TY - JOUR
AU - Rise, Leif
AB - Summary A 3-D subsurface temperature distribution within the Lofoten–Vesterålen segment of the Mid-Norwegian continental margin and adjacent areas has been studied to understand the thermal effect of late Cenozoic erosion of old sedimentary and crystalline rocks and subsequent deposition of glacial sediments during the Pleistocene. A lithosphere-scale 3-D structural model of the Lofoten–Vesterålen area has been used as a realistic approximation of the geometries of the sedimentary infill, underlying crystalline crust and lithospheric mantle during the 3-D thermal modelling. The influence of late Cenozoic erosion and sedimentation has been included during the 3-D thermal calculations. In addition, the 3-D thermal modelling has been carried out by taking also into account the influence of early Cenozoic continental breakup. The results of the 3-D thermal modelling demonstrate that the mainland is generally colder than the basin areas within the upper part of the 3-D model. The thermal influence of the early Cenozoic breakup is still clearly recognizable within the western and deep parts of the Lofoten–Vesterålen margin segment in terms of the increased temperatures. The thermal effects of the erosion and deposition within the study area also indicate that a positive thermal anomaly exists within the specific subareas where sedimentary and crystalline rocks were eroded. A negative thermal effect occurs in the subareas affected by subsidence and sedimentation. The erosion-related positive thermal anomaly reaches its maximum of more than +27 °C at depths of 17–22 km beneath the eastern part of the Vestfjorden Basin. The most pronounced deposition-related negative anomaly shows a minimum of around −70 °C at 17–20 km depth beneath the Lofoten Basin. The second negative anomaly is located within the northeastern part of the Vøring Basin and has minimal values of around −48 °C at 12–14 km depth. These prominent thermal anomalies are associated with the subareas where relatively high erosional and depositional rates were observed for late Cenozoic time. Heat flow, Atlantic Ocean, Europe, Numerical modelling, Continental margins: divergent, Neotectonics, Sedimentary basin processes 1 INTRODUCTION The Lofoten–Vesterålen margin represents an uplifted segment in the northeastern part of the Mid-Norwegian continental margin, covering the area around the Lofoten–Vesterålen archipelago (Fig. 1). The Mid-Norwegian continental margin is a rifted passive margin where a continental breakup took place in the early Cenozoic about 55 Ma ago (e.g. Talwani & Eldholm 1977; Srivastava & Tapscott 1986; Brekke 2000; Olesen et al.2007; Faleide et al.2008; Gernigon et al.2015). Figure 1. View largeDownload slide Overview map of northwestern Europe (bathymetry and topography from the Norwegian Mapping Authority) with location of the lithosphere-scale 3-D structural/thermal model of the Lofoten–Vesterålen margin segment and adjacent areas (blue frame). Figure 1. View largeDownload slide Overview map of northwestern Europe (bathymetry and topography from the Norwegian Mapping Authority) with location of the lithosphere-scale 3-D structural/thermal model of the Lofoten–Vesterålen margin segment and adjacent areas (blue frame). During the last decades, the tectonic evolution and structure of the Lofoten–Vesterålen segment and adjacent areas have been thoroughly studied by both geological and geophysical methods, including geological mapping (e.g. Sigmond 2002), drilling of wells (Olesen et al.2007b, NPD 2017), interpretation of reflection seismic data (Mokhtari & Pegrum 1992; Bergh et al.2007; Eidvin et al.2007; Ottesen et al.2009; Hansen et al.2012; Rise et al.2013; Henstra et al.2017; Montelli et al.2017) and refraction seismic data analysis (Avedik et al.1984; Drivenes et al.1984; Goldschmidt-Rokita et al.1988; Mjelde et al.1992; Kodaira et al.1995; Mjelde et al.1996; Mjelde et al.2001; Mjelde et al.2003; Mjelde et al.1995; Breivik et al.2009; Breivik et al.2017). In addition, 2-D and 3-D potential field modelling helped further to understand the deep structure of this region (e.g. Fichler et al.1999; Olesen et al.2002; Tsikalas et al.2005; Brönner et al.2013; Gradmann & Ebbing 2015; Maystrenko et al.2017). The study area is characterized by a prominent contrasting relief, changing at a relatively short distance from elevations higher than 1.5 km within the Scandes Mountains onshore to bathymetries deeper than −3 km within the oceanic Lofoten Basin offshore (Fig. 2). In addition to this contrasting relief, the crystalline rocks are exposed on the Earth's surface over most of the mainland (e.g. Sigmond 2002). The preserved sedimentary rocks are mainly represented by the relatively thin Jurassic and Cretaceous sequences in the northeastern part of the Andøya island (Dalland 1975; Smelror et al.2001). The crystalline rocks also crop out at the seafloor within the structural highs and near the coastline (Sigmond 2002). Moreover, the Nordland area is characterized by increased seismicity and neotectonic activities (Keiding et al.2015; Janutyte et al.2017). The above-mentioned direct indications of neotectonics together with the additional neotectonic features have been summarized by Olesen et al. (2013a, 2004) for this structurally complex area. Figure 2. View largeDownload slide Tectonic configuration within the Lofoten–Vesterålen and the northern Vøring segments of the Mid-Norwegian continental margin, superimposed on the bathymetry and topography, with location of the 3-D structural/thermal model (based on Blystad et al.1995; Sigmond 2002; Hansen 2009; Hansen et al.2012) (bathymetry and topography from the Norwegian Mapping Authority). Thick magenta lines correspond to the selected vertical slices, shown in Fig. 23. Black dashed line corresponds to the present-day shelf edge. COB, the continent-ocean boundary; LV/LDM, low-velocity/low-density mantle. Figure 2. View largeDownload slide Tectonic configuration within the Lofoten–Vesterålen and the northern Vøring segments of the Mid-Norwegian continental margin, superimposed on the bathymetry and topography, with location of the 3-D structural/thermal model (based on Blystad et al.1995; Sigmond 2002; Hansen 2009; Hansen et al.2012) (bathymetry and topography from the Norwegian Mapping Authority). Thick magenta lines correspond to the selected vertical slices, shown in Fig. 23. Black dashed line corresponds to the present-day shelf edge. COB, the continent-ocean boundary; LV/LDM, low-velocity/low-density mantle. In this study, the main goal has been to model and reveal the 3-D conductive thermal pattern beneath the Lofoten–Vesterålen margin, the adjacent parts of the mainland and the adjacent Atlantic Ocean. In particular, our study has been performed to recognize the temporal changes of the subsurface 3-D thermal pattern during the late Cenozoic uplift and erosion of the mainland and the northeastern part of the Lofoten–Vesterålen margin segment, and the rapid deposition of the eroded material within the southwestern part of the Lofoten–Vesterålen margin and the adjacent northeastern part of the Vøring Basin. The lithosphere-scale 3-D structural model of the Lofoten–Vesterålen segment of the Mid-Norwegian margin from Maystrenko et al. (2017) has been taken as the main structural background for the 3-D thermal modelling. This 3-D structural model represents the most recent structural approximation of the deep subsurface, covering the major tectonic units of the Lofoten–Vesterålen area and the northeastern part of the Vøring Basin (Fig. 2). 