 API (Fig. 11) and, therefore, the results of the calculation should provide realistic values for the radiogenic heat production. The reliability of radiogenic heat production obtained from the gamma-ray logs has recently been confirmed in the Fyllingsdalen and Årvollskogen boreholes, which have been drilled through crystalline rocks on the mainland in SW Norway (Maystrenko et al.2014, 2015b). In addition to natural gamma-ray logging, gamma spectrometry logging in the Årvollskogen borehole has been used to obtain values of radiogenic heat production based on concentrations of uranium (U), thorium (Th) and potassium (K). Comparative analysis indicates that curves of radiogenic heat production, calculated based on natural gamma-ray and gamma spectrometry loggings show a good match (Maystrenko et al.2014). The empirical equation (10) is possibly not the best solution for conversion in the case of sedimentary rocks compared to the crystalline rocks. However, there are no available data to validate the empirical relationship proposed for the sedimentary rocks. The average values of the radiogenic heat production for every sedimentary layer have accordingly been derived (Table 5) from the calculated values (e.g. Fig. 11). The average radiogenic heat production has then been used to produce maps by interpolation between the existing values in the boreholes (Fig. 12). The radiogenic heat production has been assigned to the different sedimentary layers but without considering compaction of sedimentary rocks when these rocks are located deeper than the sedimentary strata used in the boreholes. In contrast, the compaction effect is already included in the values derived from the drilled successions in the used boreholes (e.g. Fig. 11). According to the results of these calculations, the average radiogenic heat production of the sedimentary layers varies from 0.47 to 1.85 μW m−3 (Table 5), indicating relatively large variations within different parts of the study area and within different layers of the 3-D model. The Shetland and Cromer Knoll groups (Dalland et al. 1988; Fig. 12, Table 5) do not precisely correspond to the Upper Cretaceous (layer 6) and the Lower Cretaceous (layer 7) locally. On the other hand, the difference in average values of the radiogenic heat production between the Shetland and Cromer Knoll groups (NPD nomenclature and definition) is rather small (Table 5) and, therefore, an average radiogenic heat production for the Shetland and Cromer Knoll groups has been assigned to the Upper Cretaceous (layer 6) and the Lower Cretaceous (layer 7), respectively. Figure 12. View largeDownload slide Radiogenic heat production of the sedimentary layers, interpolated from the borehole data: the Kai-Naust (middle Miocene-Pleistocene) formations (a), the Brygge (Eocene-lower Miocene) Formation (b), the Palaeocene (c), the Upper Cretaceous (d), the Lower Cretaceous and (e) pre-Cretaceous (f). Locations of the boreholes used to estimate the radiogenic heat production of sedimentary layers are shown by the white circles. JMC, Jan Mayen Corridor; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. Figure 12. View largeDownload slide Radiogenic heat production of the sedimentary layers, interpolated from the borehole data: the Kai-Naust (middle Miocene-Pleistocene) formations (a), the Brygge (Eocene-lower Miocene) Formation (b), the Palaeocene (c), the Upper Cretaceous (d), the Lower Cretaceous and (e) pre-Cretaceous (f). Locations of the boreholes used to estimate the radiogenic heat production of sedimentary layers are shown by the white circles. JMC, Jan Mayen Corridor; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. Table 5. Average radiogenic heat production of the sedimentary rocks, derived from the gamma-ray logs, available along selected wells. Units of radiogenic heat production are in μW m−3. Well  Nordland (layer 2)  Hordaland (layer 3)  Rogaland (layer 4)  Shetland (layer 6)  Cromer Knoll (layer 7)  Pre-Cretaceous (layer 8)  34/3-1 S  1.33  0.84  0.73  1.3  1.03  1.1  35/3-2  0.5  0.72  0.76  0.74  0.8  1.0  6205/3-1R  0.7  –  1.2  1.5  1.5  1.1  6302/6-1  1.03  1.04  1.3  1.24  –  –  6305/1-1  1.22  1.0  0.9  1.32  1.4    6406/2-1R  1.53  1.5  1.4  1.7  1.85  1.14  6406/12-2  1.2  1.42  1.21  1.23  1.42  1.11  6505/10-1  0.7  1.2  0.91  1.23  1.46  –  6507/5-1  1.1  0.7  0.7  0.8  0.93  1.13  6507/12-2  0.92  0.88  0.76  0.92  –  0.78  6510/2-1R  0.68  0.72  0.68  0.7  0.94  1.65  6603/12-1  1.2  1.31  1.1  1.31  –  –  6610/7-2  0.86  0.47  0.6  0.74  0.82  1.1  6707/10-1  0.54  –  0.8  1.24  –  –  Well  Nordland (layer 2)  Hordaland (layer 3)  Rogaland (layer 4)  Shetland (layer 6)  Cromer Knoll (layer 7)  Pre-Cretaceous (layer 8)  34/3-1 S  1.33  0.84  0.73  1.3  1.03  1.1  35/3-2  0.5  0.72  0.76  0.74  0.8  1.0  6205/3-1R  0.7  –  1.2  1.5  1.5  1.1  6302/6-1  1.03  1.04  1.3  1.24  –  –  6305/1-1  1.22  1.0  0.9  1.32  1.4    6406/2-1R  1.53  1.5  1.4  1.7  1.85  1.14  6406/12-2  1.2  1.42  1.21  1.23  1.42  1.11  6505/10-1  0.7  1.2  0.91  1.23  1.46  –  6507/5-1  1.1  0.7  0.7  0.8  0.93  1.13  6507/12-2  0.92  0.88  0.76  0.92  –  0.78  6510/2-1R  0.68  0.72  0.68  0.7  0.94  1.65  6603/12-1  1.2  1.31  1.1  1.31  –  –  6610/7-2  0.86  0.47  0.6  0.74  0.82  1.1  6707/10-1  0.54  –  0.8  1.24  –  –  View Large In particular, the uppermost stratigraphic intervals, represented by Kai-Naust (middle Miocene-Pleistocene; layer 2) and Brygge (Eocene-lower Miocene; layer 3), are characterised by a similar range of values for the derived radiogenic heat production, varying from 0.5 to 1.53 μW m−3 for layer 2 and from 0.47 to 1.5 μW m−3 for layer 3 (Table 5). Nevertheless, the maps in Figs 12(a) and (b) show recognisable differences in the local pattern of radiogenic heat production. On the other hand, the general pattern is relatively similar, displaying low values within the northeastern and southeastern parts of the model area which are separated by a zone with increased radiogenic heat production (cf. Figs 12a and b). The above-described general trend in radiogenic heat production is also recognisable at the level of the Palaeocene (Fig. 12c) with the average values ranging from 0.6 to 1.4 μW m−3 (Table 5). Moreover, this pattern is still clearly visible at the level of the Upper and Lower Cretaceous units (layers 6 and 7) where a zone of increased radiogenic heat production in the central part of the model area is surrounded by reduced values (Figs 12d and e). Compared to the Cenozoic stratigraphic intervals, the Cretaceous maps show higher radiogenic heat production which ranges from 0.7 to 1.7 μW m−3 for the Upper Cretaceous and from 0.8 to 1.85 μW m−3 for the Lower Cretaceous (Table 5). In the case of the pre-Cretaceous sedimentary and metasedimentary rocks, this general pattern cannot be identified, reflecting structural changes in deposition and present-day distribution between the pre-Cretaceous and the Cretaceous-Cenozoic sedimentary rocks. Information on pre-Cretaceous radiogenic heat production is mostly limited to the uppermost part of the pre-Cretaceous (Fig. 11) and, therefore cannot be fully representative of the whole of the deeper pre-Cretaceous interval. However, sparse data and limited borehole information about the pre-Cretaceous successions have been used to partly assess the radiogenic heat production for this interval (Fig. 12f). A large part of the pre-Cretaceous in Fig. 12(f) is characterised by values of heat production which are around 1 μW m−3. In the northeast of the model area, an increase of the radiogenic heat production in well 6510/2-1R is bounded by reduced values in well 6507/12-2. The investigated pre-Cretaceous succession is particularly thick in these two boreholes (6507/12-2 and 6510/2-1R), implying that the average radiogenic heat production of the whole of the pre-Cretaceous could be more variable than it appears from the map in Fig. 12(f). The studied radiogenic heat production of the pre-Cretaceous varies from 0.78 to 1.65 μW m−3 (Table 5). Coming back to the Cretaceous-Cenozoic interval (Figs 12a–e), the increased values of radiogenic heat production in the vicinity of boreholes 6406/2-1R and 6406/12-2 are characteristic of the more than 100 million-year-long stratigraphic interval. The zone of higher radiogenic heat production shown around well 6406/2-1R is also recognisable on all Cretaceous-Cenozoic maps (Figs 12a–e), implying a possible inheritance in clastic material transport from the same erosional locality onshore where crystalline rocks are or were originally characterised by large contents of radiogenic elements. Such an inherited zone with increased radiogenic heat production could also represent and/or highlight the result of differential erosion and/or sorting of the sediments during transportation from source-to-sink. Deposition of more argillaceous fractions in particular areas of the Mid-Norwegian continental margin may explain local increases of heat production within specific depocentres. For example, McKenna & Sharp (1998) have shown that mudrocks in the Gulf of Mexico basin produce about 30–40 per cent more radiogenic heat than their lateral and stratigraphically equivalent sandstones. Nevertheless, this remarkable coincidence would require additional investigation. A more detailed study is required in order to analyse this specific pattern of radiogenic heat production within the sedimentary cover by including smaller stratigraphic intervals and by use of a larger number of boreholes. An attempt to correlate the radiogenic patterns of sedimentary rocks with potential sources for eroded material within the mainland could have significant implications for independent palaeogeographic and source-to-sink studies. 5 RESULTS AND IMPLICATIONS OF THE 3-D THERMAL MODELLING 5.1 Modelled temperature The 3-D structural model (Fig. 13a) has been successfully converted into a reliable 3-D thermal model (Fig. 13b). These results provide an overview of the present-day temperature distribution beneath the Earth's surface within the Møre and Vøring segments of the Mid-Norwegian continental margin and adjacent areas of the Norwegian mainland. Fig. 14 shows the pattern of subsurface temperature at six chosen depths below sea level within the upper part of the 3-D model where relatively low thermally conductive sedimentary rocks are present. In addition, Fig. 15 illustrates the temperature distribution within the deeper parts of the detailed 3-D model area (i.e. near the crust-mantle boundary (Figs 14a and b) and within the lithospheric mantle (Figs 14c and d)). Figure 13. View largeDownload slide (a) The lithosphere-scale 3-D model of the Mid-Norwegian continental margin and adjacent areas of the Norwegian mainland (from Maystrenko et al., 2018). (b) 3-D temperature distribution within the model shown in (a). Four times vertically exaggerated. Figure 13. View largeDownload slide (a) The lithosphere-scale 3-D model of the Mid-Norwegian continental margin and adjacent areas of the Norwegian mainland (from Maystrenko et al., 2018). (b) 3-D temperature distribution within the model shown in (a). Four times vertically exaggerated. Figure 14. View largeDownload slide Modelled temperatures within the upper part of the detailed 3-D model. Temperature maps, extracted from the 3-D thermal model (Fig. 13b), for the depths of 2 km (a), 5 km (b), 7 km (c), 10 km (d), 15 km (e) and 18 km (f). JMC, Jan Mayen Corridor; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. Figure 14. View largeDownload slide Modelled temperatures within the upper part of the detailed 3-D model. Temperature maps, extracted from the 3-D thermal model (Fig. 13b), for the depths of 2 km (a), 5 km (b), 7 km (c), 10 km (d), 15 km (e) and 18 km (f). JMC, Jan Mayen Corridor; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. Figure 15. View largeDownload slide Modelled temperatures within the deep parts of the detailed 3-D model. Temperature maps, extracted from the 3-D thermal model (Fig. 13b), at depths of 25 km (a), 40 km (b), 80 km (c) and 100 km (d). JMC, Jan Mayen Corridor; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. Figure 15. View largeDownload slide Modelled temperatures within the deep parts of the detailed 3-D model. Temperature maps, extracted from the 3-D thermal model (Fig. 13b), at depths of 25 km (a), 40 km (b), 80 km (c) and 100 km (d). JMC, Jan Mayen Corridor; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. At a large scale, the mainland is generally colder compared to the Mid-Norwegian continental margin (Fig. 14). Within the upper part of the 3-D thermal model, this regional trend of the modelled temperatures is associated mainly with the high thermal conductivity of crystalline crustal rocks (Table 4) which crop out over large parts of the mainland. This interaction between the relatively high values of thermal conductivities of the crystalline rocks and specific structural patterns is responsible for a chimney effect within the areas where the crystalline rocks are exposed at the surface. The thermal pattern related to the chimney effect on the mainland is complicated by a zone with increased temperatures beneath the Scandes mountains which is particularly pronounced at a depth of 2 km (Fig. 14a). This is mainly due to the topographic effect of the Scandes Mountains which generally reach to more than 1.5–2 km elevation above the sea level (Fig. 1). The upper thermal boundary at the Earth's surface is therefore also uplifted by more than 1.5–2 km within the Scandes compared to the rest of the mainland where the relief is lower. The latter adds an additional 1.5–2 km to the distance from the upper thermal boundary to the chosen depths below sea level beneath the Scandes Mountains. The topographic effect of the Scandes is still clearly recognisable at a depth of 7 km (b.s.l) and even deeper where it is disturbed by the structural interaction between the middle and upper crystalline crustal layers (Fig. 14) characterised by different thermal properties (Table 4). In the offshore part, the thermal effect associated with the topographic variations is also visible at shallower levels within the northwestern part of the Møre Basin and Jan Mayen Corridor (cf. Figs 1 and 14a and b). In contrast to the Scandes mountains, the modelled temperatures are notably lower within the wide area of deep bathymetry compared to the rest of the Norwegian continental shelf (e.g. Fig. 14a), reflecting the fact that the upper thermal boundary at the seafloor sinks together with the bathymetry and, therefore, brings low surface temperatures down to greater depths. The next feature of the thermal pattern within the upper crust concerns the direct relationship between areas characterised by a thick sedimentary cover and areas showing increased temperatures within the rifted margin (cf. Figs 7 and 14). This regional trend of temperature distribution is related to the low thermal conductivity of sedimentary rocks which increases the heat storage within the areas characterised by a thick and low conductive sedimentary cover. It is important to note that this thermal insulation effect is locally complicated by depth variations of the seafloor which correspond to the upper thermal boundary in our 3-D thermal model. The superimposed thermal effect of the deep bathymetry is particularly significant within the Jan Mayen Corridor where it is represented by lower modelled temperatures at 2–7 km depths in Figs 14(a)–(c). The blanketing effect of sedimentary rocks is particularly prominent within the Vøring Basin where the sedimentary infill is thickest (Fig. 14). The uppermost sedimentary layers of the detailed 3-D model, represented by the Brygge (Eocene-lower Miocene), Kai (middle Miocene-lower Pliocene) and Naust (upper Pliocene-Pleistocene) formations, are characterised by the lowest thermal conductivities. This fact is partially reflected by the distribution of the modelled temperature at depths of 2 and 5 km where the thickness pattern of these Cenozoic formations is still recognisable (cf. Figs 7a and b, and 14a and b). The blanketing effect of sedimentary rocks becomes reasonably smoother in the areas showing thinner sedimentary rocks (e.g. the Trøndelag Platform and the eastern part of the Møre Basin; Fig. 7). The Møre Basin itself is characterised by slightly lower temperatures compared to the Vøring Basin. The latter is mainly due to the thermal blanketing effect triggered both by the thicker sedimentary rocks within the Vøring Basin and the variable radiogenic heat production of the same sediments. The deepening of the bathymetry affects the modelled temperature within the Møre Basin and causes a decrease in temperatures within the northwestern part of the Møre Basin and along the Jan Mayen Corridor even at a depth of 5 km (Fig. 14b). Besides, the distribution of the subsurface temperatures along the northwestern edge of the detailed model area is strongly affected by the gradual uplift of the present-day lower thermal boundary (Fig. 3b) and the palaeo-thermal boundaries (Fig. 6) at the base of the lithosphere rising towards the oceanic lithospheric domain. The thermal influence of the lower thermal boundary configuration becomes more and more notable at greater depths where the modelled temperature increases due to the lithospheric thinning. The results of the 3-D thermal modelling within the deeper part of the 3-D thermal model are presented in Fig. 15 by four 2-D horizontal slices of the temperature distribution at depths of 25, 40, 80 and 100 km. It is important to note that the modelled temperature beneath the mainland is already lower than the temperature beneath the Mid-Norwegian continental margin at depths of 25 and 40 km (Figs 15a and b). At that level, the mantle material partially or fully predominates beneath the continental margin, whereas the crystalline crustal rocks are still present beneath the mainland (Fig. 9b). There are, however, some complications in the modelled thermal pattern beneath the mainland (Figs 15a and b) due to the interaction between crustal and mantle thermal properties (Table 4). The influence of this interaction, however, is considerably smoothed by the topography of the lower thermal boundary which is deeply located beneath the mainland and significantly uplifted beneath the oceanic domain (Figs 3b and 6). Therefore, an increased radiogenic heat production of the crystalline crust compared to the mantle material at 25 and 40 km depth levels is not large enough to overcome the thermal pattern of the heat coming from deeper parts of the Earth's interior within the study area. In this case, the configuration of the lithosphere-asthenosphere boundary is the key factor controlling the temperature distribution within the deeper levels of the detailed 3-D thermal model. One of the interesting features of the 3-D conductive thermal field predicted by these maps is the temperature variation from relatively low values within the southeastern part of the model area to the higher values in the northwest (Fig. 15). At depths of 80 and 100 km (Figs 15c and d) the distribution of the modelled temperature generally reflects the configuration of the lower thermal boundary, which is represented by the base of the lithosphere with an isotherm of 1300 °C (cf. Figs 3b, and 15c and d). The modelled temperatures at the Moho (Fig. 16a) partially mimic the shape of the Moho topography (Fig. 9b), indicating that the key factor is similar to the top of the crystalline basement and controlled by the depth position of this boundary. For that reason, the highest temperatures (more than 700 °C) are obtained beneath the northeastern part of the model area where the Moho is deepest. In contrast, this correlation between the depth position of the Moho and the modelled thermal pattern is not completely valid for the modelled heat flux (Fig. 16b) which is more sensitive to the configuration of the lower thermal boundary. The modelled heat flux at the Moho is generally in good agreement with the previous estimation by Scheck-Wenderoth & Maystrenko (2008), showing already an increase of values from the mainland towards the oceanic lithospheric domain. In particular, there is a zone with high heat flux within the northwestern part of the Møre Basin. There, the heat flux varies from 50 to more than 60 mW m−2, reflecting the influence of the early Cenozoic continental breakup and present-day position of the expected base of lithosphere. Differences between the modelled heat flux at the Moho when the continental breakup effect is either considered or disregarded in the modelling workflow is expected, on average, to be 6–7 mW m−2 within the detailed 3-D model area. However, it reaches more than 12–13 mW m−2 towards the oceanic domain outside of the detailed model. The lowest modelled heat flux has been obtained beneath the mainland where it is in the range of 30–35 mW m−2 (Fig. 16b). Figure 16. View largeDownload slide Modelled temperatures (a) and heat flux (b) at the base of the crust (Moho). JMC, Jan Mayen Corridor; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. Figure 16. View largeDownload slide Modelled temperatures (a) and heat flux (b) at the base of the crust (Moho). JMC, Jan Mayen Corridor; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. The modelled temperatures at the top of the crystalline basement (Fig. 17a) reflect the geometry of the top-basement (Fig. 9a). There is a straightforward relationship between the distribution of the modelled temperatures (Fig. 17a) and the depth to the top of the crystalline basement (Fig. 9a): when the top of the crystalline rocks is deeply situated, the modelled temperatures increased and vice versa. Consequently, the modelled temperature maxima coincides with the deepest parts of the Vøring Basin. There, the temperatures reach more than 450 °C at the present day (Fig. 17a). Regionally, the top of the crystalline basement beneath the Vøring Basin is characterised by higher modelled temperatures (350–450 °C on average) compared to the southern Møre Basin which is slightly colder with average temperatures varying from 250 to 350 °C in the southwestern part of the basin to values similar to those of the Vøring Basin in its northeastern part. Figure 17. View largeDownload slide (a) Modelled temperatures at the top of the crystalline basement within the detailed model area. Modelled heat flux at the top of the crystalline basement: (b) with the thermal influence of the Saalian and Weichselian glaciations and (c) without the influence of those glaciations. FH, Frøya High; JMC, Jan Mayen Corridor; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. Figure 17. View largeDownload slide (a) Modelled temperatures at the top of the crystalline basement within the detailed model area. Modelled heat flux at the top of the crystalline basement: (b) with the thermal influence of the Saalian and Weichselian glaciations and (c) without the influence of those glaciations. FH, Frøya High; JMC, Jan Mayen Corridor; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. The Trøndelag Platform is clearly distinguished by lower temperatures in comparison to the Vøring and Møre sag basins. At the present day, the average modelled temperatures beneath the Trøndelag Platform are in the range of 200–230 °C near the top-basement. The modelled temperatures on the mainland simply reproduce the Earth’s surface temperatures (cf. Figs 3a and 17a) due to the fact that the crystalline basement is directly exposed at the surface there. The modelled heat flux at the top of the crystalline basement (Figs 17b and c) shows a complex pattern compared to the distribution of temperature (Fig. 17a). The heat flux distribution over the mainland is partially controlled by abrupt changes in the topography (Fig. 1). In addition, there is a clear influence of the palaeoclimatic conditions related to the Saalian and Weichselian glaciations described in the previous chapter (Figs 4 and 5). Low heat flux values (around 40 mW m−2) have been modelled over parts of the continent not affected by the ice sheet during the glaciations (cf. Figs 4 and 17b) and, therefore, were affected by low surface temperatures similar to the present-day tundra conditions (Fig. 5). However, the influence of the Saalian and Weichselian glaciations is smoothed within the areas previously covered by ice sheets or seawater. For instance, there is an increased heat flux of up to 60–70 mW m−2 within the part of Scandes (Fig. 17b) which was almost permanently covered and thermally insulated by the thick ice sheet during the glacial periods. A similar situation occurs in the vicinity of the coastline which has been thermally insulated by the seawater and sedimentary rocks. The contrasting NE–SW-trending narrow zone showing an increased heat flux along the coastline (Fig. 17b) is mainly controlled by the sea level and the more than 800 m-thick sedimentary rocks over the top of the crystalline basement. The sea level could have varied during the Saalian and Weichselian glacial periods but no regional-scale data on the palaeo-position of shorelines within the study area are available. Consequently, the modelled heat flux near the coastline within the areas with shallow bathymetry still remain uncertain within the uppermost levels of the 3-D thermal model. Fig. 17(c) shows the modelled heat flux without the influence of the Saalian and Weichselian glaciations, indicating that the heat flux is relatively high over the entire mainland. This increased heat flux is mainly caused by the thickened crystalline crust beneath the mainland (Fig. 9b) which acts as an additional heat source due to its increased content of radiogenic elements. Compared to the Møre and Vøring Basins, the presence of a thicker crystalline crust easily explains the high heat flux (around 55–60 mW m−2) modelled beneath the Trøndelag Platform, and is in agreement with the results of Pascal (2015) who reached the same conclusion based on independent heat-flux calculations. The heat flux is relatively low within the eastern parts of the Vøring and Møre basins, being in the range 42–50 mW m−2. The crystalline crust is quite thin beneath almost the entire Vøring and Møre basins but the northwestern part of the model area is characterised by an increased heat flux. This is the result of proximity of the oceanic domain where both the Moho and the lithosphere-asthenosphere boundary are uplifted (Figs 3b and 9b). The increased modelled heat flux is particularly pronounced in the northwestern part of the Møre Basin, showing values higher than 70 mW m−2 (Figs 17b and c). The modelled heat flux at the seafloor offshore and at the Earth's surface onshore is shown in Fig. 18. Here, additional heat to the modelled heat flux at the top basement within the basin areas is produced internally by the sedimentary infill as a result of decay of the contained radiogenic isotopes. In contrast, the heat fluxes modelled separately at the top-model and top-basement levels are similar within the mainland due to the fact that these two levels coincide onshore where the crystalline basement is directly exposed at the Earth's surface. Similar to the top of the crystalline basement (Figs 17b and c), the highest values of the heat flux (more than 75 mW m−2) are modelled within the northwestern part of the Møre Basin (Figs 18a and b). The rest of the Mid-Norwegian margin is characterised by the high heat flux (60–65 mW m−2) within the Trøndelag Platform and the Frøya High. Lower values (46–55 mW m−2) are modelled within the eastern parts of the Vøring and Møre basins. Figure 18. View largeDownload slide Modelled heat flux at the top of the 3-D model represented by the seafloor offshore and the Earth's surface onshore: (a) with the thermal influence of the Saalian and Weichselian glaciations and (b) without the influence of those glaciations. FH, Frøya High; JMC, Jan Mayen Corridor; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. Figure 18. View largeDownload slide Modelled heat flux at the top of the 3-D model represented by the seafloor offshore and the Earth's surface onshore: (a) with the thermal influence of the Saalian and Weichselian glaciations and (b) without the influence of those glaciations. FH, Frøya High; JMC, Jan Mayen Corridor; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. Comparison of our results with previous marine heat-flux measurements (Sundvor et al.1989, 2000; Ritter et al.2004) demonstrates both quantitative coincidences and mismatches. However, clear qualitative correlation between the modelled and measured heat fluxes is not obvious and a direct comparison of our model with these two data sets (Sundvor et al.1989; Ritter et al.2004) is difficult. This is mainly due to the fact that the near-surface heat flux can change quite drastically (up to 200 per cent) over short distances if local disturbances (e.g. fluid flow) is present. However such local effects cannot be properly reproduced by our regional-scale 3-D thermal modelling. Comparison with heat flux derived from exploration boreholes (Pascal & Midttømme 2006; Pascal 2015) demonstrates that there is a relatively good qualitative agreement between the modelled and the borehole-based heat fluxes. Strong variation of the heat flux is, however, determined between closely located boreholes (e.g. 59 and 71 mW m−2) but cannot be modelled in detail if we consider the resolution of our 3-D model. Quantitatively, there is a ±5 mW m−2 deviation on average between the modelled and previous borehole-based heat fluxes (Pascal & Midttømme 2006; Pascal 2015). with both almost perfect coincidence and larger misfit locally, indicating again a possible disturbance by the fluid flow or not high enough resolution of our model. The gridded heat flux data (Slagstad et al.2009; Pascal 2015) also show a good correlation with our results, indicating that the increased heat flux over the Frøya High and the decreased values recorded observed in the eastern parts of the Vøring and Møre basins show some clear quantitative dissimilarities. In order to illustrate a cross-sectional view of the modelled subsurface temperatures, three selected 2-D vertical slices (Fig. 19) have been extracted from the 3-D thermal model (Fig. 13b). The locations of these cross-sections are the same as those extracted through the 3-D density and magnetic models (Maystrenko et al., 2018). The interesting feature along the vertical slices 1 and 3 is that an uplift of the modelled isotherms does not always correlate with the shallow position of the Moho (Fig. 19). This is due to the relatively shallow palaeo- and present-day positions of the lower thermal boundary at the base of the lithosphere within the western part of the model area. This means that the long-wavelength component of the deep heat from the Earth's interior, controlled by the geometry of the lithosphere-asthenosphere boundary, prevails over the thermal disturbance related to the Moho topography. For instance, the subhorizontal calculated isotherms are intersected by a sharp deepening of the Moho within the eastern part of line 2 (Fig. 19). The large-scale and deep thermal pattern is disturbed mainly in places where significant contrasts occur in the thermal properties of the upper mantle material, crystalline crustal rocks and/or sedimentary rocks. For example, the modelled isotherms mainly follow the depth position of the Moho along the western parts of the vertical slice 2. There, the uplift of the modelled temperatures within the crust spatially coincides with the areas where the Moho is shallow and the sedimentary rocks are thickest. Consequently, a superposition of the chimney effect of the high thermally conductive upper mantle material in the areas with the uplifted Moho and thermal blanketing of the low thermally conductive thick sedimentary infill results in an increase of the modelled temperatures within the crystalline crust. Figure 19. View largeDownload slide Subsurface modelled temperatures along three selected 2-D vertical slices through the detailed 3-D thermal model (for the location of these slices, see Fig. 2). The vertical exaggeration is 3.3 times. TB, top basement. Figure 19. View largeDownload slide Subsurface modelled temperatures along three selected 2-D vertical slices through the detailed 3-D thermal model (for the location of these slices, see Fig. 2). The vertical exaggeration is 3.3 times. TB, top basement. 5.2 Modelled temperature versus measured temperature The variations of the modelled temperatures within the uppermost part of the 3-D thermal/structural model have been compared with measured temperatures in available boreholes. The locations of all accessible boreholes with the measured temperatures are shown in Fig. 20. Locations of the boreholes only showing drill-stem test (DST) temperatures offshore, and temperatures from well loggings onshore, are shown in Fig. 20(a). The positions of the boreholes having less reliable offshore bottom-hole temperatures (BHT) in addition to the previous boreholes are shown in Fig. 20(b). BHT were measured near the bottom of the boreholes either during drilling or shortly after the drilling process was finished. Consequently, these temperature estimations often contain an element of thermal disturbance due to circulation of the drilling fluid and are not fully reliable. On the contrary, DST values represent the temperature of fluids in thermal equilibrium with the surrounding sedimentary rocks. The measured temperatures from well logs onshore are generally obtained after reaching the thermal equilibrium in the boreholes and are generally more reliable. Nevertheless, due to a shortage of DST data within the Mid-Norwegian continental margin (Fig. 20a), the BHT have also been chosen to compare the modelled temperatures with the measured ones (Figs 20 and 21, Tables 6 and 7). Furthermore, a comparison between the obtained results and the recorded measurements has been provided separately for the boreholes which are located inside (Figs 20a and b) and outside (Figs 20c and d) the detailed model area. Figure 20. View largeDownload slide Locations of the available boreholes with the measured temperatures and spatial distribution of the temperature variations (measured temperature minus the modelled one) within the whole study area. (a) Boreholes with reliable drill-stem test (DST) temperatures offshore and temperature logs onshore. (b) Boreholes with less reliable bottom-hole temperatures (BHT) combined with the DST temperatures. Figure 20. View largeDownload slide Locations of the available boreholes with the measured temperatures and spatial distribution of the temperature variations (measured temperature minus the modelled one) within the whole study area. (a) Boreholes with reliable drill-stem test (DST) temperatures offshore and temperature logs onshore. (b) Boreholes with less reliable bottom-hole temperatures (BHT) combined with the DST temperatures. Figure 21. View largeDownload slide Misfit between the calculated (blue dots) and the observed (red dots) temperatures for the boreholes which are located inside of the detailed model area (a,b) and the boreholes which are located inside and outside of the detailed model area (c,d). (a,c) Only boreholes with DST (drill-stem test) temperatures are used. (b,d) Boreholes with less reliable bottom-hole temperatures (BHT) are also included in addition to the boreholes with DST temperatures. Figure 21. View largeDownload slide Misfit between the calculated (blue dots) and the observed (red dots) temperatures for the boreholes which are located inside of the detailed model area (a,b) and the boreholes which are located inside and outside of the detailed model area (c,d). (a,c) Only boreholes with DST (drill-stem test) temperatures are used. (b,d) Boreholes with less reliable bottom-hole temperatures (BHT) are also included in addition to the boreholes with DST temperatures. Table 6. Difference between modelled temperatures and measured ones (measured values minus the modelled ones) from different boreholes located inside the detailed 3-D model area. Only the DST (drill-stem test) temperatures are used. N  Temperature range of differences between modelled and measured temperatures  Percentage of values (%)  Number of values  1  from −25 to −20  3.1  4  2  from −20 to −10  10.0  13  3  from −10 to −5  20.0  26  4  from −5 to 5  49.2  64  5  from 5 to 10  12.3  16  6  from 10 to 20  5.4  7  N  Temperature range of differences between modelled and measured temperatures  Percentage of values (%)  Number of values  1  from −25 to −20  3.1  4  2  from −20 to −10  10.0  13  3  from −10 to −5  20.0  26  4  from −5 to 5  49.2  64  5  from 5 to 10  12.3  16  6  from 10 to 20  5.4  7  View Large Table 7. Difference between modelled temperatures and measured ones (measured values minus the modelled ones) in available deep boreholes located inside the detailed 3-D model area. In addition to the DST (drill-stem test) temperatures, the less reliable bottom-hole temperatures (BHT) are also included. N  Temperature range of differences between modelled and measured temperatures  Percentage of values (%)  Number of values  1  from −35 to −25  1.3  5  2  from −25 to −20  2.1  8  3  from −20 to −10  10.9  42  4  from −10 to −5  16.3  63  5  from −5 to 5  47.4  183  6  from 5 to 10  11.4  44  7  from 10 to 20  9.8  38  8  from 20 to 25  0.2  1  9  from 25 to 40  0.5  2  N  Temperature range of differences between modelled and measured temperatures  Percentage of values (%)  Number of values  1  from −35 to −25  1.3  5  2  from −25 to −20  2.1  8  3  from −20 to −10  10.9  42  4  from −10 to −5  16.3  63  5  from −5 to 5  47.4  183  6  from 5 to 10  11.4  44  7  from 10 to 20  9.8  38  8  from 20 to 25  0.2  1  9  from 25 to 40  0.5  2  View Large The results of the 3-D conductive thermal modelling are in a reasonable agreement with the general trends of the measured temperatures at the present day (Fig. 21). In spite of a good general fit, some large misfits can be recognised in Fig. 21. In order to understand the magnitude of these large misfits, a more detailed analysis has been performed by plotting the difference between the measured and modelled temperatures (the measured temperatures minus the modelled ones) in map view (Fig. 20). From the maps in Fig. 20, it is obvious that most of the misfits between the modelled and measured temperatures are in the range of ±10 °C. The misfits are separately shown for only the DST temperatures in Table 6 and, in addition to the DST temperatures, the less reliable BHTs are also included in Table 7. Boreholes used for Tables 6 and 7 are located inside the detailed model area. When the boreholes are located inside the detailed 3-D model area, around 82 per cent of the misfits are in the range of ±10 °C, if the boreholes with only the DST are considered (Table 6). The misfits with a range of ±10 °C are slightly lower at around 75 per cent (Table 7), if the BHT are also considered. The large differences remaining in the range of ±10 °C implies that thermal conduction was most likely the dominant mechanism of heat transfer at the scale of the Mid-Norwegian continental margin. According to Fig. 20 and Tables 6 and 7, misfits higher than ±10 °C between the modelled and measured temperatures are also recorded. Some of the misfits are even greater than ±20 °C and can reach up to 40 °C locally. The spatial distribution of these larger differences demonstrates that the boreholes with large misfits are closely located to the boreholes where the misfits are suitable for this kind of regional-scale study (Fig. 20). In some places, the distance between the boreholes showing different misfit values is comparable to the horizontal resolution of the 3-D structural model. For that reason, any tendency to reduce the misfit on a specific borehole will automatically increase the misfit in the neighbouring one and vice versa. Moreover, local structural features of the Mid-Norwegian continental margin could not be resolved without sufficient details of the complete lithological section of each particular borehole. Therefore, the measured temperatures cannot always be fully reproduced by a purely conductive 3-D thermal modelling approach. Some or even most of the large misfits are probably associated with local convective or advective heat transfer phenomena in areas where geothermally heated or cooled fluids circulate through the sedimentary succession. This is particularly the case in the outer Vøring Basin where fluids passing through old fault or local fluid migration pathways initially triggered by Eocene sill intrusions and vents (Svensen et al.2004; Planke et al.2005) can be recognised on seismic data. Fluid-related thermal disturbance is most likely responsible for the large misfits in the external boreholes which are located in the vicinity of the northwestern corner of the detailed model area (see the area outlined by the red dashed line in Fig. 20b). There, the relatively large residual discrepancies between the modelled and measured temperatures are still present in the boreholes located within the western part of the Vøring Basin. These residual misfits are especially large in boreholes 6603/5-1S and 6603/12-1, reaching around 27 °C there. In other boreholes (6604/2-1, 6604/10-1, 6605/1-1 and 6705/10-1), the residual misfits are in the range of 14–23 °C. The misfits are called residual because they were almost two times larger in the 3-D thermal models without taking into account the thermal influence of the early Cenozoic continental breakup. The difference in temperature between the thermal models with and without taking into account the influence of the strongly uplifted isotherms during the continental breakup is mostly restricted to the northwestern side of the detailed model area. There, the residue of the breakup-related heating is still recognisable. This difference is more than 50 °C at the top of the crystalline basement and reaches more than 70 °C at the level of the Moho. Assuming reasonable thermal properties, these differences, highlighted by the red dashed ellipsoid in Fig. 20(b), cannot be explained by purely conductive heat transfer. For example, the measured temperature in well 6603/12-1 is already 139 °C at only 2335.5 m of the true vertical depth below the seafloor (depth below sea level is 3736.5 m), assuming a linear geothermal gradient from the sea bottom of 60 °C km-1, which is the highest value in the case of the Norwegian exploration boreholes (NPD, 2014). In well 6603/5-1 S, the estimated temperature is 190 ± 5 °C at a depth below sea level of 5254 m. These temperatures are bottom-hole temperatures (BHT) and, therefore, can differ from the equilibrium temperatures. However, from a theoretical point of view, these temperatures can be even higher rather than lower, if the equilibrium temperatures is reached after stopping circulation of the drilling fluid. Only one suitable fit between the modelled and the measured temperature is recognised in the scientific borehole ODP Site 644 (Eldholm et al.1987). The temperature here is around 5 °C in this borehole at only slightly more than 200 m below the seafloor. However, the temperature in this well is not stable and represents a shallow temperature compared to the temperatures measured in deeper exploration boreholes. Another borehole from the ocean drilling program (ODP Site 642) is located on the Vøring Plateau which is outside the area of the large-scale 3-D structural model, but this borehole is interesting in terms of the fluid inflow. In this borehole, a positive temperature deviation at a depth of around 500 m below the seafloor may indicate a significant fluid inflow which is also supported by the other well log data sets (Channell et al.2005). A similar situation is also expected for the outer boreholes located near the northwestern corner of the detailed model area. Here, the origin of the fluid flow can differ from the ODP Site 642 due to the greater depth and different structural domain. For instance, hydrothermal activities have been reported at the Gjallar Ridge (e.g. Planke et al.2005; Njone 2014) and indicate that the presence of hydrothermal vent and sill complexes together with accompanying faults could create favourable conditions for local convective heat transfer driven by fluid flow within the northwestern part of the Vøring Basin. 