2 TECTONIC OVERVIEW AND PREVIOUS WORK The Lofoten–Vesterålen continental margin and the adjacent mainland had already undergone significant uplift and erosion during the Scandian phase of the Caledonian Orogeny in Silurian-Early Devonian time (Roberts & Gee 1985) when large-scale overthrusting and subsequent uplift were caused by amalgamation of several terranes to the Baltican protomargin. During the Devonian, the Caledonian Orogen collapsed as a result of a regional extension (Braathen et al.2002; Steltenpohl et al.2004; Fossen 2010). During the Late Palaeozoic–Mesozoic, several extensional events led to the formation of Permian, Triassic and Jurassic subbasins within the Trøndelag Platform (e.g. Blystad et al.1995; Brekke 2000), the Jurassic–Cretaceous depocentres within the Ribban and Vestfjorden basins, and possibly including the Røst Basin where sedimentary rocks are overlain by lava flows (Tsikalas et al.2001; Hansen et al.2012; Færseth 2012; Eig 2012; Henstra et al.2017). During the Late Jurassic–Cretaceous, a large tectonic and thermal subsidence affected the adjacent Vøring Basin (e.g. Gernigon et al.2004; Lien 2005; Mjelde et al.2016). The continental break-up finally split the Laurasia palaeocontinent in the late Palaeocene-early Eocene and the present-day Mid-Norwegian continental margin and the oceanic Lofoten Basin started to form (Talwani & Eldholm 1977). During the Cenozoic, the Lofoten–Vesterålen segment of the Mid-Norwegian continental margin has undergone an uplift which was followed by erosion and/or non-deposition over a large part of the Lofoten–Vesterålen margin (e.g. Løseth & Tveten 1996; Riis 1996; Færseth 2012). The most recent erosion occurred during the Quaternary glacial periods when preserved sedimentary rocks and part of the existing weathered crystalline rocks were removed by glacial erosion, forming the typical present-day Norwegian coastal landscape, the so-called strandflat (Olesen et al.2013a,b, Holtedahl 1998). The strandflat is particularly well developed south of the Lofoten margin, along the coast of Helgeland (Olesen et al.2013a, Holtedahl 1998). The eroded material was deposited farther offshore, creating significant depocentres of the glacier-derived Naust Formation during Pleistocene times (e.g. Rise et al.2005; Dowdeswell et al.2010, Dowdeswell et al.2006; Ottesen et al.2009; Montelli et al.2017). Moreover, elevated passive continental margins have also been well documented in other places of the world (e.g. Greenland, NE Brazil, South Africa) but, as in the case of the Mid-Norwegian margin, there is still no common geodynamic model that can fully explain their origin (e.g. Green et al.2017). The origin and nature of the late Cenozoic uplift are still a matter of debate and obviously resulted from the superposition of several factors (Løseth & Tveten 1996; Riis 1996; Færseth 2012; Fjeldskaar et al.2000). Four major phases of the Cenozoic uplift in the Palaeogene, Middle Miocene, late Pliocene and Pleistocene have been identified by Riis (1996). The Palaeogene uplift was interpreted as a marginal uplift related to the opening of the North Atlantic Ocean and the late Pliocene event was considered to be due to unloading (Riis 1996). On the other hand, the causes of the Middle Miocene and Pleistocene phases remain unknown. Riis & Fjeldskaar (1992) have shown that the postglacial uplift is not totally isostatically compensated and Fjeldskaar et al. (2000) have proposed that this uplift has also a tectonic origin. Furthermore, the ridge-push forces associated with Cenozoic seafloor spreading in the North Atlantic Ocean have also been proposed as a primary explanation for the Fennoscandian uplift (e.g. Fejerskov & Lindholm 2000). In spite of many uncertainties about the causes of these Cenozoic uplift events, the magnitude of the uplift at different time intervals and the amount of the eroded material have been approximately quantified by use of different methods. Based on apatite fission track and (U–Th)/He analyses, the post-Caledonian denudation history of western Fennoscandia is characterized by clearly defined and relatively high cooling rates throughout the whole Cenozoic era (Hendriks & Andriessen 2002; Hendriks et al.2010; Davids et al.2013; Ksienzyk et al.2014). Particularly, the present-day exposed Earth's surface in Lofoten and Vesterålen could be characterized by relatively high palaeotemperatures at the beginning of the Cenozoic, ranging from 30 to 90 °C and recorded at different locations (Hendriks et al.2010). Hendriks et al. (2010) indicate a differential uplift of the Lofoten–Vesterålen area with magnitude variations from 1 to more than 3 km locally during the Cenozoic. Furthermore, based on the study of the weathered crystalline crust, Olesen et al. (2013a, b) have suggested that the Pleistocene erosion was about 500 m along the coastline in the Nordland area. In SW Norway, Steer et al. (2012) have proposed that significant erosion must have also taken place in close vicinity to present-day high elevation during the late Pliocene and Quaternary glaciations. However, they did not consider the erosion within the inner shelf. Based on the volume of the Pleistocene Naust Formation off mid Norway, Dowdeswell et al. (2010) suggested a similar amount of average glacial erosion over the mainland and inner shelf. The estimated thickness of the restored matrix of the Cenozoic deposits in the close vicinity of the highly elevated Scandes Mountains within the study area could possibly reach more than 3 km as modelled by Goledowski et al. (2013). The amount of fluvial and glacial erosion, predicted by the erosional model of Medvedev & Hartz (2015), suggests that it should not be more than 1.5 km over the area located near the high-altitude Scandes Mountains in the study area and should only reach c. 1.75 km locally within some fjords. Based on maximum estimated burial depth in offshore wells and wells on Andøya, a total erosion in the Lofoten and Vesterålen region could have reached up to 2 km between Andøya and the mainland (Eig 2012; NPD 2010). Moreover, a possible presence of large-scale boudinage structures beneath Lofoten–Vesterålen could be an additional factor which complicated the post-breakup development of the study area (Braun & Marquart 2004). 3 INPUT STRUCTURAL DATA SETS Bathymetry and topography have been taken from the Norwegian Mapping Authority and the sedimentary infill of the 3-D structural model has already been described in Maystrenko et al. (2017). In this paper, the uppermost sedimentary layers of the Bjørnøya Fan Slide Complex and the Kai–Naust formations (Middle Miocene-Pleistocene interval) have been subdivided into four layers in order to investigate the thermal effect of erosion and deposition during the Pleistocene time interval. Therefore, the detailed sedimentary units for the input 3-D model are represented by the following layers (Figs 3 and 4; numbering is according to Maystrenko et al. (2017)): the Naust Formation (sequences U, S and T) and analogues in the Lofoten Basin (layer 2.1; Pleistocene with an age of c. 0.6–0 Ma); the Naust Formation (sequence A) and analogues in the Lofoten Basin (layer 2.2; Pleistocene with an age of c. 1.5–0.6 Ma); the Naust Formation (sequence N) and analogues in the Lofoten Basin (layer 2.3; lower Pleistocene with an age of c. 2.7–1.5 Ma); the Kai Formation and the Molo Formation (layer 2.4; Middle Miocene–Pliocene with an age of c. 18–2.7 Ma); the Brygge Formation and the undefined Cenozoic (layer 3; mainly Eocene–lower Miocene with an age of c. 56–18 Ma); the Upper Cretaceous–Palaeocene (near top Cenomanian–top Palaeocene) without a sedimentary succession in the Røst Basin (layers 5–6); the Lower Cretaceous (base Cretaceous unconformity-near top Cenomanian) without a sedimentary succession in the Røst Basin (layer 7); the pre-Cretaceous (Jurassic, Triassic, Permian and older sedimentary rocks) without a sedimentary succession in the Røst Basin (layer 8); the undivided pre-Cretaceous, Cretaceous and Palaeocene within the Røst Basin (layers 5–8). Figure 3. View largeDownload slide Thicknesses of the Cenozoic post-breakup sedimentary rocks: (a) the Naust Formation (sequences U, S and T) and analogues (layer 2.1), (b) the Naust Formation (sequence A) and analogues (layer 2.2), (c) the Naust Formation (sequence N) and analogues (layer 2.3), (d) the Kai Formation (layer 2.4) and (e) the Brygge Formation (Eocene-lower Miocene) and the undefined Cenozoic (layer 3) (based on Fiedler & Faleide 1996; Rise et al.2005; Eidvin et al.2007; Hjelstuen et al.2007; Dowdeswell et al.2010, Rise et al.2010; Laberg et al.2012; Ottesen et al.2012). Black dashed line corresponds to the present-day shelf edge. COB, continent-ocean boundary; HG, Hel Graben; NH, Nyk High; NR, Nordland Ridge; NS, Någrind Syncline; TB, Træna Basin; TP, Trøndelag Platform; UH, Utgard High; VB, Vøring Basin. The question marks refer to the areas where the thickness pattern is not well defined. Figure 3. View largeDownload slide Thicknesses of the Cenozoic post-breakup sedimentary rocks: (a) the Naust Formation (sequences U, S and T) and analogues (layer 2.1), (b) the Naust Formation (sequence A) and analogues (layer 2.2), (c) the Naust Formation (sequence N) and analogues (layer 2.3), (d) the Kai Formation (layer 2.4) and (e) the Brygge Formation (Eocene-lower Miocene) and the undefined Cenozoic (layer 3) (based on Fiedler & Faleide 1996; Rise et al.2005; Eidvin et al.2007; Hjelstuen et al.2007; Dowdeswell et al.2010, Rise et al.2010; Laberg et al.2012; Ottesen et al.2012). Black dashed line corresponds to the present-day shelf edge. COB, continent-ocean boundary; HG, Hel Graben; NH, Nyk High; NR, Nordland Ridge; NS, Någrind Syncline; TB, Træna Basin; TP, Trøndelag Platform; UH, Utgard High; VB, Vøring Basin. The question marks refer to the areas where the thickness pattern is not well defined. Figure 4. View largeDownload slide Cumulative thickness of the pre-breakup sedimentary rocks: pre-Cretaceous, Cretaceous and Palaeocene (based on Brekke 2000; Hansen 2009; Maystrenko & Scheck-Wenderoth 2009; Eig 2012; Hansen et al.2012; Maystrenko et al.2017). Black dashed line corresponds to the present-day shelf edge. COB, continent-ocean boundary; HG, Hel Graben; NH, Nyk High; NR, Nordland Ridge; NS, Någrind Syncline; TB, Træna Basin; TP, Trøndelag Platform; UH, Utgard High; VB, Vøring Basin. Figure 4. View largeDownload slide Cumulative thickness of the pre-breakup sedimentary rocks: pre-Cretaceous, Cretaceous and Palaeocene (based on Brekke 2000; Hansen 2009; Maystrenko & Scheck-Wenderoth 2009; Eig 2012; Hansen et al.2012; Maystrenko et al.2017). Black dashed line corresponds to the present-day shelf edge. COB, continent-ocean boundary; HG, Hel Graben; NH, Nyk High; NR, Nordland Ridge; NS, Någrind Syncline; TB, Træna Basin; TP, Trøndelag Platform; UH, Utgard High; VB, Vøring Basin. It is important to note that the Kai–Naust and Brygge formations correspond to the Nordland and Hordaland groups, respectively, and the Palaeocene corresponds to the Rogaland group. The Upper Cretaceous and the Lower Cretaceous do not exactly correlate with the Shetland and Cromer Knoll groups within some local areas (e.g. Dalland et al.1988). The maps for the Brygge–Naust (Eocene–Pleistocene) interval within the Lofoten–Vesterålen and Vøring segments of the Mid-Norwegian continental margin (Fig. 3) have been compiled by using data from Rise et al. (2005), Eidvin et al. (2007), Dowdeswell et al. (2010); Rise et al. (2010) and Ottesen et al. (2012), whereas maps for the post-break-up interval in the Lofoten Basin (Fig. 3) have been derived from Fiedler & Faleide (1996), Hjelstuen et al. (2007) and Laberg et al. (2012). In particular, the mega-slide 2 of the Bjørnøya Fan Slide Complex with an age of c. 0.78–0.5 Ma from Hjelstuen et al. (2007) has been merged with the Naust Formation (U, S and T sequences; c. 0.6–0 Ma) and the mega-slide 1 of the Bjørnøya Fan Slide Complex with an age of c. 1.5–0.78 Ma has been added to the Naust Formation (A sequence; c. 1.5–0.6 Ma). In addition, thicknesses of the fluvio-glacial erosional material with an age of c. 0.7–0, 1.5–07 and 2.7–1.5 Ma from Fiedler & Faleide (1996) and Laberg et al. (2012) have been merged with the Naust Formation (U, S and T sequences; c. 0.6–0 Ma), Naust Formation (A sequence; c. 1.5–0.6 Ma) and Naust Formation (N sequence; c. 2.7–1.5 Ma), respectively. There are small differences in age between the merged successions, but the most important area of our study corresponds to the Mid-Norwegian margin rather than the Lofoten Basin. Therefore, the Naust ages from Dowdeswell et al. (2010) have been assigned to the merged sedimentary layers in Fig. 3. The thickness pattern of the Naust sequences and analogues (Figs 3a–c) is characterized by two distinct zones dominated by mega-slides within the Lofoten Basin and a more complex pattern within the SW Lofoten–Vesterålen margin and NE Vøring Basin. The sedimentary sequences in the Lofoten Basin are mostly represented by eroded sedimentary rocks from the Barents Sea area (Fiedler & Faleide 1996; Hjelstuen et al.2007; Laberg et al.2012). In contrast, the Naust sequences show a more local origin from the adjacent mainland or the northeastern part of the Lofoten–Vesterålen margin (e.g. Dowdeswell et al.2010; Rise et al.2010; Ottesen et al.2012). The thickest part of the Naust Formation corresponds to the sequence N, reaching more than 1600 m (Fig. 3c), and the thickest sedimentary rocks of the Lofoten Basin are analogues to sequence A of the Naust Formation, reaching more than 1300 m (Fig. 3b). Unfortunately, there is no direct information about the analogues of the Kai and Brygge Formations within the Lofoten Basin where the age of the sedimentary sequences still remains uncertain (Figs 3d and e). We have included the undefined Cenozoic sedimentary layers, excluding the Palaeocene, together with the Brygge Formation within the Lofoten Basin and the entire oceanic crustal domain of the study area (Fig. 3e). The Palaeocene, Cretaceous and pre-Cretaceous (Fig. 4) have been taken from Brekke (2000), Hansen (2009), Maystrenko & Scheck-Wenderoth (2009), Hansen et al. (2012), Eig (2012), NGU data (interpreted by Gernigon in 2014) and Maystrenko et al. (2018). Sedimentary rocks within the Røst Basin and the pre-Cretaceous have been described in detail by Maystrenko et al. (2017). The pre-break-up sedimentary rocks in Fig. 4 are thick and are characterized by a broad zone of distribution southwest of the Bivrost Lineament (Fig. 4). On the other hand, the Palaeocene, Cretaceous and pre-Cretaceous are generally thinner northeast of the Bivrost Lineament with relatively thick sequences restricted to the Ribban and Vestfjorden basins. The thickness pattern of the crystalline crust (Fig. 5) is based on the recent 3-D density modelling by Maystrenko et al. (2017) constrained by different geophysical data including (1) deep seismic refraction and reflection lines (Mjelde et al.1992; Mjelde et al.1993; Mjelde et al.2003; Kodaira et al.1995; Mjelde et al.2001; Breivik et al.2009; Hansen et al.2012; Breivik et al.2017), (2) teleseismic receiver function data (Ottemoller & Midzi 2003; Olsson et al.2008; Ben Mansour et al.2014) and (3) additional structural base and isopach maps (Maystrenko & Scheck-Wenderoth 2009; Ebbing & Olesen 2010; Maystrenko et al.2018). Figure 5. View largeDownload slide (a) Thicknesses of the oceanic layer 2AB (layer 4) and (b) cumulative thickness of the crystalline crust according to Maystrenko et al. (2017). COB, continent-ocean boundary; HG, Hel Graben; NH, Nyk High; NR, Nordland Ridge; NS, Någrind Syncline; TB, Træna Basin; TP, Trøndelag Platform; UH, Utgard High; VB, Vøring Basin. Figure 5. View largeDownload slide (a) Thicknesses of the oceanic layer 2AB (layer 4) and (b) cumulative thickness of the crystalline crust according to Maystrenko et al. (2017). COB, continent-ocean boundary; HG, Hel Graben; NH, Nyk High; NR, Nordland Ridge; NS, Någrind Syncline; TB, Træna Basin; TP, Trøndelag Platform; UH, Utgard High; VB, Vøring Basin. The top of the crystalline basement (Fig. 6a) (Maystrenko et al.2017) is divided into two zones by the Bivrost Lineament. The Vøring Basin and the Trøndelag Platform southwest of the lineament show a very deeply located basement (more than 15–17 km deep), whereas the Lofoten–Vesterålen margin has shallower basement depths (8–11 km). To the east, the near-coast shelf has a very shallow basement (less than 1 km deep) which crops out at the Earth's surface within the Lofoten–Vesterålen archipelago and on the mainland. The Moho topography (Fig. 6b) (Maystrenko et al.2017) is deeply located (at around 40 km on average) beneath the mainland, has moderate depths (20–28 km) beneath the continental margin and is shallow (11–14 km depths) within the ocean domain. Figure 6. View largeDownload slide (a) Depth to the top of the crystalline basement, (b) Moho topography and (c) depth to the lithosphere–asthenosphere boundary (the shaded area corresponds to an introduced positive thermal anomaly at the base of the lithosphere). Black dashed line corresponds to the present-day shelf edge. COB, continent-ocean boundary; HG, Hel Graben; LAB, lithosphere–asthenosphere boundary; LV/LDM, low-velocity/low-density mantle; NH, Nyk High; NR, Nordland Ridge; NS, Någrind Syncline; TB, Træna Basin; TP, Trøndelag Platform; UH, Utgard High; VB, Vøring Basin. Figure 6. View largeDownload slide (a) Depth to the top of the crystalline basement, (b) Moho topography and (c) depth to the lithosphere–asthenosphere boundary (the shaded area corresponds to an introduced positive thermal anomaly at the base of the lithosphere). Black dashed line corresponds to the present-day shelf edge. COB, continent-ocean boundary; HG, Hel Graben; LAB, lithosphere–asthenosphere boundary; LV/LDM, low-velocity/low-density mantle; NH, Nyk High; NR, Nordland Ridge; NS, Någrind Syncline; TB, Træna Basin; TP, Trøndelag Platform; UH, Utgard High; VB, Vøring Basin. The lithosphere-asthenosphere boundary (Fig. 6c) beneath the mainland has been derived from Calcagnile (1982), Artemieva et al. (2006) and Ebbing et al. (2012). The depth to the lithosphere-asthenosphere boundary beneath the oceanic domain has been obtained according to empirical relations between lithospheric age (Muller et al.2008) and Love and Rayleigh wave-phase velocity provided by Zhang & Lay (1999). The upper mantle of the Lofoten–Vesterålen margin and the adjacent areas is characterized by the presence of a low-velocity/low-density zone (see thick magenta line in Figs 6b and c) based on seismic tomography (Bannister et al.1991; Pilidou et al.2005; Yakovlev et al.2012; Hejrani et al.2017) and 3-D density modelling (Maystrenko et al.2017). The origin of the low-velocity/low-density mantle can be related to both thermal and compositional variations but is still not known in detail. 