5.3 Uncertainties of the results The modelled temperatures are particularly sensitive to the geometry of the layers and modifications of their thermal properties in general. It is more significant where strong contrasts in thermal properties exist, for example at top-basement, Moho or lithosphere-asthenosphere boundary levels. The inherent limitations of the 3-D thermal modelling have to be considered but have already been reduced by use of additional constraints from new boreholes, sample measurements and relatively reliable structural data. The top of the crystalline basement and depth position of the Moho are also up-to-date and relatively well constrained by a dense coverage of deep seismic data present over large parts of the modelled area (Maystrenko et al., 2018). Some uncertainties with the top of the crystalline basement depth may, however, exist within the deeper parts of the Vøring and Møre basins where the deeply located sedimentary rocks are highly compacted. At some point, the density/velocity contrast between the sedimentary cover and the crystalline rocks could be extremely low, thus enhancing the uncertainties in determining the depth to the top of the crystalline basement (Maystrenko et al., 2018). Furthermore, further uncertainties remain about the location and significance of the lithospheric-asthenospheric boundary, which is a research project in itself. Seismic methods cannot unambiguously discriminate between temperature and compositional variations within the upper mantle (e.g. Kolstrup et al.2012). The thermal influence of the probable uncertainties in the depth of the lithosphere-asthenosphere boundary have been examined by Maystrenko et al. (2014) who have examined two possible cases with ± 20 km depth to the base of the lithosphere in relation to the preferred lower thermal boundary at around 120 km depth. The obtained thermal effect on the deviations of the modelled temperature at 6 km depth is ∼4 per cent for the 20 km deeper base of the lithosphere and ∼12 per cent for the 20 km shallower one. This indicates that an influence of the lower thermal boundary at the shallower depths is non-negligible when the distance between the lower and upper boundaries becomes smaller. The predominance of the conductive heat transfer within the study area is valid only if the lateral changes in the radiogenic heat production of the crystalline rocks (Fig. 10) are present in reality. The presence of crustal blocks with different radiogenic heat production is mainly supported by the results of the 3-D magnetic modelling carried out in the same study area (Maystrenko et al., 2018). Based on the onshore distribution of the radiogenic heat production within the crystalline rocks, Slagstad (2008) has shown that there is a direct relationship between the extent of different units on the geological map (e.g. Sigmond 2002) and the average heat production on the mainland. Consequently, the inferred crustal blocks with different radiogenic heat in Fig. 10 can be considered as representatives of the geological subdivision of the crystalline crust proposed to exist beneath the sedimentary basins offshore. However, some of the inferred crustal blocks are rather hypothetical. We cannot exclude an alternative explanation for the observed thermal pattern within the drilled sedimentary cover that could involve fluid circulation through sedimentary rocks and/or crystalline crust. In this case, some of the crustal blocks offshore showing an increased radiogenic heat production could indicate the presence of heated fluids. Conversely, the inferred blocks with the reduced radiogenic heat can outline areas where advective cooling could possibly be superimposed on the conductive heat transfer. Furthermore, the limited information about the thermal conductivity of rocks within the deep part of the 3-D model implies that the used values (Table 5) can vary within a reasonable range and, therefore, the modelled temperature can slightly deviate (Figs 14–19). However, the relative correctness of the thermal properties used in our study is supported by a good correlation between the calculated and the measured temperatures in most of the available boreholes (Figs 20 and 21). A comparative analysis of the 3-D thermal modelling results with the borehole measurements indicates that there are also some large inherent misfits which cannot be explained solely by a purely conductive heat transfer system. Further tests or improvements can be achieved in the future by increasing the horizontal resolution and the number of lithologically differentiated layers of the 3-D structural model. Future modelling may also involve more complex simulations of fully coupled fluid flow and heat transfer in 3-D including a more detailed scenario for the continental breakup. At that stage, the influence of hypothetical and complex fluid flow(s) cannot be correctly established without more detailed hydrogeological, lithological and structural constraints within the regional framework of the present study. Finally, the near-surface thermal effect of the post-Palaeocene deposition has been roughly included but the effect of the simultaneous erosion over the mainland has not been properly considered. To include this effect into the modelling workflow, additional data would be required to constrain the erosional rate in time and space. The uplift and subsequent erosion could lead to an uplift of isotherms within the upper crust, causing a positive temporal thermal anomaly beneath the areas where the erosion took place. Theoretically, the magnitude of this positive anomaly should not be higher than 25 °C on average. Furthermore, the impact of palaeo- and present-day groundwater flow might significantly smooth the magnitude of the thermal anomaly due to erosion (e.g. Maystrenko et al.2015a). In particular, the thermal influence of the erosion could be significantly reduced by the possible groundwater flow active during the melting of the Quaternary ice sheets. Therefore, these two thermal effects and their opposed interaction have to be considered together. Once more, a fully coupled fluid flow and heat transfer modelling will be required to include all processes that control the subsurface temperature distribution within the study area. Finally, the results of the modelling are also limited by the model resolution and computing facilities. 6 CONCLUSIONS The 3-D conductive thermal field within the Mid-Norwegian continental margin and the adjacent areas of the mainland has been deduced from a pre-existing 3-D density/magnetic structural model. The new model considers all available data about the measured temperatures and thermal properties. In general, the results of the 3-D thermal modelling help us to further understand the main characteristics of the 3-D conductive thermal field within the Mid-Norwegian continental margin and adjacent areas. The thermal results can be used to better estimate the maturation of organic matter, reservoir quality and, therefore, to make progress in regional strategies for hydrocarbon exploration within the Trøndelag Platform and Vøring and Møre basins, as well as to evaluate the geothermal potential on the mainland. A clear zone of increased radiogenic heat production is easily traceable through the Cretaceous and Cenozoic stratigraphic intervals, implying a possible source-to-sink inheritance scenario for the eroded clastic material. The radiogenic pattern of the sedimentary rocks may indicate a differentiation and sorting of the eroded clastics by grain size during their transportation. A comparison between modelled temperatures and the measured ones in the boreholes indicates that there is a good correlation between the measurements and our simulations. However, a purely conductive thermal field within the Mid-Norwegian continental margin is most likely disturbed locally by fluid flow (convection and/or advection). This is most likely the case in the distal part of the margin where large and atypical residual misfits between the measured and the modelled temperatures are recorded in some of the boreholes. Based on a simple palaeo-scenario for the continental breakup, the modelling results indicate that the thermal influence of the lithospheric rupture in the early Cenozoic is still persistent within the western part of the model area. Further improvements of the results can be achieved by increasing the resolution of the 3-D structural model and by involving simulations of fully coupled fluid flow and heat transfer. A better constrained palaeo-scenario for the continental breakup and the post-break relationship between erosion onshore and sedimentation offshore may also contribute to an improvement in the results. ACKNOWLEDGEMENTS The authors would like to acknowledge comprehensive support of this regional-scale investigation from Aker BP, BayernGas, BKK, Centrica Energi, ConocoPhillips, Dea, DONG, Engie, Eni, E.ON, Lundin, Maersk, NGU, Noreco, NPD, Repsol, Statoil, Suncor, Total, VNG, and Wintershall in the framework of ‘Crustal Onshore-Offshore Project, Phase 2’. We are grateful to Odleiv Olesen for coordination of this project and for very fruitful discussions. Special thanks go to the Marine Geology group at the Geological Survey of Norway (personally to Leif Rise) for providing us with the most recent data on post-Palaeocene sedimentary layers. We would also like to thank Mauro Cacace from the Helmholtz Centre Potsdam, GFZ German Research Centre for Geosciences for his help with the code for creating complex 3-D mesh. Christophe Pascal and an anonymous reviewer are thanked for their very useful comments which helped us to improve our manuscript. 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# 3-D temperature distribution beneath the Mid-Norwegian continental margin (the Vøring and Møre basins)

, Volume 212 (1) – Jan 1, 2018
31 pages

/lp/ou_press/3-d-temperature-distribution-beneath-the-mid-norwegian-continental-ysew2qaSIb
Publisher
The Royal Astronomical Society
ISSN
0956-540X
eISSN
1365-246X
D.O.I.
10.1093/gji/ggx377
Publisher site
See Article on Publisher Site

### Abstract

SUMMARY A 3-D thermal model of the Møre and Vøring segments of the Mid-Norwegian continental margin and adjacent areas of the continent has been calculated in a recent 3-D lithospheric and potential field model. The thermal model correlates well with the main tectonic units of the study area, showing a clear increase of the temperatures towards the oceanic domain where the lithosphere-asthenosphere boundary is still shallow at the present day. This long-wavelength thermal effect prevails over other thermal and semi-regional disturbances observed within the model area. In addition, the blanketing effect of the thick sedimentary infill in the Vøring Basin causes the modelled temperatures to be highest within this basin where the sedimentary infill is thickest. On the other hand, the Møre Basin is characterised by slightly lower temperatures and the modelled temperatures are even lower within the Trøndelag Platform, less affected by crustal thinning. A comparison between the modelled and measured temperatures indicates that there is a good correlation between the borehole measurements and the results of our simulations. However, some large residual misfits between the measured and the modelled temperatures in some of the boreholes indicate that a purely conductive thermal field within the Mid-Norwegian continental margin can be locally disrupted by fluid flow circulation (convection and/or advection). A clearly distinguished zone of increased radiogenic heat production has been traced through the Cretaceous and Cenozoic sedimentary intervals suggesting a possible source-to-sink correlation between the clastic material and the eroded rocks. This radiogenic pattern of the sedimentary rocks may also indicate a differentiation of the eroded clastics by grain size during their transportation. Heat flow, Atlantic Ocean, Europe, Numerical modelling, Continental margins: divergent, Heat generation and transport 1 INTRODUCTION Understanding the temperature distribution at different depths within a continental rifted margin is a challenging topic especially around the ambiguous continental-ocean transition (Clerc et al.2015). Located between Fennoscandia and the Norwegian-Greenland Sea, the Mid-Norwegian passive volcanic (and rifted) margin is not an exception (Fig. 1). Figure 1. View largeDownload slide Overview map of northwestern Europe (bathymetry and topography from the Norwegian Mapping Authority), showing location of the detailed 3-D thermal model (orange frame) and the large, low-resolution, 3-D thermal model (magenta dashed frame). Figure 1. View largeDownload slide Overview map of northwestern Europe (bathymetry and topography from the Norwegian Mapping Authority), showing location of the detailed 3-D thermal model (orange frame) and the large, low-resolution, 3-D thermal model (magenta dashed frame). The Mid-Norwegian continental margin comprises three tectonically different segments, such as the Lofoten-Vesterålen margin segment in the northeast and the Møre and Vøring segments in the southwest. The pre-breakup tectonic history of the study area was dominated by the Caledonian Orogeny (Roberts & Gee 1985; Gee et al.2008), structural features of which are still easily observed within western Scandinavia in terms of several tectonic sheets or nappes, overthrusted onto the Precambrian Fennoscandian Shield (e.g. Sigmond 2002; Gee et al.2017). The Caledonian orogen collapsed during a Devonian extensional event coeval with the formation of several Devonian basins (Fossen 2010). Later on, several Late Palaeozoic and Mesozoic extensional events led to the formation of Permo-Jurassic sub-basins within the Trøndelag Platform, as well as the deposition of thick Cretaceous sedimentary sequences along major and ‘superextended’ Cretaceous sag basins observed offshore Norway (Fig. 2; Blystad et al.1995; Doré et al.1999; Brekke 2000; Mosar et al.2002; Gernigon et al.2003; Scheck-Wenderoth et al.2007; Faleide et al.2008; Lundin & Doré 2011). The final stage of the Mid-Norwegian margin culminated in the early Cenozoic when continental breakup initiated the formation of a relatively young oceanic lithosphere between Laurentia and Baltica (Talwani & Eldholm 1977; Srivastava & Tapscott 1986; Brekke 2000; Skogseid et al.2000; Olesen et al.2007; Faleide et al.2008; Gaina et al.2009; Gernigon et al.2015a). Figure 2. View largeDownload slide Tectonic configuration of the Mid-Norwegian continental margin (simplified after Blystad et al.1995) with location of the large and detailed 3-D structural models. The bold black lines indicate the location of the three selected vertical slices through the model. Figure 2. View largeDownload slide Tectonic configuration of the Mid-Norwegian continental margin (simplified after Blystad et al.1995) with location of the large and detailed 3-D structural models. The bold black lines indicate the location of the three selected vertical slices through the model. Since the first oil discoveries on the Norwegian continental shelf in the 1960s–1970s, the structure of the Mid-Norwegian margin has been intensively investigated by both the oil and gas industry and academia, providing a large amount of borehole and reflection/refraction seismic data which are sufficient to constrain basin-scale 3-D structural and crustal models within the study area (Torne et al.2003; Ebbing et al.2006; Scheck-Wenderoth et al.2007; Maystrenko & Scheck-Wenderoth 2009; Reynisson 2010; Reynisson et al.2010; Maystrenko et al.2018). In addition, several attempts were already made to model the 2-D/3-D thermal state of the Mid-Norwegian margin (e.g. Fernandez et al. 2004, 2005; Gernigon et al.2006; Pascal & Ebbing 2007; Scheck-Wenderoth & Maystrenko 2008; Wangen et al.2008; Ebbing et al.2009; Rüpke et al. 2013), showing that detailed knowledge about the configuration and physical properties of the sedimentary cover, crystalline crust and uppermost mantle is a major and primary constraint for obtaining a consistent thermal structure of the deep parts of the continental margin. In addition, several heat-flow studies have been performed within the Mid-Norwegian margin (Sundvor et al.1989, 2000; Ritter et al.2004; Pascal & Midttømme 2006; Slagstad et al.2009; Pascal 2015) and the adjacent mainland (e.g. Slagstad et al.2009; Pascal 2015). In this paper, the most recent 3-D structural model by Maystrenko et al. (2018) has been used as a structural background for a new 3-D thermal modelling study within the Mid-Norwegian margin. The main aim of this study was to understand and simulate the conductive thermal regime beneath the Mid-Norwegian continental margin and adjacent areas. The background 3-D model from Maystrenko et al. (2018) is based on the most recently published/released structural data and has been validated by the 3-D density and magnetic modelling. It represents the most up-to-date data-based approximation of the Mid-Norwegian continental margin and its crustal configuration. The 3-D structural/crustal model has been accordingly transformed into a present-day 3-D thermal model by means of a full 3-D thermal modelling calculation. The method and results of this 3-D conductive thermal modelling are presented in this contribution, revealing the present-day temperature distribution and pattern of the subsurface within the Møre and Vøring segments of the Mid-Norwegian continental margin. This approach helps to test and better understand the present-day nature and composition of the basement rocks that are expected to occur underneath the sedimentary basins of the Norwegian shelf. 