4 METHODOLOGY 4.1 Reconstruction of erosion In order to reconstruct the Cenozoic erosion history of the Lofoten–Vesterålen margin, the estimated thickness of the eroded material from NPD (2010) and Eig (2012) has been mainly used. The reconstruction is based on maximum burial depths from wells located offshore and on Andøya, which have been estimated according to the degree of maturation of organic matter in sedimentary rocks (NPD 2010). It can, therefore, be considered as a reasonable estimate of the magnitude of the erosion within the Lofoten–Vesterålen region. The total thickness of the eroded material (Eig 2012; NPD 2010) has been reconstructed only for the offshore part of the study area. The estimates for onshore areas have been calculated by interpolation and/or extrapolation of the existing offshore values. Technically, the Kriging and Minimum Curvature gridding methods have been used for interpolation and extrapolation. In addition, results of the apatite fission track analyses (Hendriks & Andriessen 2002; Hendriks et al.2010; Davids et al.2013) have been considered to control the reconstructed thickness of the eroded rocks onshore in order to avoid unrealistic artefacts due to extrapolation. Besides, the reconstructed thickness onshore has been modified to consider the topography (the positive topography has been subtracted from the extrapolated values), assuming that the present-day relief of the Earth's surface was similar to the palaeotopography of the top basement prior to the erosion. This assumption is supported by the presence of the thin Jurassic-Cretaceous sedimentary rocks in the northeastern part of Andøya island (Dalland 1975; Smelror et al.2001) and by the pre-existence of a deeply weathered Mesozoic surfaces until the present day in Norway (Olesen et al.2013b, Fredin et al. 2017). In this case, the eroded material could be represented mainly by the Cretaceous, Jurassic and older sedimentary rocks, the weathered crystalline rocks, as well as by the Cenozoic sedimentary sequences locally. Comparison of the derived thickness of the reconstructed eroded rocks at the end of the Kai interval (Fig. 7d) with the results of the combined study by Medvedev & Hartz (2015) on the vertical motions caused by the Quaternary glacial erosion, using published results of Apatite Fission Track (AFT) analysis demonstrates, in general, some qualitative and quantitative similarities over the greater part of the mainland. However, some values are slightly different locally. Figure 7. View largeDownload slide Reconstructed thicknesses of the eroded material during the Cenozoic: at the end of the Cretaceous (a), at the end of the Palaeocene (b), at the end of the Brygge (c), at the end of the Kai (d), at the end of the Naust N (e) and at the end of the Naust A (f). Black dashed line corresponds to the present-day shelf edge. COB, continent-ocean boundary; HG, Hel Graben; NH, Nyk High; NR, Nordland Ridge; NS, Någrind Syncline; TB, Træna Basin; TP, Trøndelag Platform; UH, Utgard High; VB, Vøring Basin. Figure 7. View largeDownload slide Reconstructed thicknesses of the eroded material during the Cenozoic: at the end of the Cretaceous (a), at the end of the Palaeocene (b), at the end of the Brygge (c), at the end of the Kai (d), at the end of the Naust N (e) and at the end of the Naust A (f). Black dashed line corresponds to the present-day shelf edge. COB, continent-ocean boundary; HG, Hel Graben; NH, Nyk High; NR, Nordland Ridge; NS, Någrind Syncline; TB, Træna Basin; TP, Trøndelag Platform; UH, Utgard High; VB, Vøring Basin. The reconstructed total thickness of the eroded rocks in Fig. 7(a) can represent the distribution of the eroded material (mainly sedimentary rocks with the partial presence of weathered crystalline rocks) at the end of the Cretaceous prior to the well-known latest Cretaceous–earliest Cenozoic tectonic events (Gernigon et al.2003; Lundin et al.2013; Ren et al.2003; Ren et al.1998). Therefore, this total thickness could still have existed at the end of the Cretaceous, indicating that the Lofoten–Vesterålen archipelago and part of the mainland represented continental shelf at that time. This is supported by the reflection seismic data offshore by the regionally traced near base Cenozoic unconformity in the Vøring and Møre basins (e.g. Brekke 2000) which indicates a regional uplift and local erosion. The next step of reconstruction of the erosional history within the study area aims to estimate the amount of erosion during the different Cenozoic time intervals and main depositional stages. The amount of erosion has been calculated for the Palaeocene, Brygge, Kai, Naust (N), Naust (A) and Naust (U, S and T) intervals for which we have the present-day thicknesses (Figs 3 and 4). The reconstruction of the erosion during each stage has been done proportionally to the volume of the deposited sediments. In other words, the percentage of the deposited volume from the total volume of the deposited Cenozoic for each interval has been used to calculate the volume of eroded material in relation to the total volume of erosion (Table 1), represented by the thickness in Fig. 7(a). In this case, the erosion rate is proportional to the sedimentation rate of each selected interval, reflecting changes of the erosion intensity during the Cenozoic. It is important to note that the volume of the post-breakup Cenozoic from the Lofoten Basin has been excluded from our calculations since these sedimentary rocks are mostly the result of extensive erosion in the Western Barents Sea region (Fiedler & Faleide 1996; Hjelstuen et al.2007; Laberg et al.2012). Therefore, the sedimentary sequences within the Lofoten Basin do not really have a strong and direct relationship with regard to the reconstructed and specific erosion of the Lofoten–Vesterålen margin and adjacent mainland. Furthermore, the thick Palaeocene within the Hel Graben (Lundin et al.2013; Zastrozhnov et al. 2018) and a possibly similar Palaeocene sequence in the Røst Basin have also been excluded from the total volume of the deposited Cenozoic since these deposits represent the eroded material sourced from Lower and Upper Cretaceous sedimentary rocks (NPD 2017) at the conjugate Greenland side of the proto-Atlantic region (Petersen et al.2015; Meinhold et al.2013). Table 1. Volume of rocks deposited and eroded during the Cenozoic within the Lofoten-–Vesterålen margin and the adjacent continent. The Naust analogues in the Lofoten Basin, the undefined Cenozoic of layer 3 and the Palaeocene in the Hel Graben and Røst Basin are excluded from the calculations. No.  Layer  Age [Ma]  Volume of the deposited material, Vdeposited (km3)  Percentage of total Cz (per cent)  Volume of eroded material, Veroded (km3)  2.1  Naust U, S, T  0.6–0  6956  11.1  15134  2.2  Naust A  1.5–0.6  6722  10.7  14541  2.3  Naust N  2.7–1.5  18645  29.7  40428  2.4  Kai  18–2.7  3882  6.2  8440  3  Brygge  56–18  13612  21.7  29538  5  Palaeocene  66–56  12901  20.6  28041    Total Cenozoic    62718  100  136122  No.  Layer  Age [Ma]  Volume of the deposited material, Vdeposited (km3)  Percentage of total Cz (per cent)  Volume of eroded material, Veroded (km3)  2.1  Naust U, S, T  0.6–0  6956  11.1  15134  2.2  Naust A  1.5–0.6  6722  10.7  14541  2.3  Naust N  2.7–1.5  18645  29.7  40428  2.4  Kai  18–2.7  3882  6.2  8440  3  Brygge  56–18  13612  21.7  29538  5  Palaeocene  66–56  12901  20.6  28041    Total Cenozoic    62718  100  136122  View Large According to Table 1, the volume of the eroded material is slightly more than two times higher than the volume of the deposited sedimentary rocks. The volume of the undefined Cenozoic in the case of layer 3 is around 27 782 km3. Some of the eroded material on the eastern slopes of the Scandes Mountains was not transported to the Lofoten–Vesterålen margin and the estimated volume of this material is approximately 14 430 km3. The volume of the total deposited material is estimated to be 62 718 + 27 782 = 90 500 km3 and the total eroded material is approximately 136 122 − 14 430 = 121 692 km3. The estimated uncertainty of the volume calculations is ± 7 per cent and can be definitely higher if the uncertainties in the original data and the reconstructed maps are considered. In this case, the total volume of the eroded material is only 34 per cent larger than the deposited one. This mismatch can be explained by several processes including: differential erosion and transportation of the fine-grained eroded material to the Atlantic Ocean, dissolution of carbonates, loss due to wind transport and other processes related to transport and deposition of the eroded products. Based on Table 1, the thickness of the eroded rocks has been calculated for each stage and, finally, has been subtracted step-by-step from the total thickness of the eroded material at the end of the Cretaceous (Fig. 7a). The derived thicknesses of the eroded rocks (Fig. 7) show a gradual decrease of the reconstructed thicknesses throughout the Cenozoic as a result of continuous erosion. 4.2 3-D thermal modelling A 3-D temperature model within the Lofoten–Vesterålen margin and adjacent areas has been obtained with the help of COMSOL Multiphysics, which is a finite-element analysis software package. During the 3-D thermal simulations, the Heat Transfer Module has been used to model the stationary and time-dependent heat transfer in solid materials by heat conduction through the lithosphere. A detailed description of the methodology has already been given by Maystrenko & Gernigon (2018) and here only the most important points of the used approach will be repeated, and particular features of the 3-D thermal modelling applied in this study will be described. The 3-D conductive thermal field has been calculated between two thermal boundary conditions at the Earth's surface/seafloor and the lithosphere–asthenosphere boundary. In particular, the upper thermal boundary condition has been set as time-dependent average temperatures at the Earth's surface and the seafloor. The annual average air temperatures from Raab & Vedin (1995) and Tveito et al. (2000) represent the present-day temperature at the Earth´s surface onshore, whereas the temperature at the seafloor offshore has been taken to be dependent on the bathymetry (Table 2) based on Ottersen (2009) and Korablev et al. (2014) (Fig. 8). Table 2. Average annual present-day 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 In addition, the detailed palaeoclimatic changes of the surface temperature during the last two glaciations (the Saalian and Weichselian glacial periods) have been considered during the 3-D thermal modelling. A model of the spatiotemporal variations of the ice cover within Scandinavia during the Weichselian glacial period (Fig. 9) by Olsen et al. (2013) has been used for reconstruction of the palaeoclimatic conditions during the Weichselian glaciation. When the study area was covered by the ice sheet, a temperature of −0.5 °C has been chosen at the Earth´s surface beneath the ice cover, as previously used and discussed by Slagstad et al. (2009). Seafloor palaeotemperatures during the glacial periods have been set to be 0 °C, which is in agreement with reconstructed temperature anomalies for the Norwegian Sea by Eldevik et al. (2014). Palaeotemperatures at the ice-free Earth's surface have been taken from Schmittner et al. (2011), indicating that the near-surface air temperature difference could be about −20 °C lower compared to the pre-industrial period and is only valid for the Last Glacial Maximum when the air temperatures were at their lowest level during the last glaciation. In order to take into account this fact, temperatures lower than −11 °C from Schmittner et al. (2011) have been decreased by 1–4 °C. Palaeotemperatures along the marginal parts of the ice cover have been obtained by an interpolation between −0.5 °C beneath the ice cover and the palaeotemperatures over the ice-free land areas. The same palaeoclimatic scenario was also applied for the Saalian glacial/Eemian interglacial period (220 000–118 000 yr BP), considering that palaeoclimatic conditions were relatively similar during the Weichselian and Saalian glacial periods (e.g. Andersen & Borns 1994). The palaeotemperatures during the last 8000 yr (Table 3; Fig. 10) have been taken from to Davis et al. (2003), Nesje et al. (2008), Mann et al. (2009) and Seppä et al. (2009). Table 3. Relative changes of the palaeotemperatures in comparison to the present-day temperature for the last 8000 yr. Time, years before present BP  0 Present day  400 Little Ice Age  7500 Holocene Climate 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 Climate Optimum  8000  Temperature difference in relation to present day (°C)  0  −0.4  +1  −1  View Large During the Weichselian glaciation, the global palaeo-sea level was 80–120 m lower than the present-day one (e.g. Hasenclever et al.2017). However, the glacial erosion of the sedimentary cover could have been locally significant (Fig. 7). We expect that the present-day bathymetry was different from the one that existed during Wechselian time. Therefore, 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 Weichselian glaciation (Fig. 10), including the present-day offshore areas covered by the reconstructed eroded sediments in Fig. 7. The reconstructed average palaeotemperatures (Fig. 10) show that the study area was mostly characterized by much lower temperatures during the Weichselian glaciation compared to the present-day conditions (Fig. 8). Figure 8. View largeDownload slide Present-day upper thermal boundary: annual average air temperatures at the Earth's surface and average seafloor temperatures (based on Raab & Vedin 1995; Tveito et al.2000; Ottersen 2009; Korablev et al.2014). COB, continent-ocean boundary; HG, Hel Graben; LV/LDM, low-velocity/low-density mantle; NH, Nyk High; NR, Nordland Ridge; NS, Någrind Syncline; TB, Træna Basin; TP, Trøndelag Platform; UH, Utgard High; VB, Vøring Basin. Figure 8. View largeDownload slide Present-day upper thermal boundary: annual average air temperatures at the Earth's surface and average seafloor temperatures (based on Raab & Vedin 1995; Tveito et al.2000; Ottersen 2009; Korablev et al.2014). COB, continent-ocean boundary; HG, Hel Graben; LV/LDM, low-velocity/low-density mantle; NH, Nyk High; NR, Nordland Ridge; NS, Någrind Syncline; TB, Træna Basin; TP, Trøndelag Platform; UH, Utgard High; VB, Vøring Basin. The Cenozoic palaeoclimatic scenario reflects a continuous decrease of the palaeotemperature from 18 °C 66 Ma ago to the present-day air temperature over the mainland (Zachos et al.2001; Pekar et al.2006; Rise et al.2006; Eldrett et al.2009; Ehlers et al.2011; Hansen et al.2013; Inglis et al.2017). A temperature variation from 8 °C 45 Ma ago to 0 °C at the present-day seafloor within the deep sea was also considered (Zachos et al.2001; Ravelo et al.2004; Pekar et al.2006; Filippelli & Flores 2009; Hansen et al.2013). The lithosphere–asthenosphere boundary (Fig. 6c) has been chosen as a lower thermal boundary condition with a 1300 °C isotherm (e.g. Turcotte & Schubert 2002). Alternatively, the constant heat flux density can also be used on the bottom lithospheric isotherm as the lower thermal boundary condition (e.g. Doin & Fleitout 1996). Besides, the temperature at the lower thermal boundary has been enhanced within the low-velocity/low-density zone of the upper mantle (Figs 6b and c). This has been done in accordance with the results of seismic tomography which indicate a decrease of an S-velocity by c. 3 per cent at 100–200 km depth in relation to the reference velocity model, or even by more than 3 per cent in relation to the surrounding mantle (e.g. Pilidou et al.2005; Hejrani et al.2017). Taking