2 METHODOLOGY The 3-D temperature distribution within the structurally complex 3-D model of the Mid-Norwegian continental margin and adjacent mainland has been calculated using the commercial software package COMSOL Multiphysics. COMSOL Multiphysics is a finite-element analysis software package often used for a variety of physical processes. During the 3-D thermal modelling, the Heat Transfer Module was considered to simulate the stationary and time-dependent heat transfer in solid materials by heat conduction, which is considered to be the dominant mechanism of heat transfer at the regional scale within the subsurface of the investigated area. These calculations have been performed based on physical principles of the conductive 3-D thermal field by solving the heat equation (1):   \begin{eqnarray} \rho {C_{\rm{p}}}(\partial T/\partial t) &=& \nabla \cdot (k\nabla T) + Q \end{eqnarray} (1)where ρ is the density [kg m−3], Cp is the specific heat capacity [J kg−1 K−1], T is the temperature [K], k is the thermal conductivity [W m−1 K−1], ∇T is the temperature gradient [K m−1], t is the time [s], Q is the internal heat production (radioactive heat production) [W m−3], ∂T/∂t denotes the change of temperature with time, and ∇ is the operator giving the spatial variation in temperature. Consequently, the solution of the heat equation (1) is sensitive to the values of the thermal properties (specific heat capacity, thermal conductivity and radiogenic heat production) and density as well as the thermal boundary conditions. During the thermal simulation, the heat flux q [W m−2] has been calculated according to Fourier's law of heat conduction (2):   $$q = - k\nabla T$$ (2)where k is the thermal conductivity [W m−1 K−1] and ∇T is the temperature gradient [K m−1]. The thermal modelling has been performed in 3-D which is a suitable approach taking into consideration the rather complex geometry of the Mid-Norwegian continental margin and adjacent areas. The lateral boundaries are closed to heat transfer, assuming that the temperature gradient is zero across the thermally insulated lateral boundaries. The time-dependent temperatures at the seafloor and at the Earth’s surface (Fig. 3a) have been set as the upper thermal boundary condition, whereas the base of the lithosphere (Fig. 3b) has been taken as a lower thermal boundary, assuming that the lower thermal boundary corresponds to the ‘conventional’ 1300 °C isotherm (e.g. Turcotte & Schubert 2002). The importance of the lower thermal boundary configuration within the continent-ocean transition has been previously examined by Scheck-Wenderoth & Maystrenko (2008), indicating that lithospheric thickness from seismology, according to Zhang & Lay (1999), is a suitable and first-order assumption for 3-D thermal modelling. The depth to the lithosphere–asthenosphere boundary beneath the oceanic crustal domain has been obtained based on the age of the oceanic lithosphere (Müller et al.2008) and Love and Rayleigh wave-phase velocity empirical relations in Zhang & Lay (1999), reflecting a gradual cooling of the oceanic lithosphere after the continental breakup. The base of the lithosphere beneath the continent has been taken from Gradmann et al. (2013). Finally, an almost linear interpolation has been applied in order to fill the data gaps between the oceanic and the continental domains. Figure 3. View largeDownload slide (a) Present-day upper thermal boundary: annual average air temperatures during 1961–1990 for Norway (Tveito et al.2000) and Sweden (Raab & Vedin 1995). Average sea-bottom temperature, derived from Ottersen (2009); ICES (2012) and Korablev et al. (2014). (b) Depth to the present-day lower thermal boundary (represented by the 1300 °C isotherm at the lithosphere-asthenosphere boundary). COB, continent-ocean boundary (from Gernigon et al.2015a); JMC, Jan Mayen Corridor; JMFZ, Jan Mayen Fracture Zone; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. Figure 3. View largeDownload slide (a) Present-day upper thermal boundary: annual average air temperatures during 1961–1990 for Norway (Tveito et al.2000) and Sweden (Raab & Vedin 1995). Average sea-bottom temperature, derived from Ottersen (2009); ICES (2012) and Korablev et al. (2014). (b) Depth to the present-day lower thermal boundary (represented by the 1300 °C isotherm at the lithosphere-asthenosphere boundary). COB, continent-ocean boundary (from Gernigon et al.2015a); JMC, Jan Mayen Corridor; JMFZ, Jan Mayen Fracture Zone; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. The present-day temperature at the Earth’s surface (Fig. 3a) is represented by the annual average air temperatures of the region during the period 1961–1990 provided by the Norwegian Meteorological Institute (Tveito et al.2000) and the National Atlas of Sweden (Raab & Vedin 1995). The temperature at the seafloor (Fig. 3a) has been inferred from published values of bottom temperatures within the Norwegian Sea (Ottersen 2009; Korablev et al.2014), being set to be dependent on the bathymetry (Table 1) with a slight decrease of temperature towards the northeast (Fig. 3a). In addition, published seasonal values of average sea-bottom temperatures within the North Sea during 1997–2002 (ICES 2012) have been used to cross-check the sea-bottom temperatures within the northernmost part of the North Sea. Table 1. Present-day average annual temperature at the seafloor of the Norwegian Sea. Bathymetry (m)  100  300  500  600  700  750  800  850 and deeper  Temperature (°C)  7  6  5  4  3  2  1  0  Bathymetry (m)  100  300  500  600  700  750  800  850 and deeper  Temperature (°C)  7  6  5  4  3  2  1  0  View Large The 3-D thermal modelling also takes into account the detailed palaeoclimatic changes of the surface temperature during the last 228 000 yr before present (BP). During this time interval, the study area was affected by glaciations during the Saalian glacial period with interruptions during the Eemian interglacial period (220 000–118 000 yr BP) and the Weichselian glacial period (∼110 000–10 000 yr BP; Fig. 4), as well as by the Holocene interglacial period (10 000 yr BP to present day). The palaeotemperatures during the last 8000 yr (Table 2) are represented by almost 0.4 °C below the present-day average air temperature during the Little Ice Age (Nesje et al.2008; Mann et al.2009; Fig. 5a) and by 1 °C above the present-day average air temperature during the Holocene Climate Optimum (e.g. Seppä et al.2009; Fig. 5b). Palaeotemperature at 8000 yr BP (Fig. 5c) has been set to be 1 °C below the present-day surface temperature (Davis et al.2003; Fig. 3a). Figure 4. View largeDownload slide Ice cover during the Weichselian glaciation (after Olsen et al.2013). The detailed 3-D model is defined by the orange frame and the large-scale structural model by the magenta dashed frame. JMC, Jan Mayen Corridor; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. Figure 4. View largeDownload slide Ice cover during the Weichselian glaciation (after Olsen et al.2013). The detailed 3-D model is defined by the orange frame and the large-scale structural model by the magenta dashed frame. JMC, Jan Mayen Corridor; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. Figure 5. View largeDownload slide Annual average palaeotemperatures at the Earth’s surface and the sea bottom during the Weichselian glaciation. JMC, Jan Mayen Corridor; MB, Møre Basin; SM, Scandes Mountains; TP, Trøndelag Platform; VB, Vøring Basin. Figure 5. View largeDownload slide Annual average palaeotemperatures at the Earth’s surface and the sea bottom during the Weichselian glaciation. JMC, Jan Mayen Corridor; MB, Møre Basin; SM, Scandes Mountains; TP, Trøndelag Platform; VB, Vøring Basin. Table 2. Difference between palaeotemperatures and the present-day temperature for the last 8000 yr. Time, years before present BP  0 Present day  400 Little Ice Age  7500 Holocene Optimum  8000  Temperature difference in relation to present day (°C)  0  −0.4  +1  −1  Time, years before present BP  0 Present day  400 Little Ice Age  7500 Holocene Optimum  8000  Temperature difference in relation to present day (°C)  0  −0.4  +1  −1  View Large To reconstruct the palaeoclimatic thermal conditions at the Earth's surface within the Mid-Norwegian continental margin and surrounding areas, a model showing the spatio-temporal variations of the ice cover within Scandinavia during the Weichselian glacial period has been used according to a set of maps published in Olsen et al. (2013). The spatial distribution of the ice cover through time is reproduced in Fig. 4, showing the position of the large-scale and detailed 3-D structural models. According to these data (Olsen et al.2013; Fig. 4), the continent within the study area was almost continuously covered by a variably shaped Weichselian ice cover which could have reached up to 3 km thickness during the Last Glacial Maximum (Siegert et al.2001). The same palaeoclimatic scenario was also applied for the Saalian glacial/Eemian interglacial period (220 000–118 000 yr BP), taking into account that palaeoclimatic conditions were relatively similar during the Weichselian glacial/Holocene interglacial and the Saalian glacial/Eemian interglacial periods (Andersen & Borns 1994; Slagstad et al.2009). When the study area was glaciated, a temperature of −0.5 °C has been set at the Earth’s surface beneath the ice cover as previously used and discussed by Slagstad et al. (2009). A near-melting point temperature of −0.5 °C is in agreement with published estimations of the subglacial thermal regime beneath the large polar ice sheets in Antarctica, which is presumably a comparable analogue to the ice sheets developed during the Quaternary glacial cycles in northern Europe. The main features of the Antarctic subglacial conditions have been discussed by Pattyn (2010) who has shown that the mean basal temperature of the ice is in the range of −1 to 0 °C for the greater part of Antarctica. Besides, an airborne radar survey detected approximately 100 lakes under the Antarctic ice cap (Price et al.2002), the largest of which, Lake Vostok, has already been drilled (Jones 2012; Lake Vostok Drilling Project 2014). Palaeotemperature at the seafloor during the glacial periods was set as 0 °C which is in agreement with reconstructed temperature anomalies for the Norwegian Sea during the period 12 000–23 000 yr BP (Eldevik et al.2014). According to Eldevik et al. (2014), the palaeotemperatures were 6–7 °C less than the present-day temperatures within the Norwegian Sea. Palaeotemperatures have been taken from Schmittner et al. (2011) who modelled the annual mean surface temperatures during the Last Glacial Maximum. The estimated temperatures from Schmittner et al. (2011) are similar to other estimations of the surface temperatures during the Last Glacial Maximum (e.g. Otto-Bliesner et al.2006; Bartlein et al.1998; Hofer et al.2012; Ziemen et al.2012), showing that the near-surface air temperature difference could be about −20 °C lower compared to the pre-industrial period (present day before the Industrial Revolution). However, this estimation is only valid for the Last Glacial Maximum when the air temperatures were at their lowest estimation during the Weichselian glaciation. In order to consider this fact, temperatures lower than −11 °C from Schmittner et al. (2011) have been reduced slightly by 1–4 °C to become more similar to the modelled mean annual temperatures for the Younger Dryas (Renssen & Isarin 1998) when the palaeoclimate was warmer. Consequently, the reduced palaeotemperatures from Schmittner et al. (2011) have been considered at the Earth’s surface where the ice cover was absent. Temperatures along the marginal parts of the ice sheet are unknown in detail. For that reason, these temperatures have been obtained by a simple interpolation between −0.5 °C beneath the internal parts of the ice cover and the derived temperature over the remaining land areas. The reconstruction of the annual average palaeotemperatures at the sea bottom and the Earth’s surface demonstrates that the detailed 3-D model area was mostly characterised by much lower palaeotemperatures during the Weichselian glaciation compared to the present day (cf. Figs 3a and 5). In particular, the surface temperature could be locally less than −15 °C over the continent where the ice cover was absent or very thin. These sub-zero temperatures imply the persistence of permanently frozen ground during the glacial periods. From a theoretical point of view, the palaeopermafrost could have reached a depth of more than 1–2 km (e.g. Dobinski 2011). The global palaeo sea level was 80–120 m lower than the present-day one during the Weichselian glaciation (e.g. Hasenclever et al.2017). Moreover, the glacial erosion of the sedimentary cover could have been quite significant locally especially near the coastline that is marked by the presence of an erosional unconformity and the deposition of the relatively thick and youngest part of the Naust Formation (sequence T; e.g. Ottesen et al.2009; Montelli et al.2017). Therefore, the present-day bathymetry does not necessarily reflect the one that existed during Weichselian time. Due to the above-mentioned uncertainties, a zone showing a gradual transition of temperatures from the mainland conditions towards the sea has been included into the palaeotemperature scenario for the whole of the Weichselian glacial period (Fig. 5), covering the present-day 120 m bathymetry and a deeper one parallel to the coast. In general, a more complex palaeoclimatic scenario could apply for time intervals when some parts of the Mid-Norwegian continental margin were free of ice and seawater. However, more precise and regional-scale positions of the palaeo-shorelines within the study area are not yet available. We cannot exclude the possibility that a real temperature near the coastline within the areas with shallow bathymetry may differ from the temperatures which have been obtained during the thermal simulations of the uppermost levels of our 3-D model. In addition, the influence of the early Cenozoic continental breakup has been roughly taken into account during the 3-D thermal modelling. Two scenarios for the lithosphere-asthenosphere boundaries have been considered: (1) almost immediately after the continental breakup, around 55 Ma ago (Fig. 6a), and (2) almost at the end of the deposition of the Brygge Formation (23 Ma ago; Fig. 6b). These two time-periods (55 Ma and 23 Ma) provide an opportunity to simulate the effect of the increased geothermal gradient due to continental breakup in the early Cenozoic and the subsequent cooling of the oceanic lithosphere during the rest of the Cenozoic. However, it is worth noting that the position of the base of the lithosphere at the end of the Palaeocene is not known in detail especially if the controversial icelandic plume, alternatively small-scale convection and/or asthenospheric plumbing, was involved (or not) during the processes of breakup of the volcanic margin (e.g. Geoffroy 2005; Gernigon et al.2006). On the other hand, most numerical models predict a relatively shallow position of the 1300 °C isotherm within the present-day axis of the oceanic spreading centre beneath the mid-oceanic ridges (e.g. Chen & Lin 2004). In this study, the depth position of the lithosphere-asthenosphere boundary at the end of the Palaeocene has been tentatively set to be around 15 km deep beneath the present-day oceanic domain, representing the new accreted lithosphere there. According to seismic models for 0 Ma oceanic lithosphere by Zhang & Lay (1999), the chosen depth position of the lithosphere-asthenosphere boundary at the end of the Palaeocene could vary in the range of ±5 km if two average models for the Atlantic Ocean and three other oceans (Atlantic, Pacific and Indian oceans) are considered. Moreover, the present-day depth position of the base of the lithosphere, which is deeper than 85–95 km, has been kept constant beneath the mainland and over a large part of the continental margin. The depth to the lithosphere-asthenosphere boundary between the oceanic domain and the more than 85–95 km-deep continental lithosphere has been obtained by linear interpolation, assuming that the adjacent continental lithosphere has also been thinned in the vicinity of the oceanic domain (Fig. 6a). The lithosphere-asthenosphere boundary for the early Miocene (Fig. 6b) has been calculated as a half of the difference between the present-day base of the lithosphere (Fig. 3a) and the base after the continental breakup in the earliest Eocene (Fig. 6a) within the oceanic domain and the adjacent continental part. However, there are definitely large inherent uncertainties in these palaeo-depth estimations of the palaeobase of the lithosphere (Fig. 6). Figure 6. View largeDownload slide Estimated depth of the lithosphere–asthenosphere boundary corresponding to the 1300 °C isotherm after the continental breakup 55 Ma ago (a) and near the end of the Brygge interval 23 Ma ago (b). COB, continent–ocean boundary (from Gernigon et al.2015a); JMC, Jan Mayen Corridor; JMFZ, Jan Mayen Fracture Zone; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. Figure 6. View largeDownload slide Estimated depth of the lithosphere–asthenosphere boundary corresponding to the 1300 °C isotherm after the continental breakup 55 Ma ago (a) and near the end of the Brygge interval 23 Ma ago (b). COB, continent–ocean boundary (from Gernigon et al.2015a); JMC, Jan Mayen Corridor; JMFZ, Jan Mayen Fracture Zone; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. The next factor involving the thermal disturbance of the study area related to the syn-breakup magmatism is represented by the lower-crustal underplating, middle- to upper-crustal dykes and surface volcanic activity. The problem is that magmatic activity can locally increase the geothermal gradient, but the process itself is very complex and requires more detailed investigations which are outside the scope of the present study. Moreover, the real nature of the so-called underplating and its thermal implication is still under discussion (e.g. Fjeldskaar et al.2003; Gernigon et al.2006; Wangen et al.2011). For that reason, the influence of the syn-breakup magmatism has been mainly neglected in the present study. In addition to the above-mentioned factors, an influence of the post-breakup deposition of the Kai-Naust (middle Miocene-Pleistocene) and Brygge (Eocene-lower Miocene) formations (layers 2 and 3, respectively; Figs 7a and b) has been roughly included into the 3-D thermal modelling. This helps in considering the transient perturbations in the near-surface thermal regime as a result of the post-Palaeocene sedimentation. The Cenozoic palaeoclimatic scenario only reflects a gradual decrease of the palaeotemperature from 19 °C 55 Ma ago to present-day temperature at the mainland surface (e.g. Zachos et al.2001; Eldrett et al.2009). A temperature variation from 4 °C 18 Ma ago to 0 °C at the present-day seafloor within the deep sea was also considered (e.g. Hansen et al.2013). Palaeotemperature between the mainland and the deep sea has been obtained by interpolation of temperatures from the deep sea and the mainland. Figure 7. View largeDownload slide Thicknesses of the Cenozoic sedimentary rocks showing (a) the Kai-Naust formations (middle Miocene–Pleistocene; layer 2), (b) the Brygge Formation (Eocene-lower Miocene; layer 3) and (c) the Palaeocene (Base Tertiary Unconformity-top Palaeocene; layer 4). Thicknesses of the Cretaceous sedimentary rocks are represented by (d) the Upper Cretaceous (near top Cenomanian-Base Tertiary Unconformity; layer 6) and (e) the Lower Cretaceous (base Cretaceous unconformity-near top Cenomanian; layer 7). (f) Thickness of pre-Cretaceous sedimentary rocks. JMC, Jan Mayen Corridor; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. Figure 7. View largeDownload slide Thicknesses of the Cenozoic sedimentary rocks showing (a) the Kai-Naust formations (middle Miocene–Pleistocene; layer 2), (b) the Brygge Formation (Eocene-lower Miocene; layer 3) and (c) the Palaeocene (Base Tertiary Unconformity-top Palaeocene; layer 4). Thicknesses of the Cretaceous sedimentary rocks are represented by (d) the Upper Cretaceous (near top Cenomanian-Base Tertiary Unconformity; layer 6) and (e) the Lower Cretaceous (base Cretaceous unconformity-near top Cenomanian; layer 7). (f) Thickness of pre-Cretaceous sedimentary rocks. JMC, Jan Mayen Corridor; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. The thermal modelling workflow includes: A steady-state calculation of the 3-D conductive thermal field after the continental breakup 55 Ma ago. The lower thermal boundary (1300 °C) has been set to the inferred lithosphere-asthenosphere boundary at 55 Ma ago (Fig. 6a), whereas the top of Palaeocene deposits has been used as an upper thermal boundary. Top of the older rocks has been taken as the upper thermal boundary in places where the Palaeocene is absent. The Brygge and Kai-Naust formations (Eocene-Pleistocene interval) have been excluded from calculations. The porosity of the pre-breakup sedimentary rocks has been adjusted to shallower depth conditions compared to the present-day ones by subtraction of the thickness of the post-breakup sedimentary package (e.g. Brygge and Kai-Naust formations; Eocene-Pleistocene interval) from the present-day depths and correction of the present-day deep seafloor position. Accordingly, the porosity-dependent thermal conductivities and densities of the sedimentary cover have been adjusted to shallower depths. A time-dependent (transient) calculation of the 3-D conductive thermal field from 55 Ma ago to the end of Brygge interval in the early Miocene 18 Ma ago. The modelled 3-D temperature distribution from step (1) has been used as the initial temperature condition at the beginning of the time-dependent calculations (55 Ma ago). The lower thermal boundary (1300 °C) has been set to the lithosphere-asthenosphere boundary inferred for the late Brygge interval (23 Ma ago; Fig. 6b), whereas the top of the Brygge Formation (Eocene-lower Miocene) has been used as the upper thermal boundary. Top of the older rocks has been taken as the upper thermal boundary in places where the Brygge (Eocene-lower Miocene) Formation is absent. The Kai-Naust formations (middle Miocene-Pleistocene interval) have been excluded from the calculations. Porosity of the pre-breakup and Brygge (Eocene-lower Miocene) sedimentary rocks has been adjusted to new depth conditions by subtraction of the thickness of the Kai-Naust (middle Miocene-Pleistocene) formation from the present-day depths and correction of the present-day deep seafloor position. Therefore, due to technical simplifications, only the full thickness of the Brygge Formation has been considered during this step and does not consider any gradual infilling of the sedimentary basin. The final step includes a time-dependent (transient) calculation of the 3-D conductive thermal field from 18 Ma ago to the present day. The final modelled 3-D temperature distribution from step (2) has been used as the initial temperature condition at the beginning of the time-dependent calculations (18 Ma ago). The lower thermal boundary (1300 °C) has been set to the present-day lithosphere-asthenosphere boundary (Fig. 3b), whereas the seafloor offshore and Earth's surface onshore have been considered as the upper thermal boundary. Porosity has been estimated according to the present-day depths. During all steps, temperatures at the upper thermal boundary have been set to be time-dependent according to Tables 1–3 and Fig. 5. Table 3. Palaeotemperatures during the Cenozoic (based on Zachos et al.2001; Ravelo et al. 2004; Pekar et al.2006; Rise et al.2006; Eldrett et al.2009; Ehlers et al.2011; Hansen et al.2013; Inglis et al.2017). No.  Time, Ma ago  Mainland temperature (°C)  Deep sea temperature (°C)  1  55  19  –  2  45  15  9  3  34  11  4  4  25  12.5  6  5  18  11.5  5  6  5  7  2  7  3.6  +3 °C to present-day temperature  0  8  0.45  present-day temperature  present-day temperature  9  0.35  the same as glacial maximum 27 000 years ago in Fig. 5  the same as glacial maximum 27 000 yr ago in Fig. 5  10  0.228  present-day temperature  present-day temperature  11  0.220–0.118  the same as 0.110–0.0105 Ma ago  the same as 0.110–0.0105 Ma ago  12  0.110–0.0105  Fig. 5  Fig. 5  No.  Time, Ma ago  Mainland temperature (°C)  Deep sea temperature (°C)  1  55  19  –  2  45  15  9  3  34  11  4  4  25  12.5  6  5  18  11.5  5  6  5  7  2  7  3.6  +3 °C to present-day temperature  0  8  0.45  present-day temperature  present-day temperature  9  0.35  the same as glacial maximum 27 000 years ago in Fig. 5  the same as glacial maximum 27 000 yr ago in Fig. 5  10  0.228  present-day temperature  present-day temperature  11  0.220–0.118  the same as 0.110–0.0105 Ma ago  the same as 0.110–0.0105 Ma ago  12  0.110–0.0105  Fig. 5  Fig. 5  View Large 3 DATABASE Bathymetry and topography for the investigated area have been taken from the Norwegian Mapping Authority. The altitude of the Scandes mountains is more than 2100 m and depth to the seafloor is locally more than −2200 m, showing more than 4 km difference in relief between the Mid-Norwegian continental margin and the surrounding areas (Fig. 1). This large difference is one of the key factors which control the distribution of the subsurface temperature at the shallow levels of the 3-D model. It is important to note that the 3-D thermal modelling has been performed within a smaller area already covered by the large-scale 3-D structural model further described in detail in Maystrenko et al. (2018). This has been done in order to consider the long wavelengths and regional thermal influence between the oceanic and the continental lithospheric domains which are not completely covered by the NE-SW-oriented and detailed 3-D model described in this study (Figs 1 and 2). Use of the large 3-D model makes it possible to consider as much as possible the thermal effects of the lithosphere-asthenosphere boundary and Moho positions from the ocean (shallow) towards the Fennoscandian Shield (deep). The detailed 3-D thermal modelling has been restricted to the detailed 3-D model, whereas the larger model has been used only to consider the large-scale thermal influence. The sedimentary cover of the detailed 3-D model is described in detail in Masytrenko et al. (2018). This background model is characterised by six structural layers (Fig. 7): the Kai-Naust (base Kai-sea floor; middle Miocene-Pleistocene) (layer 2), the Brygge Formation (top Palaeocene-base Kai; Eocene-lower Miocene) (layer 3), the Palaeocene units (base Tertiary unconformity-top Palaeocene) (layer 4), Upper Cretaceous unit (near top Cenomanian-base Tertiary unconformity) (layer 6), the Lower Cretaceous unit (base Cretaceous unconformity-near top Cenomanian) (layer 7) and the pre-Cretaceous unit (Jurassic, Triassic and older sedimentary rocks) (layer 8). It is important to mention that the Kai-Naust, Brygge and Palaeocene correspond to the Nordland, Hordaland and Rogaland groups (Dalland et al.1988), respectively, whereas the Shetland and Cromer Knoll groups are not correlated exactly with the Upper Cretaceous and the Lower Cretaceous in some regions of the study area. The maps for the Brygge-Naust (Eocene-Pleistocene) interval (Figs 7a and b) have been derived based on data from Rise et al. (2005, 2010) Eidvin et al. (2007), Dowdeswell et al. (2010), and Ottesen et al. (2012), whereas maps for the Palaeocene and Cretaceous (Figs 7c–e) have been taken from Gernigon (NGU unpublished data). The thickness of the pre-Cretaceous (Fig. 7f) has been calculated as the difference between the base of the Cretaceous-Cenozoic sedimentary rocks and the top of the crystalline basement (Maystrenko et al., 2018). Configuration of the crystalline crust (Fig. 8) is an outcome of the combined 3-D density/magnetic modelling (Maystrenko et al., 2018) with use of the most recent geophysical data set mainly represented by the deep seismic profiles (Mjelde et al. 1997, 2001, 2002, 2003, 2005, 2009; Raum 2000, Raum et al.2002, 2006; Breivik et al. 2006, 2009, 2011; Kvarven et al. 2014, 2016), including structural data from Maystrenko & Scheck-Wenderoth (2009); Ebbing & Olesen (2010); Nirrengarten et al. (2014) and Gernigon et al. (2015b). Figure 8. View largeDownload slide Thicknesses: (a) the oceanic layer 2AB and upper crustal high-density rocks (layers 5 and 9, respectively), (b) the low-density upper-crustal layer (layer 10), (c) the regional upper-crustal layer (layer 11), (d) the middle crust (layer 12), (e) the lower crust including the high-density intracrustal layer (layers 13 and 14, respectively) and (f) the deep high-density lower-crustal layer (layer 15). JMC, Jan Mayen Corridor; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. Figure 8. View largeDownload slide Thicknesses: (a) the oceanic layer 2AB and upper crustal high-density rocks (layers 5 and 9, respectively), (b) the low-density upper-crustal layer (layer 10), (c) the regional upper-crustal layer (layer 11), (d) the middle crust (layer 12), (e) the lower crust including the high-density intracrustal layer (layers 13 and 14, respectively) and (f) the deep high-density lower-crustal layer (layer 15). JMC, Jan Mayen Corridor; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. The top of the crystalline basement (Maystrenko et al., 2018) is relatively complex (Fig. 9a), demonstrating that the Vøring and Møre basins are characterised by a very deeply located basement, whereas the Trøndelag Platform shows moderate basement depths that progressively shallow and crop out towards the coastline. The Moho topography (Maystrenko et al., 2018) used in this study shows that the crust-mantle boundary is deeply located beneath the Norwegian mainland and is much shallower beneath the Mid-Norwegian continental margin and the oceanic part of the model (Fig. 9b). Figure 9. View largeDownload slide Depth to the base of the sedimentary cover (top of the crystalline basement) (a) and Moho topography (b) beneath the study area. COB, continent-ocean boundary (from Gernigon et al.2015a); JMC, Jan Mayen Corridor; JMFZ, Jan Mayen Fracture Zone; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. Figure 9. View largeDownload slide Depth to the base of the sedimentary cover (top of the crystalline basement) (a) and Moho topography (b) beneath the study area. COB, continent-ocean boundary (from Gernigon et al.2015a); JMC, Jan Mayen Corridor; JMFZ, Jan Mayen Fracture Zone; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. 4 THERMAL PROPERTIES Prior to the 3-D thermal modelling, thermal properties represented by specific heat capacity, thermal conductivity and radiogenic heat production have been assigned for each layer of the 3-D model (Table 4). Table 4. Thermal properties of the layers of the 3-D structural model used during the 3-D thermal modelling (lithology of sediments is derived from Bell et al. (2014) and from NPD (2014)). No.  Layer of the 3-D structural model  Dominant lithology  Specific heat capacity Cp (J kg−1 K−1)  Thermal conductivity of the matrix kr (W m−1 K−1)  Radiogenic heat production S (μW m−3)  2  Kai and Naust (middle Miocene-Pleistocene)  92% shale, 8% sandstone  1180  2.3  0.5–1.5  3  Brygge (Eocene-lower Miocene)  98% shale, 2% sandstone  1180  2.2  0.47–1.5  4  Palaeocene  80% shale, 20% sandstone  1180  3.0  0.6–1.39  5  Oceanic layer 2AB  basalts and tuffs  880  1.8  0.4  6  Upper Cretaceous  95% shale, 5% sandstone  1180  2.5  0.7–1.68  7  Lower Cretaceous  92% shale, 3% sandstone, 5% limestone  1180  2.4  0.81–1.83  8  Pre-Cretaceous  80% shale, 20% sandstone  1180  3.3  0.8–1.64  9  Upper-crustal high-density crystalline rocks  gabbro to anorthositic rocks, metamorphic rocks  880  2.9  0.4  10  Low-density upper-crustal body  metasediments or granite  880  3.0  0.4–2.2  11  Upper-crustal regional layer  granite and gneiss  880  3.2  1.5 (0.9–2.5)  12  Middle crust  granitoids and/or gneiss  950  3.1  0.9 (0.4–2.5)  13  Lower crust  metamorphic rocks  1050  3.0  0.32  14  High-density intracrustal layer  mafic granulites, gabbros  1050  3.0  0.32  15  High-density Lower-crustal layer  gabbros, high-grade metamorphic rocks  1100  2.8 and 3.2  0.2  16  Lithospheric upper mantle  peridotite  1200  4.79  0.03  No.  Layer of the 3-D structural model  Dominant lithology  Specific heat capacity Cp (J kg−1 K−1)  Thermal conductivity of the matrix kr (W m−1 K−1)  Radiogenic heat production S (μW m−3)  2  Kai and Naust (middle Miocene-Pleistocene)  92% shale, 8% sandstone  1180  2.3  0.5–1.5  3  Brygge (Eocene-lower Miocene)  98% shale, 2% sandstone  1180  2.2  0.47–1.5  4  Palaeocene  80% shale, 20% sandstone  1180  3.0  0.6–1.39  5  Oceanic layer 2AB  basalts and tuffs  880  1.8  0.4  6  Upper Cretaceous  95% shale, 5% sandstone  1180  2.5  0.7–1.68  7  Lower Cretaceous  92% shale, 3% sandstone, 5% limestone  1180  2.4  0.81–1.83  8  Pre-Cretaceous  80% shale, 20% sandstone  1180  3.3  0.8–1.64  9  Upper-crustal high-density crystalline rocks  gabbro to anorthositic rocks, metamorphic rocks  880  2.9  0.4  10  Low-density upper-crustal body  metasediments or granite  880  3.0  0.4–2.2  11  Upper-crustal regional layer  granite and gneiss  880  3.2  1.5 (0.9–2.5)  12  Middle crust  granitoids and/or gneiss  950  3.1  0.9 (0.4–2.5)  13  Lower crust  metamorphic rocks  1050  3.0  0.32  14  High-density intracrustal layer  mafic granulites, gabbros  1050  3.0  0.32  15  High-density Lower-crustal layer  gabbros, high-grade metamorphic rocks  1100  2.8 and 3.2  0.2  16  Lithospheric upper mantle  peridotite  1200  4.79  0.03  View Large The thermal conductivities for the sedimentary rocks have been mostly derived from the previous estimations of the matrix thermal conductivity within boreholes of the northern Viking Graben (Brigaud et al.1992), the Mid-Norwegian continental margin and adjacent areas (Eldholm et al.2005; Pascal & Midttømme 2006; Pascal 2015), and other unconsolidated sampled sedimentary rocks from the Vøring Basin (Midttømme et al.1995). The obtained thermal conductivities of sedimentary rocks have been cross-validated with (1) the measured thermal conductivities from the North Sea boreholes (Evans 1977), (2) laboratory measurements of rock samples showing similar lithology (Čermak & Rybach 1982a; Clauser 2011) and (3) a comprehensive overview of different thermal conductivity values of sedimentary rocks (Midttømme & Roaldset 1999). The thermal conductivity of basalts (layer 5) has been set to be 1.8 W m−1 K−1 on average according to Balling et al. (2006) who measured thermal conductivity of basalts and tuffs for a depth interval of more than 3 km in the Lopra-1/1A borehole on the Faroe Islands, located south of the study area. Thermal conductivities of the upper crystalline crustal rocks have been set to be in the range of appropriate rock-sample measurements from within the Norwegian mainland (e.g. Olesen et al.1993; Slagstad et al.2009; Maystrenko et al.2015b). The mentioned thermal conductivities of the sedimentary infill, basalts and upper-crustal rocks have been supplemented with published values for the deeper crystalline crust and the lithospheric mantle (Čermak & Rybach 1982a; Wollenberg & Smith 1987; Hofmeister 1999; Artemieva et al.2006; Scheck-Wenderoth & Maystrenko 2008, 2013; Maystrenko et al.2014). The thermal conductivities of rocks have been set to be dependent on temperature. This has been done in order to consider a significant change in the thermal conductivities of sedimentary rocks as a result of increasing temperature and decreasing porosity of the sedimentary rocks with depth. Temperature-dependent values of the thermal conductivities for the uppermost crystalline crust have been calculated according to the empirical equation (3) from Sass et al. (1992):   $$k\left( T \right) = {k_{\rm{o}}}/\left( {1.007 + T\left( {0.036 - 0.0072/{k_{\rm{o}}}} \right)} \right)$$ (3)where k(T) is the thermal conductivity [W m−1 K−1] at temperature T in [°C], k(0) is the thermal conductivity [W m−1 K−1] at 0 °C and T is the temperature [°C]. The empirical equation (4) from Vosteen & Schellschmidt (2003) has been used to calculate the temperature-dependent thermal conductivities for the rest of the crystalline crust where the temperature is higher than 300 °C:   $$k\left( T \right) = {k_{\rm{o}}}/\left( {0.99 + T\left( {a - b/{k_{\rm{o}}}} \right)} \right)$$ (4)where k(T) is the thermal conductivity of crystalline rocks [W m−1 K−1] at temperature T in [K], ko is the thermal conductivity [W m−1 K−1] at 0 °C, T is the temperature [K], a and b are constants: a = 0.0030 ± 0.0015 and b = 0.0042 ± 0.0006. To define the temperature- and pressure-dependent thermal conductivities within the lithospheric mantle, the empirical equations (5) and (6) from Hofmeister (1999) have been taken:   \begin{eqnarray} k\left( {T,P} \right) &=& {k_r}{\left( {298/T} \right)^a}\exp [ - (4\gamma + 1/3)\alpha \left( {T - 298} \right)]\nonumber \\ &&\times \,\left( {1 + K{'_{\rm{o}}}P/{K_{\rm{o}}}} \right) + {k_{{\rm{rad}}}} \end{eqnarray} (5)  \begin{eqnarray} {k_{\rm{rad}}} &=& 4.7 ( \,{0.01753 - 0.00010365T} \nonumber\\ &&+\, {2.2451{T^2}/{{10}^7} - 3.407{T^3}/{{10}^{11}}} ) \end{eqnarray} (6)where k(T, P) is thermal conductivity [W m−1 K−1] at temperature T in [K] and under pressure P in [Pa], kr is the thermal conductivity [W m−1 K−1] at room temperature, γ is Grueneisen parameter (γ = 1 to 1.4), a is the phonon fitting parameter (a = 0.25 to 0.45), α is the volume coefficient of thermal expansion as a function of temperature, Ko is the bulk modulus [Pa] (Ko = 261 GPA), K΄o is the pressure derivative of the bulk modulus (K΄o = 5) and krad is the radiative component of the thermal conductivity, enhanced according to van den Berg et al. (2001). In addition, the empirical equation (4) has been used to calculate the temperature-dependent thermal conductivities for the solid material (porous matrix) of the sedimentary cover. In this case, constants a and b vary within the following range: a = 0.0034 ± 0.0006 and b = 0.0039 ± 0.0014. In addition, the thermal conductivity of the sedimentary rocks has also been set to be dependent on compaction by introducing the equivalent thermal conductivity. The thermal conductivity of the solid–fluid system keq is the so-called equivalent thermal conductivity and can be inferred by use of this equation:   $${k_{{\rm{eq}}}} = {\theta _{\rm{s}}}{k_{\rm{s}}} + {\theta _{\rm{f}}}{k_{\rm{f}}}$$ (7)where ks is the thermal conductivity of the solid material (porous matrix) and kf is the thermal conductivity of the fluid (water in the case of the present study), θs is the solid material's volume fraction, which is related to the volume fraction of the fluid θf as in the following:   $${\theta _{\rm{s}}} + {\theta _{\rm{f}}} = 1$$ (8) The thermal conductivity of the fluid in the pores of sedimentary rocks has been taken as the temperature-dependent thermal conductivity of water based on the thermodynamic properties of water and steam according to the International Association for Properties of Water and Steam Industrial Formulation 1997 (Wagner & Kretzschmar 2008). The volume fraction of the fluid θf is represented by porosity (Φ) which is assumed to decrease with depth according to eq. (9):   $$\Phi = 1 - \rho \left( z \right)/{\rho _{\rm{m}}}$$ (9)where Φ is the porosity, ρ(z) is depth-dependent density [kg m−3] which is specified for each layer according to exponential functions of increasing densities with depth from Maystrenko et al. (2018), z is depth [m], and ρm is matrix density [kg m−3] assumed to be the same (2700 kg m−3 on average) for all sedimentary layers due to uncertainties in defining the lithological composition. It is important to note that the densities of the rocks comprising the sedimentary cover have been locally reduced within the Jan Mayen Corridor compared to the rest of the study area. This has been done in accordance with the previous results of the 3-D density analysis (Maystrenko et al., 2018). Within the Jan Mayen Corridor, the calculated thermal conductivities have been accordingly reduced due to the very low degree of compaction within the uppermost sedimentary rocks (Maystrenko et al., 2018). In contrast, porosities of the crystalline rocks have been neglected during the 3-D thermal modelling because these rocks have, in general, extremely low porosities compared to the sedimentary rocks. For instance, according to the porosity measurements of crystalline rocks in Sweden (Tullborg & Larson 2006), porosities of crystalline rocks vary from 1.5 per cent at relatively shallow levels to 0.98 per cent in the deep crust. Densities of the crystalline rocks have been set based on the 3-D density modelling (Maystrenko et al., 2018). The assigned values of the specific heat capacity have also been set to be constant during the 3-D thermal modelling (Table 4) and have been derived mainly from values published in Clauser (2011). For the specific heat capacity of rock matrix, the dependence on temperature has been considered in terms of significant changes by assigning the average values for the layers at different temperature intervals, depending on the depth of the layer. These temperature-dependent average values of the specific heat capacity have been derived from the literature based on laboratory measurements at different temperature conditions (e.g. Čermak & Rybach 1982a; Afonso et al.2005; Clauser 2011). We used radiogenic heat productions of the upper and middle-crustal layers mostly derived from average values calculated from airborne gamma spectrometry surveys and/or based on average heat production for geological units in Norway according to rock-sample measurements (e.g. Slagstad 2008; Slagstad et al.2009; Slagstad & Lauritsen 2013). The values of radiogenic heat production for the lower-crustal layers and the lithospheric mantle have been considered to be constant (Table 4). In the case of the radiogenic heat production, there is no accurate mathematical way to predict the content of radiogenic elements within the deep-crustal layers. The radiogenic heat production is mostly dependent on the specific lithological composition of the layer rather than on depth, pressure and/or temperature. A decreasing content of the radiogenic elements with depth is generally observed. Accordingly, the average constant values of the radiogenic heat production rely on published values for the assumed lithological composition of each layer (Čermak & Rybach 1982b; Scheck-Wenderoth & Maystrenko 2008; Vila et al.2010). In order to obtain a reasonable fit between the observed and modelled temperatures in the available boreholes offshore, lateral and realistic variations of the radiogenic heat production have been applied for the low-density upper-crustal body (layer 10; Fig. 8b), upper-crustal regional layer (layer 11; Fig. 8c) and middle crust (layer 12; Fig. 8d). On the other hand, alternative explanations for local changes of the measured temperature should not be excluded and could also be explained by enforced fluid flow (convection and/or advection), significant variations in thermal conductivities, structural uncertainties and/or limited horizontal resolution of the 3-D model. However, these additional reasons require supplementary structural data, extra sampling material and further simulation of more complex physical processes (e.g. fluid flow). Absence of reliable data and difficulties in such a regional 3-D modelling approach do not allow us to test theses various aspects at this stage. The observed variations in the radiogenic heat production of the crystalline rocks on the mainland (e.g. Slagstad 2008; Pascal & Rudlang 2016) provide a possibility for assuming that a similar situation could also apply within the crystalline rocks offshore. Meanwhile, we