into account that the S-velocity changes by 1–2 per cent per 100 °C (Cammarano et al.2003) or even by 1 per cent per 100 °C (Lee 2003), we can infer that a thermal anomaly of about +250 °C at 150 km depth can be at least partially responsible for the origin of the low-velocity zone within the upper mantle. Moreover, the density contrast between the low-density lithospheric mantle and the surrounding mantle of 18–35 kg m−3 within the entire column of the lithospheric mantle (Maystrenko et al.2017) can be translated to an even higher temperature contrast than 250 °C at 100–150 km depth. A +250 °C mantle low-velocity/low-density zone at 150 km depth has been chosen as a compromise value because the origin of the low-velocity/low-density mantle can also be the result of compositional variations in addition to changes of temperature (e.g. Slagstad et al.2018). Therefore, the thermal anomaly of +250 °C has been set for the 150 km depth or slightly shallower base of the anomalous lithospheric mantle. This thermal anomaly at 150 km depth has been further projected, proportionally to the thickness of the lithosphere, to the base of the shallower lithosphere within the zone with the low-velocity/low-density lithospheric mantle. Therefore, the 1300 °C isotherm has to be shallower within the zone of the low-velocity/low-density mantle, pointing to an uplift of the lithosphere–asthenosphere boundary beneath the study area (Fig. 6c). The influence of the early Cenozoic continental breakup has been roughly estimated in the 3-D thermal modelling workflow in terms of two additional lithosphere–asthenosphere boundaries: the first one represents the lithospheric configuration immediately after the continental breakup, c. 55 Ma ago (Fig. 11a) and the second one represents a colder and thickened lithosphere expected at the end of the deposition of the Brygge Formation (18 Ma ago; Fig. 11b). These two time steps (55 and 18 Ma) allow us to roughly simulate the increased thermal effect during the continental breakup in the early Cenozoic and the subsequent cooling of the oceanic lithosphere during the rest of the Cenozoic. As a major limitation of the model, the precise position of the lithosphere–asthenosphere boundary during the Early Eocene breakup is still poorly known, but numerical models (e.g. Chen & Lin 2004; Kawakatsu et al.2009) along modern spreading axe predict a shallow position of the 1300 °C isotherm. In our study, the depth to the base of the lithosphere 55 Ma ago has been tentatively taken to be 13–17 km deep beneath the present-day oceanic domain, representing the newly formed Cenozoic lithosphere. According to estimations for 0 Ma oceanic lithosphere by Zhang & Lay (1999), the taken depth position of the lithosphere–asthenosphere boundary 55 Ma ago could theoretically vary in the range of ±5 km. In addition, the modelled heat flux density over the imposed lithospheric configuration immediately after the continental breakup has been compared with the present-day heat flux density values at the Mid-Atlantic oceanic ridge (Hasterok et al.2011), demonstrating that the modelled values are in the proper range. The present-day depths of the lithosphere–asthenosphere boundary deeper than 95 km have not been changed, whereas the depth to the base of the lithosphere between the Cenozoic oceanic domain and the more than 95 km deep lithosphere has been obtained by linear interpolation, assuming that the continental lithosphere has been at least partially affected by thinning in the vicinity of the oceanic domain (Fig. 11a). The lithosphere–asthenosphere boundary at 18 Ma ago (Fig. 11b) has been calculated in the same way as the present-day one according to empirical relations between the age of the lithosphere and seismic velocities in Zhang & Lay (1999). We cannot exclude the large inherent uncertainties in our palaeo-depth estimations of lithosphere–asthenosphere boundaries (Fig. 11). They could be related to potential small-scale changes in the intensity of the syn-breakup magmatism, which could locally enhance the geothermal gradient and modify the thermal properties of the deep continental crust. However, breakup and associated magmatic processes are still unclear and require a more detailed study which is outside the scope of our investigation. Consequently, the influence of the local syn-breakup magmatism has been mainly neglected in the present study, whereas the large-scale one is considered in terms of the uplifted lithosphere–asthenosphere boundary 55 Ma ago (Fig. 11a). The thermal effects of the post-breakup uplift and erosion within the study area with further deposition of the Naust (Pleistocene), Kai (Middle Miocene–Pliocene) and Brygge (Eocene–lower Miocene) formations (layers 2.1–2.3, 2.4 and 3, respectively; Fig. 3) have been included into the 3-D thermal modelling workflow, allowing us to focus more specifically on the time-dependent perturbations in the subsurface thermal regime due to the post-Palaeocene erosion and sedimentation. The 3-D thermal modelling workflow includes the following six steps: (1) Calculation of the steady-state 3-D conductive thermal field after the continental breakup 55 Ma ago. The Brygge, Kai and Naust formations (Eocene–Pleistocene interval; Fig. 3) have been excluded from these calculations, whereas a new layer, represented by the reconstructed eroded rocks at the end of the Palaeocene (Fig. 7b), has been added to the top of the model. The lower thermal boundary has been represented by the 1300 °C isotherm at the inferred lithosphere–asthenosphere boundary 55 Ma ago (Fig. 11a) and the top of the eroded rocks is set as a new upper thermal boundary. The top of the Upper Cretaceous–Palaeocene deposits (layers 5–6) or deeper/older rocks have been used as the upper thermal boundary in places where the eroded rocks were not restored. Porosity of the pre-breakup sedimentary succession has been readjusted to shallower depth conditions by subtraction of the thickness of the post-breakup sedimentary package (Brygge, Kai and Naust formations; Eocene–Pleistocene interval) from the present-day depths and correction of the present-day position of deep seafloor. Accordingly, the porosity-dependent thermal conductivities and densities of the sedimentary cover have been adjusted to shallower depths. (2)–(6) Calculation of the time-dependent (transient) 3-D conductive thermal field: (2) For the period from 55 Ma ago to the end of the Brygge interval in the early Miocene 18 Ma ago. The calculated 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 Kai and Naust formations (Middle Miocene–Pleistocene interval; Figs 3a–d) have been excluded from these calculations, whereas a new layer, represented by the reconstructed eroded rocks for the end of the Brygge interval (Fig. 7c), has been added to the top of the model. The lower thermal boundary has been represented by the 1300 °C isotherm at the inferred lithosphere–asthenosphere boundary at 18 Ma ago (Fig. 11b) and the top of the eroded rocks has been set as a new upper thermal boundary. The top of the Brygge Formation (layers 3) or deeper/older rocks have been used as the upper thermal boundary in places where the eroded rocks were not restored. Accordingly, the porosity of the pre-breakup sedimentary succession and Brygge sequence have been adjusted to shallower depth conditions compared to the present-day ones by subtracting the total thickness of the Kai and Naust formations (Eocene–Pleistocene interval) from the present-day depths and correction of the present-day position of deep seafloor. (3) During the Kai interval from 18 to 2.7 Ma ago. The final calculated 3-D temperature distribution from the previous step (2) has been used as the initial temperature condition at the beginning of the time-dependent calculations (18 Ma ago). The whole of the Naust Formation (Pleistocene interval; Figs 3a–c) has been excluded from these calculations, whereas a new layer, represented by the reconstructed eroded rocks at the end of the Kai interval (Fig. 7d), has been added to the top of the model. The lower thermal boundary has been represented by the 1300 °C isotherm at the present-day as a new upper thermal boundary. The top of the Kai Formation (layer 2.4) or deeper/older rocks have been used as the upper thermal boundary in places where the eroded rocks were not restored. Accordingly, the porosity of the pre-breakup sedimentary succession and Brygge and Kai sequences has been