consider that variable radiogenic heat production within the crystalline crust is the most reasonable and easiest applicable procedure for the 3-D thermal modelling. Several testing models including different values of the radiogenic heat production have been generated and validated to obtain a reasonable fit between the modelled and measured temperatures in the available boreholes. These assumptions also consider the result of the 3-D potential field modelling described in the companion paper of Maystrenko et al. (2018). In particular, the low-density upper-crustal body (layer 10) has been subdivided into two blocks with different radiogenic heat production (Fig. 10a). The southwesternmost part of this layer has been assigned a radiogenic heat production of 2.2 μW m−3. In contrast, the rest of this layer has been given a lower value of radiogenic heat production (0.4 μW m−3), implying possible lithological changes within this layer towards the northeast. The crustal block with the increased radiogenic heat production can most likely represent granitic rocks whereas the block with the reduced radiogenic heat production can possibly represent metasedimentary rocks. Figure 10. View largeDownload slide Radiogenic heat production of (a) the low-density upper-crustal layer, (b) the regional upper-crustal layer and (c) the middle crust. FH, Frøya High; JMC, Jan Mayen Corridor; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. Figure 10. View largeDownload slide Radiogenic heat production of (a) the low-density upper-crustal layer, (b) the regional upper-crustal layer and (c) the middle crust. FH, Frøya High; JMC, Jan Mayen Corridor; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. The upper-crustal regional layer (layer 11) is characterised by a relatively complex pattern of the assigned values of radiogenic heat production (Fig. 10b). Different blocks with increased or decreased values of radiogenic heat production match the basement configuration deduced from the 3-D magnetic modelling (Maystrenko et al., 2018). The block with increased radiogenic heat production within the northeastern part of the detailed 3-D model area is most likely related and/or similar to the granitoid rocks of the Transscandinavian Igneous Belt (Åhäll & Larson 2000). Based on more than 500 samples (Slagstad et al.2008), these Precambrian granitoids show a median heat production of 2.57 μW m−3. In the case of the present study, a lower value of 2.2 μW m−3 compared to the median heat production (Slagstad et al.2008) has been assigned to similar rocks. This lower value of the radiogenic heat production has been chosen to represent a possible decrease of radiogenic heat production with depth as observed within the Transscandinavian Igneous Belt onshore. To the west of the Transscandinavian Igneous Belt, a second block with anomalous magnetic susceptibility has been set with the same increased value of radiogenic heat production of 2.2 μW m−3. This block can also be associated with the Transscandinavian Igneous Belt and is possibly covered by relatively thick, upper-crustal, high-density crystalline rocks (layer 9) associated with younger and shallower Caledonian nappes (cf. Figs 8a and c and 10b). The two blocks within the southeastern corner of the detailed 3-D study area (Fig. 10b) are probably related to granitoids which are in general characterised by relatively high contents of radiogenic elements. Such basement rocks may explain the increased values of radiogenic heat production towards the south from the study area (e.g. Killeen & Heier 1975; Wilson et al.1977; Slagstad & Lauritsen 2013). The Frøya High and the neighbouring areas also have prominent and characteristic magnetic signatures and the upper-crustal blocks have been subdivided into three blocks (Fig. 10b): two blocks with increased radiogenic heat production (2.2 μW m−3) and one block in between with a lower heat production (1.2 μW m−3). Farther north, a small and speculative crustal block with an increased radiogenic heat production (2.5 μW m−3) has been set up within the northern part of the Trøndelag Platform (Fig. 10b) in order to raise the modelled temperatures. However, this upper-crustal block is not reflected in any specific gravity or magnetic anomalies and there is a possibility that the increased measured temperatures in that area are simply the local result of different processes. The transition zone from the Trøndelag Platform to the Vøring Basin is characterised by the presence of the hypothetical zone with relatively low values of radiogenic heat production in the necking zone, ranging from 0.9 to 1.1 μW m−3. In addition, a small crustal block with increased radiogenic heat production (2.2 μW m−3) has been included into the regional upper-crustal layer in the northwestern corner of the model area and a small block with decreased radiogenic heat production (1.0 μW m−3) has been set up within the southern part of the Møre Basin (Fig. 10b). A differentiation of the middle crust (layer 12) in terms of the radiogenic heat production was also considered in places where either a decreased or increased heat production has been assigned to the previously described layer (layer 11, cf. Figs 10b and c). Consequently, the block with increased values of radiogenic heat production (2.5 μW m−3) has been hypothetically distinguished within the northern part of the Trøndelag Platform and could represent potential Precambrian granitoids. The crustal blocks with the lowest heat production (0.4-0.6 μW m−3) are located at the transition between the Trøndelag Platform to the Vøring Basin and in the vicinity of the Frøya High (Fig. 10c). These crustal blocks are most likely gneisses derived from metamorphosed sedimentary rocks with low contents of radiogenic elements. The need to include middle-crustal blocks with a variable radiogenic heat production is partially related to the fact that the regional upper-crustal layer is locally too thin to reduce the misfit between the measured and the modelled temperatures. In the Møre and Vøring basin, the crystalline crust is indeed relatively thin and strongly attenuated but not necessary enough to develop large zones of mantle exhumation before breakup (e.g. Nirrengarten et al. 2014; Gernigon et al. 2015b; Maystrenko et al., 2018). On the other hand, the sedimentary cover is extremely thick in that area as well as in the Trøndelag Platform. Therefore, radiogenic heat production of sedimentary rocks could play an important role as an additional heat source. For instance, heat production varies from approximately 0.07 μW m−3 to about 2.21 μW m−3 in the Gulf of Mexico (McKenna & Sharp 1998) and has an average range of 0.4–2.1 μW m−3 in the Northeast German Basin (Norden & Förster 2006). In the present study, all sedimentary layers of the 3-D model have been assigned with variable radiogenic heat production values based on the results of gamma-ray logging in the selected boreholes, one of which is shown in Fig. 11. These boreholes have been chosen to cover the whole model area, giving a large range of values which are assumed to be representative of the thermal properties of the sedimentary rocks in the vicinity of each well. Figure 11. View largeDownload slide Plot showing stratigraphy, measured total natural gamma and derived radiogenic heat production for one of the boreholes (borehole 6406/12-2) used to calculate the radiogenic heat production of sedimentary cover (stratigraphy and gamma-ray log are from NPD 2014). Figure 11. View largeDownload slide Plot showing stratigraphy, measured total natural gamma and derived radiogenic heat production for one of the boreholes (borehole 6406/12-2) used to calculate the radiogenic heat production of sedimentary cover (stratigraphy and gamma-ray log are from NPD 2014). In order to obtain values of the radiogenic heat production for sedimentary rocks, natural gamma-ray logs have been collected from the NPD web site and were ultimately digitised (Fig. 11). The empirical relationship between total natural gamma and radiogenic heat production (10) from Bücker & Rybach (1996) has been applied to calculate the radiogenic heat production of the sedimentary infill in the selected boreholes (Figs 11 and 12; Table 5).   $$S = 0.0158\left( {{\rm{GR}} - 0.8} \right)$$ (10)where S is the radiogenic heat production (μW m−3) and GR is the total gamma (API units). The results of the calculation represent scaling values of the radiogenic heat production rather than precise ones. The empirical relationship (10) has been derived by Bücker & Rybach (1996) for the range of total natural gamma of 0–350 API. Values of the total natural gamma obtained for the sedimentary rocks of the Mid-Norwegian margin are mainly in the range 0–150 API (Fig. 11) and, therefore, the results of the calculation should provide realistic values for the radiogenic heat production. The reliability of radiogenic heat production obtained from the gamma-ray logs has recently been confirmed in the Fyllingsdalen and Årvollskogen boreholes, which have been drilled through crystalline rocks on the mainland in SW Norway (Maystrenko et al.2014, 2015b). In addition to natural gamma-ray logging, gamma spectrometry logging in the Årvollskogen borehole has been used to obtain values of radiogenic heat production based on concentrations of uranium (U), thorium (Th) and potassium (K). Comparative analysis indicates that curves of radiogenic heat production, calculated based on natural gamma-ray and gamma spectrometry loggings show a good match (Maystrenko et al.2014). The empirical equation (10) is possibly not the best solution for conversion in the case of sedimentary rocks compared to the crystalline rocks. However, there are no available data to validate the empirical relationship proposed for the sedimentary rocks. The average values of the radiogenic heat production for every sedimentary layer have accordingly been derived (Table 5) from the calculated values (e.g. Fig. 11). The average radiogenic heat production has then been used to produce maps by interpolation between the existing values in the boreholes (Fig. 12). The radiogenic heat production has been assigned to the different sedimentary layers but without considering compaction of sedimentary rocks when these rocks are located deeper than the sedimentary strata used in the boreholes. In contrast, the compaction effect is already included in the values derived from the drilled successions in the used boreholes (e.g. Fig. 11). According to the results of these calculations, the average radiogenic heat production of the sedimentary layers varies from 0.47 to 1.85 μW m−3 (Table 5), indicating relatively large variations within different parts of the study area and within different layers of the 3-D model. The Shetland and Cromer Knoll groups (Dalland et al. 1988; Fig. 12, Table 5) do not precisely correspond to the Upper Cretaceous (layer 6) and the Lower Cretaceous (layer 7) locally. On the other hand, the difference in average values of the radiogenic heat production between the Shetland and Cromer Knoll groups (NPD nomenclature and definition) is rather small (Table 5) and, therefore, an average radiogenic heat production for the Shetland and Cromer Knoll groups has been assigned to the Upper Cretaceous (layer 6) and the Lower Cretaceous (layer 7), respectively. Figure 12. View largeDownload slide Radiogenic heat production of the sedimentary layers, interpolated from the borehole data: the Kai-Naust (middle Miocene-Pleistocene) formations (a), the Brygge (Eocene-lower Miocene) Formation (b), the Palaeocene (c), the Upper Cretaceous (d), the Lower Cretaceous and (e) pre-Cretaceous (f). Locations of the boreholes used to estimate the radiogenic heat production of sedimentary layers are shown by the white circles. JMC, Jan Mayen Corridor; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. Figure 12. View largeDownload slide Radiogenic heat production of the sedimentary layers, interpolated from the borehole data: the Kai-Naust (middle Miocene-Pleistocene) formations (a), the Brygge (Eocene-lower Miocene) Formation (b), the Palaeocene (c), the Upper Cretaceous (d), the Lower Cretaceous and (e) pre-Cretaceous (f). Locations of the boreholes used to estimate the radiogenic heat production of sedimentary layers are shown by the white circles. JMC, Jan Mayen Corridor; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. Table 5. Average radiogenic heat production of the sedimentary rocks, derived from the gamma-ray logs, available along selected wells. Units of radiogenic heat production are in μW m−3. Well  Nordland (layer 2)  Hordaland (layer 3)  Rogaland (layer 4)  Shetland (layer 6)  Cromer Knoll (layer 7)  Pre-Cretaceous (layer 8)  34/3-1 S  1.33  0.84  0.73  1.3  1.03  1.1  35/3-2  0.5  0.72  0.76  0.74  0.8  1.0  6205/3-1R  0.7  –  1.2  1.5  1.5  1.1  6302/6-1  1.03  1.04  1.3  1.24  –  –  6305/1-1  1.22  1.0  0.9  1.32  1.4    6406/2-1R  1.53  1.5  1.4  1.7  1.85  1.14  6406/12-2  1.2  1.42  1.21  1.23  1.42  1.11  6505/10-1  0.7  1.2  0.91  1.23  1.46  –  6507/5-1  1.1  0.7  0.7  0.8  0.93  1.13  6507/12-2  0.92  0.88  0.76  0.92  –  0.78  6510/2-1R  0.68  0.72  0.68  0.7  0.94  1.65  6603/12-1  1.2  1.31  1.1  1.31  –  –  6610/7-2  0.86  0.47  0.6  0.74  0.82  1.1  6707/10-1  0.54  –  0.8  1.24  –  –  Well  Nordland (layer 2)  Hordaland (layer 3)  Rogaland (layer 4)  Shetland (layer 6)  Cromer Knoll (layer 7)  Pre-Cretaceous (layer 8)  34/3-1 S  1.33  0.84  0.73  1.3  1.03  1.1  35/3-2  0.5  0.72  0.76  0.74  0.8  1.0  6205/3-1R  0.7  –  1.2  1.5  1.5  1.1  6302/6-1  1.03  1.04  1.3  1.24  –  –  6305/1-1  1.22  1.0  0.9  1.32  1.4    6406/2-1R  1.53  1.5  1.4  1.7  1.85  1.14  6406/12-2  1.2  1.42  1.21  1.23  1.42  1.11  6505/10-1  0.7  1.2  0.91  1.23  1.46  –  6507/5-1  1.1  0.7  0.7  0.8  0.93  1.13  6507/12-2  0.92  0.88  0.76  0.92  –  0.78  6510/2-1R  0.68  0.72  0.68  0.7  0.94  1.65  6603/12-1  1.2  1.31  1.1  1.31  –  –  6610/7-2  0.86  0.47  0.6  0.74  0.82  1.1  6707/10-1  0.54  –  0.8  1.24  –  –  View Large In particular, the uppermost stratigraphic intervals, represented by Kai-Naust (middle Miocene-Pleistocene; layer 2) and Brygge (Eocene-lower Miocene; layer 3), are characterised by a similar range of values for the derived radiogenic heat production, varying from 0.5 to 1.53 μW m−3 for layer 2 and from 0.47 to 1.5 μW m−3 for layer 3 (Table 5). Nevertheless, the maps in Figs 12(a) and (b) show recognisable differences in the local pattern of radiogenic heat production. On the other hand, the general pattern is relatively similar, displaying low values within the northeastern and southeastern parts of the model area which are separated by a zone with increased radiogenic heat production (cf. Figs 12a and b). The above-described general trend in radiogenic heat production is also recognisable at the level of the Palaeocene (Fig. 12c) with the average values ranging from 0.6 to 1.4 μW m−3 (Table 5). Moreover, this pattern is still clearly visible at the level of the Upper and Lower Cretaceous units (layers 6 and 7) where a zone of increased radiogenic heat production in the central part of the model area is surrounded by reduced values (Figs 12d and e). Compared to the Cenozoic stratigraphic intervals, the Cretaceous maps show higher radiogenic heat production which ranges from 0.7 to 1.7 μW m−3 for the Upper Cretaceous and from 0.8 to 1.85 μW m−3 for the Lower Cretaceous (Table 5). In the case of the pre-Cretaceous sedimentary and metasedimentary rocks, this general pattern cannot be identified, reflecting structural changes in deposition and present-day distribution between the pre-Cretaceous and the Cretaceous-Cenozoic sedimentary rocks. Information on pre-Cretaceous radiogenic heat production is mostly limited to the uppermost part of the pre-Cretaceous (Fig. 11) and, therefore cannot be fully representative of the whole of the deeper pre-Cretaceous interval. However, sparse data and limited borehole information about the pre-Cretaceous successions have been used to partly assess the radiogenic heat production for this interval (Fig. 12f). A large part of the pre-Cretaceous in Fig. 12(f) is characterised by values of heat production which are around 1 μW m−3. In the northeast of the model area, an increase of the radiogenic heat production in well 6510/2-1R is bounded by reduced values in well 6507/12-2. The investigated pre-Cretaceous succession is particularly thick in these two boreholes (6507/12-2 and 6510/2-1R), implying that the average radiogenic heat production of the whole of the pre-Cretaceous could be more variable than it appears from the map in Fig. 12(f). The studied radiogenic heat production of the pre-Cretaceous varies from 0.78 to 1.65 μW m−3 (Table 5). Coming back to the Cretaceous-Cenozoic interval (Figs 12a–e), the increased values of radiogenic heat production in the vicinity of boreholes 6406/2-1R and 6406/12-2 are characteristic of the more than 100 million-year-long stratigraphic interval. The zone of higher radiogenic heat production shown around well 6406/2-1R is also recognisable on all Cretaceous-Cenozoic maps (Figs 12a–e), implying a possible inheritance in clastic material transport from the same erosional locality onshore where crystalline rocks are or were originally characterised by large contents of radiogenic elements. Such an inherited zone with increased radiogenic heat production could also represent and/or highlight the result of differential erosion and/or sorting of the sediments during transportation from source-to-sink. Deposition of more argillaceous fractions in particular areas of the Mid-Norwegian continental margin may explain local increases of heat production within specific depocentres. For example, McKenna & Sharp (1998) have shown that mudrocks in the Gulf of Mexico basin produce about 30–40 per cent more radiogenic heat than their lateral and stratigraphically equivalent sandstones. Nevertheless, this remarkable coincidence would require additional investigation. A more detailed study is required in order to analyse this specific pattern of radiogenic heat production within the sedimentary cover by including smaller stratigraphic intervals and by use of a larger number of boreholes. An attempt to correlate the radiogenic patterns of sedimentary rocks with potential sources for eroded material within the mainland could have significant implications for independent palaeogeographic and source-to-sink studies. 5 RESULTS AND IMPLICATIONS OF THE 3-D THERMAL MODELLING 5.1 Modelled temperature The 3-D structural model (Fig. 13a) has been successfully converted into a reliable 3-D thermal model (Fig. 13b). These results provide an overview of the present-day temperature distribution beneath the Earth's surface within the Møre and Vøring segments of the Mid-Norwegian continental margin and adjacent areas of the Norwegian mainland. Fig. 14 shows the pattern of subsurface temperature at six chosen depths below sea level within the upper part of the 3-D model where relatively low thermally conductive sedimentary rocks are present. In addition, Fig. 15 illustrates the temperature distribution within the deeper parts of the detailed 3-D model area (i.e. near the crust-mantle boundary (Figs 14a and b) and within the lithospheric mantle (Figs 14c and d)). Figure 13. View largeDownload slide (a) The lithosphere-scale 3-D model of the Mid-Norwegian continental margin and adjacent areas of the Norwegian mainland (from Maystrenko et al., 2018). (b) 3-D temperature distribution within the model shown in (a). Four times vertically exaggerated. Figure 13. View largeDownload slide (a) The lithosphere-scale 3-D model of the Mid-Norwegian continental margin and adjacent areas of the Norwegian mainland (from Maystrenko et al., 2018). (b) 3-D temperature distribution within the model shown in (a). Four times vertically exaggerated. Figure 14. View largeDownload slide Modelled temperatures within the upper part of the detailed 3-D model. Temperature maps, extracted from the 3-D thermal model (Fig. 13b), for the depths of 2 km (a), 5 km (b), 7 km (c), 10 km (d), 15 km (e) and 18 km (f). JMC, Jan Mayen Corridor; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. Figure 14. View largeDownload slide Modelled temperatures within the upper part of the detailed 3-D model. Temperature maps, extracted from the 3-D thermal model (Fig. 13b), for the depths of 2 km (a), 5 km (b), 7 km (c), 10 km (d), 15 km (e) and 18 km (f). JMC, Jan Mayen Corridor; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. Figure 15. View largeDownload slide Modelled temperatures within the deep parts of the detailed 3-D model. Temperature maps, extracted from the 3-D thermal model (Fig. 13b), at depths of 25 km (a), 40 km (b), 80 km (c) and 100 km (d). JMC, Jan Mayen Corridor; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. Figure 15. View largeDownload slide Modelled temperatures within the deep parts of the detailed 3-D model. Temperature maps, extracted from the 3-D thermal model (Fig. 13b), at depths of 25 km (a), 40 km (b), 80 km (c) and 100 km (d). JMC, Jan Mayen Corridor; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. At a large scale, the mainland is generally colder compared to the Mid-Norwegian continental margin (Fig. 14). Within the upper part of the 3-D thermal model, this regional trend of the modelled temperatures is associated mainly with the high thermal conductivity of crystalline crustal rocks (Table 4) which crop out over large parts of the mainland. This interaction between the relatively high values of thermal conductivities of the crystalline rocks and specific structural patterns is responsible for a chimney effect within the areas where the crystalline rocks are exposed at the surface. The thermal pattern related to the chimney effect on the mainland is complicated by a zone with increased temperatures beneath the Scandes mountains which is particularly pronounced at a depth of 2 km (Fig. 14a). This is mainly due to the topographic effect of the Scandes Mountains which generally reach to more than 1.5–2 km elevation above the sea level (Fig. 1). The upper thermal boundary at the Earth's surface is therefore also uplifted by more than 1.5–2 km within the Scandes compared to the rest of the mainland where the relief is lower. The latter adds an additional 1.5–2 km to the distance from the upper thermal boundary to the chosen depths below sea level beneath the Scandes Mountains. The topographic effect of the Scandes is still clearly recognisable at a depth of 7 km (b.s.l) and even deeper where it is disturbed by the structural interaction between the middle and upper crystalline crustal layers (Fig. 14) characterised by different thermal properties (Table 4). In the offshore part, the thermal effect associated with the topographic variations is also visible at shallower levels within the northwestern part of the Møre Basin and Jan Mayen Corridor (cf. Figs 1 and 14a and b). In contrast to the Scandes mountains, the modelled temperatures are notably lower within the wide area of deep bathymetry compared to the rest of the Norwegian continental shelf (e.g. Fig. 14a), reflecting the fact that the upper thermal boundary at the seafloor sinks together with the bathymetry and, therefore, brings low surface temperatures down to greater depths. The next feature of the thermal pattern within the upper crust concerns the direct relationship between areas characterised by a thick sedimentary cover and areas showing increased temperatures within the rifted margin (cf. Figs 7 and 14). This regional trend of temperature distribution is related to the low thermal conductivity of sedimentary rocks which increases the heat storage within the areas characterised by a thick and low conductive sedimentary cover. It is important to note that this thermal insulation effect is locally complicated by depth variations of the seafloor which correspond to the upper thermal boundary in our 3-D thermal model. The superimposed thermal effect of the deep bathymetry is particularly significant within the Jan Mayen Corridor where it is represented by lower modelled temperatures at 2–7 km depths in Figs 14(a)–(c). The blanketing effect of sedimentary rocks is particularly prominent within the Vøring Basin where the sedimentary infill is thickest (Fig. 14). The uppermost sedimentary layers of the detailed 3-D model, represented by the Brygge (Eocene-lower Miocene), Kai (middle Miocene-lower Pliocene) and Naust (upper Pliocene-Pleistocene) formations, are characterised by the lowest thermal conductivities. This fact is partially reflected by the distribution of the modelled temperature at depths of 2 and 5 km where the thickness pattern of these Cenozoic formations is still recognisable (cf. Figs 7a and b, and 14a and b). The blanketing effect of sedimentary rocks becomes reasonably smoother in the areas showing thinner sedimentary rocks (e.g. the Trøndelag Platform and the eastern part of the Møre Basin; Fig. 7). The Møre Basin itself is characterised by slightly lower temperatures compared to the Vøring Basin. The latter is mainly due to the thermal blanketing effect triggered both by the thicker sedimentary rocks within the Vøring Basin and the variable radiogenic heat production of the same sediments. The deepening of the bathymetry affects the modelled temperature within the Møre Basin and causes a decrease in temperatures within the northwestern part of the Møre Basin and along the Jan Mayen Corridor even at a depth of 5 km (Fig. 14b). Besides, the distribution of the subsurface temperatures along the northwestern edge of the detailed model area is strongly affected by the gradual uplift of the present-day lower thermal boundary (Fig. 3b) and the palaeo-thermal boundaries (Fig. 6) at the base of the lithosphere rising towards the oceanic lithospheric domain. The thermal influence of the lower thermal boundary configuration becomes more and more notable at greater depths where the modelled temperature increases due to the lithospheric thinning. The results of the 3-D thermal modelling within the deeper part of the 3-D thermal model are presented in Fig. 15 by four 2-D horizontal slices of the temperature distribution at depths of 25, 40, 80 and 100 km. It is important to note that the modelled temperature beneath the mainland is already lower than the temperature beneath the Mid-Norwegian continental margin at depths of 25 and 40 km (Figs 15a and b). At that level, the mantle material partially or fully predominates beneath the continental margin, whereas the crystalline crustal rocks are still present beneath the mainland (Fig. 9b). There are, however, some complications in the modelled thermal pattern beneath the mainland (Figs 15a and b) due to the interaction between crustal and mantle thermal properties (Table 4). The influence of this interaction, however, is considerably smoothed by the topography of the lower thermal boundary which is deeply located beneath the mainland and significantly uplifted beneath the oceanic domain (Figs 3b and 6). Therefore, an increased radiogenic heat production of the crystalline crust compared to the mantle material at 25 and 40 km depth levels is not large enough to overcome the thermal pattern of the heat coming from deeper parts of the Earth's interior within the study area. In this case, the configuration of the lithosphere-asthenosphere boundary is the key factor controlling the temperature distribution within the deeper levels of the detailed 3-D thermal model. One of the interesting features of the 3-D conductive thermal field predicted by these maps is the temperature variation from relatively low values within the southeastern part of the model area to the higher values in the northwest (Fig. 15). At depths of 80 and 100 km (Figs 15c and d) the distribution of the modelled temperature generally reflects the configuration of the lower thermal boundary, which is represented by the base of the lithosphere with an isotherm of 1300 °C (cf. Figs 3b, and 15c and d). The modelled temperatures at the Moho (Fig. 16a) partially mimic the shape of the Moho topography (Fig. 9b), indicating that the key factor is similar to the top of the crystalline basement and controlled by the depth position of this boundary. For that reason, the highest temperatures (more than 700 °C) are obtained beneath the northeastern part of the model area where the Moho is deepest. In contrast, this correlation between the depth position of the Moho and the modelled thermal pattern is not completely valid for the modelled heat flux (Fig. 16b) which is more sensitive to the configuration of the lower thermal boundary. The modelled heat flux at the Moho is generally in good agreement with the previous estimation by Scheck-Wenderoth & Maystrenko (2008), showing already an increase of values from the mainland towards the oceanic lithospheric domain. In particular, there is a zone with high heat flux within the northwestern part of the Møre Basin. There, the heat flux varies from 50 to more than 60 mW m−2, reflecting the influence of the early Cenozoic continental breakup and present-day position of the expected base of lithosphere. Differences between the modelled heat flux at the Moho when the continental breakup effect is either considered or disregarded in the modelling workflow is expected, on average, to be 6–7 mW m−2 within the detailed 3-D model area. However, it reaches more than 12–13 mW m−2 towards the oceanic domain outside of the detailed model. The lowest modelled heat flux has been obtained beneath the mainland where it is in the range of 30–35 mW m−2 (Fig. 16b). Figure 16. View largeDownload slide Modelled temperatures (a) and heat flux (b) at the base of the crust (Moho). JMC, Jan Mayen Corridor; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. Figure 16. View largeDownload slide Modelled temperatures (a) and heat flux (b) at the base of the crust (Moho). JMC, Jan Mayen Corridor; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. The modelled temperatures at the top of the crystalline basement (Fig. 17a) reflect the geometry of the top-basement (Fig. 9a). There is a straightforward relationship between the distribution of the modelled temperatures (Fig. 17a) and the depth to the top of the crystalline basement (Fig. 9a): when the top of the crystalline rocks is deeply situated, the modelled temperatures increased and vice versa. Consequently, the modelled temperature maxima coincides with the deepest parts of the Vøring Basin. There, the temperatures reach more than 450 °C at the present day (Fig. 17a). Regionally, the top of the crystalline basement beneath the Vøring Basin is characterised by higher modelled temperatures (350–450 °C on average) compared to the southern Møre Basin which is slightly colder with average temperatures varying from 250 to 350 °C in the southwestern part of the basin to values similar to those of the Vøring Basin in its northeastern part. Figure 17. View largeDownload slide (a) Modelled temperatures at the top of the crystalline basement within the detailed model area. Modelled heat flux at the top of the crystalline basement: (b) with the thermal influence of the Saalian and Weichselian glaciations and (c) without the influence of those glaciations. FH, Frøya High; JMC, Jan Mayen Corridor; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. Figure 17. View largeDownload slide (a) Modelled temperatures at the top of the crystalline basement within the detailed model area. Modelled heat flux at the top of the crystalline basement: (b) with the thermal influence of the Saalian and Weichselian glaciations and (c) without the influence of those glaciations. FH, Frøya High; JMC, Jan Mayen Corridor; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. The Trøndelag Platform is clearly distinguished by lower temperatures in comparison to the Vøring and Møre sag basins. At the present day, the average modelled temperatures beneath the Trøndelag Platform are in the range of 200–230 °C near the top-basement. The modelled temperatures on the mainland simply reproduce the Earth’s surface temperatures (cf. Figs 3a and 17a) due to the fact that the crystalline basement is directly exposed at the surface there. The modelled heat flux at the top of the crystalline basement (Figs 17b and c) shows a complex pattern compared to the distribution of temperature (Fig. 17a). The heat flux distribution over the mainland is partially controlled by abrupt changes in the topography (Fig. 1). In addition, there is a clear influence of the palaeoclimatic conditions related to the Saalian and Weichselian glaciations described in the previous chapter (Figs 4 and 5). Low heat flux values (around 40 mW m−2) have been modelled over parts of the continent not affected by the ice sheet during the glaciations (cf. Figs 4 and 17b) and, therefore, were affected by low surface temperatures similar to the present-day tundra conditions (Fig. 5). However, the influence of the Saalian and Weichselian glaciations is smoothed within the areas previously covered by ice sheets or seawater. For instance, there is an increased heat flux of up to 60–70 mW m−2 within the part of Scandes (Fig. 17b) which was almost permanently covered and thermally insulated by the thick ice sheet during the glacial periods. A similar situation occurs in the vicinity of the coastline which has been thermally insulated by the seawater and sedimentary rocks. The contrasting NE–SW-trending narrow zone showing an increased heat flux along the coastline (Fig. 17b) is mainly controlled by the sea level and the more than 800 m-thick sedimentary rocks over the top of the crystalline basement. The sea level could have varied during the Saalian and Weichselian glacial periods but no regional-scale data on the palaeo-position of shorelines within the study area are available. Consequently, the modelled heat flux near the coastline within the areas with shallow bathymetry still remain uncertain within the uppermost levels of the 3-D thermal model. Fig. 17(c) shows the modelled heat flux without the influence of the Saalian and Weichselian glaciations, indicating that the heat flux is relatively high over the entire mainland. This increased heat flux is mainly caused by the thickened crystalline crust beneath the mainland (Fig. 9b) which acts as an additional heat source due to its increased content of radiogenic elements. Compared to the Møre and Vøring Basins, the presence of a thicker crystalline crust easily explains the high heat flux (around 55–60 mW m−2) modelled beneath the Trøndelag Platform, and is in agreement with the results of Pascal (2015) who reached the same conclusion based on independent heat-flux calculations. The heat flux is relatively low within the eastern parts of the Vøring and Møre basins, being in the range 42–50 mW m−2. The crystalline crust is quite thin beneath almost the entire Vøring and Møre basins but the northwestern part of the model area is characterised by an increased heat flux. This is the result of proximity of the oceanic domain where both the Moho and the lithosphere-asthenosphere boundary are uplifted (Figs 3b and 9b). The increased modelled heat flux is particularly pronounced in the northwestern part of the Møre Basin, showing values higher than 70 mW m−2 (Figs 17b and c). The modelled heat flux at the seafloor offshore and at the Earth's surface onshore is shown in Fig. 18. Here, additional heat to the modelled heat flux at the top basement within the basin areas is produced internally by the sedimentary infill as a result of decay of the contained radiogenic isotopes. In contrast, the heat fluxes modelled separately at the top-model and top-basement levels are similar within the mainland due to the fact that these two levels coincide onshore where the crystalline basement is directly exposed at the Earth's surface. Similar to the top of the crystalline basement (Figs 17b and c), the highest values of the heat flux (more than 75 mW m−2) are modelled within the northwestern part of the Møre Basin (Figs 18a and b). The rest of the Mid-Norwegian margin is characterised by the high heat flux (60–65 mW m−2) within the Trøndelag Platform and the Frøya High. Lower values (46–55 mW m−2) are modelled within the eastern parts of the Vøring and Møre basins. Figure 18. View largeDownload slide Modelled heat flux at the top of the 3-D model represented by the seafloor offshore and the Earth's surface onshore: (a) with the thermal influence of the Saalian and Weichselian glaciations and (b) without the influence of those glaciations. FH, Frøya High; JMC, Jan Mayen Corridor; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. Figure 18. View largeDownload slide Modelled heat flux at the top of the 3-D model represented by the seafloor offshore and the Earth's surface onshore: (a) with the thermal influence of the Saalian and Weichselian glaciations and (b) without the influence of those glaciations. FH, Frøya High; JMC, Jan Mayen Corridor; MB, Møre Basin; TP, Trøndelag Platform; VB, Vøring Basin. Comparison of our results with previous marine heat-flux measurements (Sundvor et al.1989, 2000; Ritter et al.2004) demonstrates both quantitative coincidences and mismatches. However, clear qualitative correlation between the modelled and measured heat fluxes is not obvious and a direct comparison of our model with these two data sets (Sundvor et al.1989; Ritter et al.2004) is difficult. This is mainly due to the fact that the near-surface heat flux can change quite drastically (up to 200 per cent) over short distances if local disturbances (e.g. fluid flow) is present. However such local effects cannot be properly reproduced by our regional-scale 3-D thermal modelling. Comparison with heat flux derived from exploration boreholes (Pascal & Midttømme 2006; Pascal 2015) demonstrates that there is a relatively good qualitative agreement between the modelled and the borehole-based heat fluxes. Strong variation of the heat flux is, however, determined between closely located boreholes (e.g. 59 and 71 mW m−2) but cannot be modelled in detail if we consider the resolution of our 3-D model. Quantitatively, there is a ±5 mW m−2 deviation on average between the modelled and previous borehole-based heat fluxes (Pascal & Midttømme 2006; Pascal 2015). with both almost perfect coincidence and larger misfit locally, indicating again a possible disturbance by the fluid flow or not high enough resolution of our model. The gridded heat flux data (Slagstad et al.2009; Pascal 2015) also show a good correlation with our results, indicating that the increased heat flux over the Frøya High and the decreased values recorded observed in the eastern parts of the Vøring and Møre basins show some clear quantitative dissimilarities. In order to illustrate a cross-sectional view of the modelled subsurface temperatures, three selected 2-D vertical slices (Fig. 19) have been extracted from the 3-D thermal model (Fig. 13b). The locations of these cross-sections are the same as those extracted through the 3-D density and magnetic models (Maystrenko et al., 2018). The interesting feature along the vertical slices 1 and 3 is that an uplift of the modelled isotherms does not always correlate with the shallow position of the Moho (Fig. 19). This is due to the relatively shallow palaeo- and present-day positions of the lower thermal boundary at the base of the lithosphere within the western part of the model area. This means that the long-wavelength component of the deep heat from the Earth's interior, controlled by the geometry of the lithosphere-asthenosphere boundary, prevails over the thermal disturbance related to the Moho topography. For instance, the subhorizontal calculated isotherms are intersected by a sharp deepening of the Moho within the eastern part of line 2 (Fig. 19). The large-scale and deep thermal pattern is disturbed mainly in places where significant contrasts occur in the thermal properties of the upper mantle material, crystalline crustal rocks and/or sedimentary rocks. For example, the modelled isotherms mainly follow the depth position of the Moho along the western parts of the vertical slice 2. There, the uplift of the modelled temperatures within the crust spatially coincides with the areas where the Moho is shallow and the sedimentary rocks are thickest. Consequently, a superposition of the chimney effect of the high thermally conductive upper mantle material in the areas with the uplifted Moho and thermal blanketing of the low thermally conductive thick sedimentary infill results in an increase of the modelled temperatures within the crystalline crust. Figure 19. View largeDownload slide Subsurface modelled temperatures along three selected 2-D vertical slices through the detailed 3-D thermal model (for the location of these slices, see Fig. 2). The vertical exaggeration is 3.3 times. TB, top basement. Figure 19. View largeDownload slide Subsurface modelled temperatures along three selected 2-D vertical slices through the detailed 3-D thermal model (for the location of these slices, see Fig. 2). The vertical exaggeration is 3.3 times. TB, top basement. 