adjusted to shallower depth conditions compared to the present-day ones by subtracting the total thickness of the Naust Formation (Pleistocene interval) from the present-day depths and correction of the present-day position of deep seafloor. (4) During the Naust (N) interval from 2.7 to 1.5 Ma ago. The final calculated 3-D temperature distribution from step (3) has been used as the initial temperature condition at the beginning of the time-dependent calculations (2.7 Ma ago). The sequences A, U, S and T of the Naust Formation (Pleistocene interval; Figs 3a and b) have been excluded from these calculations, whereas a new layer, represented by the reconstructed eroded rocks for the end of the Naust (N) interval (Fig. 7e), has been added to the top of the model. The lower thermal boundary has been represented by the 1300 °C isotherm at the present-day lithosphere–asthenosphere boundary (Fig. 6c) and the top of the eroded rocks has been taken to be an upper thermal boundary. The top of the sequence N of the Naust Formation (layer 2.3) or deeper/older rocks have been used as the upper thermal boundary in places where the eroded rocks were not restored. The porosity of the pre-breakup sedimentary succession and Brygge, Kai and Naust (N) sequences have been adjusted to shallower depth conditions compared to the present-day ones by subtracting the total thickness of the sequences A, U, S and T of the Naust Formation (Pleistocene interval; Figs 3a and b) from the present-day depths and correction of the present-day position of deep seafloor. (5) During the Naust (A) interval from 1.5 to 0.6 Ma ago. The final calculated 3-D temperature distribution from step (4) has been used as the initial temperature condition at the beginning of the time-dependent calculations (1.5 Ma ago). The sequences U, S and T of the Naust Formation (Pleistocene interval; Fig. 3a) have been excluded from these calculations, whereas a new layer, represented by the reconstructed eroded rocks at the end of the Naust (A) interval (Fig. 7d), has been added to the top of the model. The lower thermal boundary has been represented by the 1300 °C isotherm at the present-day lithosphere–asthenosphere boundary (Fig. 6c) and the top of the eroded rocks has been taken to be an upper thermal boundary. The top of sequence A of the Naust Formation (layer 2.2) or deeper/older rocks have been used as the upper thermal boundary in places where the eroded rocks were not restored. The porosity of the pre-breakup sedimentary succession and Brygge, Kai and Naust (N and A) sequences has been adjusted to shallower depth conditions compared to the present-day ones by subtracting the total thickness of the sequences U, S and T of the Naust Formation (Pleistocene interval; Fig. 3a) from the present-day depths and correction of the present-day position of deep seafloor. (6) For the period from 0.6 Ma ago to the present-day. The final calculated 3-D temperature distribution from step (5) has been used as the initial temperature condition at the beginning of the time-dependent calculations (0.6 Ma ago). The lower thermal boundary has been represented by the 1300 °C isotherm at the present-day lithosphere–asthenosphere boundary (Fig. 6c) and the top of the 3-D structural model (present-day seafloor and Earth's surface onshore) has been considered as the upper thermal boundary. Porosity has been estimated according to the present-day depths. During all steps, the lower thermal boundary has been thermally enhanced within the low-velocity/low-density zone of the upper mantle as it is described above. During all steps, palaeotemperature at the upper thermal boundary has been taken to be time-dependent in accordance with Tables 2–4 and Fig. 10. Table 4. Palaeotemperatures during the Cenozoic (based on Zachos et al.2001; Pekar et al.2006; Rise et al.2006; Eldrett et al.2009; Filippelli & Flores 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  66  18  –  2  55  17.5  –  3  45  14  8  4  34  10  3  5  25  11.5  5  6  18  10.5  4  7  16  12  6  8  12  9  3  9  5  6  1  10  3.6  +3 °C to present-day temperature  0  11  0.45  Present-day temperature  Present-day temperature  12  0.35  The same as glacial maximum 27 000 yr ago in Fig. 10  The same as glacial maximum 27 000 yr ago in Fig. 10  13  0.228  Present-day temperature  Present-day temperature  14  0.220–0.118  The same as 0.110–0.0105 Ma ago  The same as 0.110–0.0105 Ma ago  15  0.110–0.0105  Fig. 10  Fig. 10  No.  Time (Ma ago)  Mainland temperature (°C)  Deep sea temperature (°C)  1  66  18  –  2  55  17.5  –  3  45  14  8  4  34  10  3  5  25  11.5  5  6  18  10.5  4  7  16  12  6  8  12  9  3  9  5  6  1  10  3.6  +3 °C to present-day temperature  0  11  0.45  Present-day temperature  Present-day temperature  12  0.35  The same as glacial maximum 27 000 yr ago in Fig. 10  The same as glacial maximum 27 000 yr ago in Fig. 10  13  0.228  Present-day temperature  Present-day temperature  14  0.220–0.118  The same as 0.110–0.0105 Ma ago  The same as 0.110–0.0105 Ma ago  15  0.110–0.0105  Fig. 10  Fig. 10  View Large During the 3-D thermal modelling, the eroded rocks have been assumed to be mainly represented by sedimentary rocks and weathered crystalline crust which is characterized by a density and a porosity similar to sedimentary rocks rather than crystalline ones. The porosity of the eroded rocks has been kept the same for all steps as it is in the case of a completely reconstructed eroded sequence (Fig. 7a) with zero-level at the top of this complete sequence, assuming that a possible decompaction of these rocks due to erosion was very minor or even absent at each time step. Compaction of the deposited sedimentary rocks has only been considered in terms of changes in porosity/density according to exponential functions in Maystrenko et al. (2017), but thicknesses/volume of the deposited successions have been kept constant due to some limitations of the used software. This approach is sufficient for the Pleistocene, which is the key interval of our study. Changes in thicknesses of the Pleistocene sequences due to compaction are estimated to be less than 12 per cent (c. 200 m) for the thickest (1700 m thick) succession and is less than 4–8 per cent on average. 4–8 per cent of the total Pleistocene thickness is in the range of uncertainties of the used thicknesses and can therefore be neglected at the first-order approximation. Isostatic readjustment due the re-distribution of mass during erosion/deposition has not been applied during the modelling because the main goal of this study is related to the thermal effect of late Cenozoic erosion and deposition. This thermal effect has been investigated by step-by-step moving of the upper thermal boundary to the base of the eroded rocks (top of the remining rocks) and to the top of the deposited sedimentary rocks. In this case the main controlling factor of the conductive heat transfer is related to the distance between the lower and upper thermal boundaries and thermal properties in between. On the other hand, the real vertical position of the surface played a very minor role, especially if the properties of rocks have always been adjacent according to new depth position in our workflow. Therefore, our approach is sufficient for the subvertical conductive heat transfer. On the other hand, possible changes in the subhorizontal heat transfer could disturb the calculated thermal field locally, if there were significant vertical movements of the closely located local areas but this is actually not the case in the Lofoten area. 5 THERMAL PROPERTIES Thermal properties represented by specific heat capacity, thermal conductivity and radiogenic heat production (Table 5) have been assigned for each layer of the 3-D structural model. The thermal conductivity for the sedimentary cover has been taken from the previous estimations of the matrix thermal conductivity from wells within the northern part of the Viking Graben (Brigaud et al.1992), the Mid-Norwegian continental margin and adjacent areas (Eldholm et al.2005; Pascal & Midttømme 2006; Pascal 2015), and based on unconsolidated sampled sedimentary rocks from the Vøring Basin according to Midttømme et al. (1995). The obtained thermal conductivities of sedimentary rocks have been cross-validated with results of measurements of rock samples with similar lithology (Čermak & Rybach 1982; Clauser 2011) and the wide-ranging thermal conductivities of different sedimentary