5.2 Modelled temperature versus measured temperature The variations of the modelled temperatures within the uppermost part of the 3-D thermal/structural model have been compared with measured temperatures in available boreholes. The locations of all accessible boreholes with the measured temperatures are shown in Fig. 20. Locations of the boreholes only showing drill-stem test (DST) temperatures offshore, and temperatures from well loggings onshore, are shown in Fig. 20(a). The positions of the boreholes having less reliable offshore bottom-hole temperatures (BHT) in addition to the previous boreholes are shown in Fig. 20(b). BHT were measured near the bottom of the boreholes either during drilling or shortly after the drilling process was finished. Consequently, these temperature estimations often contain an element of thermal disturbance due to circulation of the drilling fluid and are not fully reliable. On the contrary, DST values represent the temperature of fluids in thermal equilibrium with the surrounding sedimentary rocks. The measured temperatures from well logs onshore are generally obtained after reaching the thermal equilibrium in the boreholes and are generally more reliable. Nevertheless, due to a shortage of DST data within the Mid-Norwegian continental margin (Fig. 20a), the BHT have also been chosen to compare the modelled temperatures with the measured ones (Figs 20 and 21, Tables 6 and 7). Furthermore, a comparison between the obtained results and the recorded measurements has been provided separately for the boreholes which are located inside (Figs 20a and b) and outside (Figs 20c and d) the detailed model area. Figure 20. View largeDownload slide Locations of the available boreholes with the measured temperatures and spatial distribution of the temperature variations (measured temperature minus the modelled one) within the whole study area. (a) Boreholes with reliable drill-stem test (DST) temperatures offshore and temperature logs onshore. (b) Boreholes with less reliable bottom-hole temperatures (BHT) combined with the DST temperatures. Figure 20. View largeDownload slide Locations of the available boreholes with the measured temperatures and spatial distribution of the temperature variations (measured temperature minus the modelled one) within the whole study area. (a) Boreholes with reliable drill-stem test (DST) temperatures offshore and temperature logs onshore. (b) Boreholes with less reliable bottom-hole temperatures (BHT) combined with the DST temperatures. Figure 21. View largeDownload slide Misfit between the calculated (blue dots) and the observed (red dots) temperatures for the boreholes which are located inside of the detailed model area (a,b) and the boreholes which are located inside and outside of the detailed model area (c,d). (a,c) Only boreholes with DST (drill-stem test) temperatures are used. (b,d) Boreholes with less reliable bottom-hole temperatures (BHT) are also included in addition to the boreholes with DST temperatures. Figure 21. View largeDownload slide Misfit between the calculated (blue dots) and the observed (red dots) temperatures for the boreholes which are located inside of the detailed model area (a,b) and the boreholes which are located inside and outside of the detailed model area (c,d). (a,c) Only boreholes with DST (drill-stem test) temperatures are used. (b,d) Boreholes with less reliable bottom-hole temperatures (BHT) are also included in addition to the boreholes with DST temperatures. Table 6. Difference between modelled temperatures and measured ones (measured values minus the modelled ones) from different boreholes located inside the detailed 3-D model area. Only the DST (drill-stem test) temperatures are used. N  Temperature range of differences between modelled and measured temperatures  Percentage of values (%)  Number of values  1  from −25 to −20  3.1  4  2  from −20 to −10  10.0  13  3  from −10 to −5  20.0  26  4  from −5 to 5  49.2  64  5  from 5 to 10  12.3  16  6  from 10 to 20  5.4  7  N  Temperature range of differences between modelled and measured temperatures  Percentage of values (%)  Number of values  1  from −25 to −20  3.1  4  2  from −20 to −10  10.0  13  3  from −10 to −5  20.0  26  4  from −5 to 5  49.2  64  5  from 5 to 10  12.3  16  6  from 10 to 20  5.4  7  View Large Table 7. Difference between modelled temperatures and measured ones (measured values minus the modelled ones) in available deep boreholes located inside the detailed 3-D model area. In addition to the DST (drill-stem test) temperatures, the less reliable bottom-hole temperatures (BHT) are also included. N  Temperature range of differences between modelled and measured temperatures  Percentage of values (%)  Number of values  1  from −35 to −25  1.3  5  2  from −25 to −20  2.1  8  3  from −20 to −10  10.9  42  4  from −10 to −5  16.3  63  5  from −5 to 5  47.4  183  6  from 5 to 10  11.4  44  7  from 10 to 20  9.8  38  8  from 20 to 25  0.2  1  9  from 25 to 40  0.5  2  N  Temperature range of differences between modelled and measured temperatures  Percentage of values (%)  Number of values  1  from −35 to −25  1.3  5  2  from −25 to −20  2.1  8  3  from −20 to −10  10.9  42  4  from −10 to −5  16.3  63  5  from −5 to 5  47.4  183  6  from 5 to 10  11.4  44  7  from 10 to 20  9.8  38  8  from 20 to 25  0.2  1  9  from 25 to 40  0.5  2  View Large The results of the 3-D conductive thermal modelling are in a reasonable agreement with the general trends of the measured temperatures at the present day (Fig. 21). In spite of a good general fit, some large misfits can be recognised in Fig. 21. In order to understand the magnitude of these large misfits, a more detailed analysis has been performed by plotting the difference between the measured and modelled temperatures (the measured temperatures minus the modelled ones) in map view (Fig. 20). From the maps in Fig. 20, it is obvious that most of the misfits between the modelled and measured temperatures are in the range of ±10 °C. The misfits are separately shown for only the DST temperatures in Table 6 and, in addition to the DST temperatures, the less reliable BHTs are also included in Table 7. Boreholes used for Tables 6 and 7 are located inside the detailed model area. When the boreholes are located inside the detailed 3-D model area, around 82 per cent of the misfits are in the range of ±10 °C, if the boreholes with only the DST are considered (Table 6). The misfits with a range of ±10 °C are slightly lower at around 75 per cent (Table 7), if the BHT are also considered. The large differences remaining in the range of ±10 °C implies that thermal conduction was most likely the dominant mechanism of heat transfer at the scale of the Mid-Norwegian continental margin. According to Fig. 20 and Tables 6 and 7, misfits higher than ±10 °C between the modelled and measured temperatures are also recorded. Some of the misfits are even greater than ±20 °C and can reach up to 40 °C locally. The spatial distribution of these larger differences demonstrates that the boreholes with large misfits are closely located to the boreholes where the misfits are suitable for this kind of regional-scale study (Fig. 20). In some places, the distance between the boreholes showing different misfit values is comparable to the horizontal resolution of the 3-D structural model. For that reason, any tendency to reduce the misfit on a specific borehole will automatically increase the misfit in the neighbouring one and vice versa. Moreover, local structural features of the Mid-Norwegian continental margin could not be resolved without sufficient details of the complete lithological section of each particular borehole. Therefore, the measured temperatures cannot always be fully reproduced by a purely conductive 3-D thermal modelling approach. Some or even most of the large misfits are probably associated with local convective or advective heat transfer phenomena in areas where geothermally heated or cooled fluids circulate through the sedimentary succession. This is particularly the case in the outer Vøring Basin where fluids passing through old fault or local fluid migration pathways initially triggered by Eocene sill intrusions and vents (Svensen et al.2004; Planke et al.2005) can be recognised on seismic data. Fluid-related thermal disturbance is most likely responsible for the large misfits in the external boreholes which are located in the vicinity of the northwestern corner of the detailed model area (see the area outlined by the red dashed line in Fig. 20b). There, the relatively large residual discrepancies between the modelled and measured temperatures are still present in the boreholes located within the western part of the Vøring Basin. These residual misfits are especially large in boreholes 6603/5-1S and 6603/12-1, reaching around 27 °C there. In other boreholes (6604/2-1, 6604/10-1, 6605/1-1 and 6705/10-1), the residual misfits are in the range of 14–23 °C. The misfits are called residual because they were almost two times larger in the 3-D thermal models without taking into account the thermal influence of the early Cenozoic continental breakup. The difference in temperature between the thermal models with and without taking into account the influence of the strongly uplifted isotherms during the continental breakup is mostly restricted to the northwestern side of the detailed model area. There, the residue of the breakup-related heating is still recognisable. This difference is more than 50 °C at the top of the crystalline basement and reaches more than 70 °C at the level of the Moho. Assuming reasonable thermal properties, these differences, highlighted by the red dashed ellipsoid in Fig. 20(b), cannot be explained by purely conductive heat transfer. For example, the measured temperature in well 6603/12-1 is already 139 °C at only 2335.5 m of the true vertical depth below the seafloor (depth below sea level is 3736.5 m), assuming a linear geothermal gradient from the sea bottom of 60 °C km-1, which is the highest value in the case of the Norwegian exploration boreholes (NPD, 2014). In well 6603/5-1 S, the estimated temperature is 190 ± 5 °C at a depth below sea level of 5254 m. These temperatures are bottom-hole temperatures (BHT) and, therefore, can differ from the equilibrium temperatures. However, from a theoretical point of view, these temperatures can be even higher rather than lower, if the equilibrium temperatures is reached after stopping circulation of the drilling fluid. Only one suitable fit between the modelled and the measured temperature is recognised in the scientific borehole ODP Site 644 (Eldholm et al.1987). The temperature here is around 5 °C in this borehole at only slightly more than 200 m below the seafloor. However, the temperature in this well is not stable and represents a shallow temperature compared to the temperatures measured in deeper exploration boreholes. Another borehole from the ocean drilling program (ODP Site 642) is located on the Vøring Plateau which is outside the area of the large-scale 3-D structural model, but this borehole is interesting in terms of the fluid inflow. In this borehole, a positive temperature deviation at a depth of around 500 m below the seafloor may indicate a significant fluid inflow which is also supported by the other well log data sets (Channell et al.2005). A similar situation is also expected for the outer boreholes located near the northwestern corner of the detailed model area. Here, the origin of the fluid flow can differ from the ODP Site 642 due to the greater depth and different structural domain. For instance, hydrothermal activities have been reported at the Gjallar Ridge (e.g. Planke et al.2005; Njone 2014) and indicate that the presence of hydrothermal vent and sill complexes together with accompanying faults could create favourable conditions for local convective heat transfer driven by fluid flow within the northwestern part of the Vøring Basin. 5.3 Uncertainties of the results The modelled temperatures are particularly sensitive to the geometry of the layers and modifications of their thermal properties in general. It is more significant where strong contrasts in thermal properties exist, for example at top-basement, Moho or lithosphere-asthenosphere boundary levels. The inherent limitations of the 3-D thermal modelling have to be considered but have already been reduced by use of additional constraints from new boreholes, sample measurements and relatively reliable structural data. The top of the crystalline basement and depth position of the Moho are also up-to-date and relatively well constrained by a dense coverage of deep seismic data present over large parts of the modelled area (Maystrenko et al., 2018). Some uncertainties with the top of the crystalline basement depth may, however, exist within the deeper parts of the Vøring and Møre basins where the deeply located sedimentary rocks are highly compacted. At some point, the density/velocity contrast between the sedimentary cover and the crystalline rocks could be extremely low, thus enhancing the uncertainties in determining the depth to the top of the crystalline basement (Maystrenko et al., 2018). Furthermore, further uncertainties remain about the location and significance of the lithospheric-asthenospheric boundary, which is a research project in itself. Seismic methods cannot unambiguously discriminate between temperature and compositional variations within the upper mantle (e.g. Kolstrup et al.2012). The thermal influence of the probable uncertainties in the depth of the lithosphere-asthenosphere boundary have been examined by Maystrenko et al. (2014) who have examined two possible cases with ± 20 km depth to the base of the lithosphere in relation to the preferred lower thermal boundary at around 120 km depth. The obtained thermal effect on the deviations of the modelled temperature at 6 km depth is ∼4 per cent for the 20 km deeper base of the lithosphere and ∼12 per cent for the 20 km shallower one. This indicates that an influence of the lower thermal boundary at the shallower depths is non-negligible when the distance between the lower and upper boundaries becomes smaller. The predominance of the conductive heat transfer within the study area is valid only if the lateral changes in the radiogenic heat production of the crystalline rocks (Fig. 10) are present in reality. The presence of crustal blocks with different radiogenic heat production is mainly supported by the results of the 3-D magnetic modelling carried out in the same study area (Maystrenko et al., 2018). Based on the onshore distribution of the radiogenic heat production within the crystalline rocks, Slagstad (2008) has shown that there is a direct relationship between the extent of different units on the geological map (e.g. Sigmond 2002) and the average heat production on the mainland. Consequently, the inferred crustal blocks with different radiogenic heat in Fig. 10 can be considered as representatives of the geological subdivision of the crystalline crust proposed to exist beneath the sedimentary basins offshore. However, some of the inferred crustal blocks are rather hypothetical. We cannot exclude an alternative explanation for the observed thermal pattern within the drilled sedimentary cover that could involve fluid circulation through sedimentary rocks and/or crystalline crust. In this case, some of the crustal blocks offshore showing an increased radiogenic heat production could indicate the presence of heated fluids. Conversely, the inferred blocks with the reduced radiogenic heat can outline areas where advective cooling could possibly be superimposed on the conductive heat transfer. Furthermore, the limited information about the thermal conductivity of rocks within the deep part of the 3-D model implies that the used values (Table 5) can vary within a reasonable range and, therefore, the modelled temperature can slightly deviate (Figs 14–19). However, the relative correctness of the thermal properties used in our study is supported by a good correlation between the calculated and the measured temperatures in most of the available boreholes (Figs 20 and 21). A comparative analysis of the 3-D thermal modelling results with the borehole measurements indicates that there are also some large inherent misfits which cannot be explained solely by a purely conductive heat transfer system. Further tests or improvements can be achieved in the future by increasing the horizontal resolution and the number of lithologically differentiated layers of the 3-D structural model. Future modelling may also involve more complex simulations of fully coupled fluid flow and heat transfer in 3-D including a more detailed scenario for the continental breakup. At that stage, the influence of hypothetical and complex fluid flow(s) cannot be correctly established without more detailed hydrogeological, lithological and structural constraints within the regional framework of the present study. Finally, the near-surface thermal effect of the post-Palaeocene deposition has been roughly included but the effect of the simultaneous erosion over the mainland has not been properly considered. To include this effect into the modelling workflow, additional data would be required to constrain the erosional rate in time and space. The uplift and subsequent erosion could lead to an uplift of isotherms within the upper crust, causing a positive temporal thermal anomaly beneath the areas where the erosion took place. Theoretically, the magnitude of this positive anomaly should not be higher than 25 °C on average. Furthermore, the impact of palaeo- and present-day groundwater flow might significantly smooth the magnitude of the thermal anomaly due to erosion (e.g. Maystrenko et al.2015a). In particular, the thermal influence of the erosion could be significantly reduced by the possible groundwater flow active during the melting of the Quaternary ice sheets. Therefore, these two thermal effects and their opposed interaction have to be considered together. Once more, a fully coupled fluid flow and heat transfer modelling will be required to include all processes that control the subsurface temperature distribution within the study area. Finally, the results of the modelling are also limited by the model resolution and computing facilities. 6 CONCLUSIONS The 3-D conductive thermal field within the Mid-Norwegian continental margin and the adjacent areas of the mainland has been deduced from a pre-existing 3-D density/magnetic structural model. The new model considers all available data about the measured temperatures and thermal properties. In general, the results of the 3-D thermal modelling help us to further understand the main characteristics of the 3-D conductive thermal field within the Mid-Norwegian continental margin and adjacent areas. The thermal results can be used to better estimate the maturation of organic matter, reservoir quality and, therefore, to make progress in regional strategies for hydrocarbon exploration within the Trøndelag Platform and Vøring and Møre basins, as well as to evaluate the geothermal potential on the mainland. A clear zone of increased radiogenic heat production is easily traceable through the Cretaceous and Cenozoic stratigraphic intervals, implying a possible source-to-sink inheritance scenario for the eroded clastic material. The radiogenic pattern of the sedimentary rocks may indicate a differentiation and sorting of the eroded clastics by grain size during their transportation. A comparison between modelled temperatures and the measured ones in the boreholes indicates that there is a good correlation between the measurements and our simulations. However, a purely conductive thermal field within the Mid-Norwegian continental margin is most likely disturbed locally by fluid flow (convection and/or advection). This is most likely the case in the distal part of the margin where large and atypical residual misfits between the measured and the modelled temperatures are recorded in some of the boreholes. Based on a simple palaeo-scenario for the continental breakup, the modelling results indicate that the thermal influence of the lithospheric rupture in the early Cenozoic is still persistent within the western part of the model area. Further improvements of the results can be achieved by increasing the resolution of the 3-D structural model and by involving simulations of fully coupled fluid flow and heat transfer. A better constrained palaeo-scenario for the continental breakup and the post-break relationship between erosion onshore and sedimentation offshore may also contribute to an improvement in the results. ACKNOWLEDGEMENTS The authors would like to acknowledge comprehensive support of this regional-scale investigation from Aker BP, BayernGas, BKK, Centrica Energi, ConocoPhillips, Dea, DONG, Engie, Eni, E.ON, Lundin, Maersk, NGU, Noreco, NPD, Repsol, Statoil, Suncor, Total, VNG, and Wintershall in the framework of ‘Crustal Onshore-Offshore Project, Phase 2’. We are grateful to Odleiv Olesen for coordination of this project and for very fruitful discussions. Special thanks go to the Marine Geology group at the Geological Survey of Norway (personally to Leif Rise) for providing us with the most recent data on post-Palaeocene sedimentary layers. We would also like to thank Mauro Cacace from the Helmholtz Centre Potsdam, GFZ German Research Centre for Geosciences for his help with the code for creating complex 3-D mesh. Christophe Pascal and an anonymous reviewer are thanked for their very useful comments which helped us to improve our manuscript. 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All for just $49/month ### Explore the DeepDyve Library ### Unlimited reading Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere. ### Stay up to date Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates. ### Organize your research It’s easy to organize your research with our built-in tools. ### Your journals are on DeepDyve Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more. All the latest content is available, no embargo periods. ### Monthly Plan • Read unlimited articles • Personalized recommendations • No expiration • Print 20 pages per month • 20% off on PDF purchases • Organize your research • Get updates on your journals and topic searches$49/month

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