rocks, summarized by Midttømme & Roaldset (1999). The thermal conductivity of basalts (layer 4) has been set to be 1.8 W m−1 K−1 on average according to Balling et al. (2006). Thermal conductivities of the upper crystalline crustal rocks have been set to be in the range of the rock-sample measurements 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 1982; Wollenberg & Smith 1987; Hofmeister 1999; Artemieva et al.2006; Scheck-Wenderoth & Maystrenko 2008; Scheck-Wenderoth & Maystrenko 2013; Maystrenko et al.2014). The thermal conductivity of sedimentary rocks has been set to be temperature- and porosity-dependent to take into account changes of the thermal conductivity as a result of increasing temperature and decreasing porosity with depth. The thermal conductivity of the fluid in the pores of sedimentary rocks has been set to be the temperature-dependent thermal conductivity of water according to Wagner & Kretzschmar (2008). The thermal conductivities of the crystalline rocks have been set to be dependent only on temperature because the average porosities of the crystalline rocks are usually extremely low at the regional scale and can, therefore, be neglected. The empirical equations from Sass et al. (1992) and Vosteen & Schellschmidt (2003) have been used to describe a dependence of thermal conductivities of sedimentary and crystalline rocks on temperature. The thermal conductivity of the lithospheric mantle has been set to be both pressure- and temperature-dependent according to Hofmeister (1999) and van den Berg et al. (2001). Porosity and density of the sedimentary rocks have been obtained based on exponential functions of increasing densities with depth in Maystrenko et al. (2017) and densities of the crystalline rocks have also been taken from Maystrenko et al. (2017). The depth-dependent porosities have been calculated by use of the same density of 2700 kg m−3 for all sedimentary layers due to uncertainties in defining the lithological composition. The detailed description of how the temperature-, pressure- and porosity-dependent thermal conductivities have been calculated is given in Maystrenko & Gernigon (2018). The chosen specific heat capacity (Table 5) has been set to be constant for each layer of the 3-D model during the 3-D thermal modelling, representing the temperature-dependent average values of the specific heat capacity based on laboratory measurements at different temperature conditions according to Čermak & Rybach (1982), Afonso et al. (2005) and Clauser (2011). The radiogenic heat production of sedimentary layers of the 3-D model has been derived from the results of gamma-ray logging in selected wells according to the empirical relationship between total natural gamma and radiogenic heat production in Bücker & Rybach (1996). An example of the used natural gamma ray logs and the derived radiogenic heat production is shown in Fig. 12. The chosen wells are located within the southwestern part of the model area (Fig. 13) where the sedimentary cover has been drilled for the purposes of the petroleum industry. There are only a few shallow wells drilled through the sedimentary cover within the rest of the Lofoten–Vesterålen margin and, unfortunately, well logs of these shallow wells are not easily accessible. Based on the results of calculations, the average radiogenic heat production of the sedimentary rocks shows a wide range of values from 0.47 to 2.02 μW m−3 (Table 6). The stratigraphic subdivision of the used wells does not include sequences N, A, U, S and T of the Naust Formation (NPD 2017) and, therefore, the average values for the total Naust Formation have been used for the Naust (N), Naust (A) and Naust (U, S and T) intervals (layers 2.1–2.3). Moreover, the Nordland Group (Naust plus Kai formations) has only been indicated in some of the wells. In this case, the same value of the radiogenic heat production has been used for both the Naust and the Kai formations. This is actually supported by well 6510/2-1 R where the Naust and Kai formations are characterized by the same values of the radiogenic heat production (Table 6). The derived average values of the radiogenic heat production for each sedimentary layer have been further used to construct maps by interpolation between these values in the used wells with extrapolation to the areas without the well data (Fig. 13). The uppermost layers, represented by Naust (layers 2.1–2.3) and Kai (layer 2.4), are characterized by a very similar pattern of the derived radiogenic heat production (cf. Figs 13a and b) in spite of the fact that some values are different (Table 6). A similar distribution of the radiogenic heat production is also found for the Brygge (Fig. 13c) and the Upper Cretaceous–Palaeocene layers (Fig. 13d). Moreover, the relatively high radiogenic heat production in well 6607/5-1 and the relatively low one in wells 6507/5-1, 6510/2-1 R and 6608/8-1, representative for the southwestern corner of the model area, are clearly or partially recognizable in maps for the Naust, Kai and Brygge formations, the Upper Cretaceous–Palaeocene and the Lower Cretaceous (cf. Figs 13a–e). This means that the similar pattern of radiogenic heat production is characteristic for the more than 100 million-year-long stratigraphic interval. This long-term inheritance for the Cretaceous–Cenozoic interval has already been identified in the Vøring and Møre basins by Maystrenko & Gernigon (2018), indicating a possible inheritance in clastic material transportation from original localities with an increased or decreased content of the radiogenic elements. Alternatively, it may indicate a differential sorting of the eroded products during transportation from source to sink. The deposition of sedimentary rocks with a more argillaceous composition in particular areas of the Mid-Norwegian continental margin may explain the local increase of heat production within specific areas because argillaceous rocks are usually characterized by a higher radiogenic heat production compared to more sandy sedimentary rocks (e.g. Čermak & Rybach 1982; McKenna & Sharp 1998; Villa et al.2010). The assigned radiogenic heat productions of the upper and middle-crustal layers (layers 9, 10–11 and 12) onshore are mainly based on the measured radiogenic heat production for different geological/lithological units in Norway (Slagstad 2008; Slagstad et al.2009; Slagstad & Lauritsen 2013). The radiogenic heat production of the oceanic crust, lower continental crust and the lithospheric mantle (layers 13–18) have been set to be constant (Table 5) according to published values for the assumed lithological composition of each layer (Čermak & Rybach 1982; Scheck-Wenderoth & Maystrenko 2008; Villa et al.2010). To remove a misfit between measured and modelled temperatures in the available wells offshore, lateral changes in the radiogenic heat production of the upper and middle continental crust have been applied. Other possible explanations for some local changes of the observed temperature could be associated with atypical fluid flow, strong variations in thermal conductivities, structural uncertainties and/or limited resolution of our 3-D model. The above-mentioned alternative hypotheses would, however, require additional structural data and sampling material to be tested, as well as simulation of other physical processes, such as fluid flow etc. The absence of detailed structural data and supplementary measurements together with technical difficulties in modelling the detailed fluid flow at the scale of our 3-D model do not allow us to test the variety of other possible reasons in addition to the variable radiogenic heat production. On the other hand, the radiogenic heat production of the crystalline rocks varies within the mainland (e.g. Slagstad 2008; Pascal & Rudlang 2016), implying that a possible similar variability exists offshore as well. During the 3-D thermal modelling, several models with different values of the radiogenic heat production have been tested to fit the measured and modelled temperatures in the available wells. Table 5. 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 NPD 2017). No.  Layer of the 3-D structural model  Dominant lithology  Specific heat capacity Cp (J kg−1 K−1)  Thermal conductivity scale value kr [W m−1 K−1]  Radiogenic heat production S [μW m−3]  2.1–2.3  Naust  Mainly shale and sandstone  1180  2.3  0.59–2.0  2.4  Kai  Mainly shale and sandstone  1180  2.3  0.57–1.9  3  Brygge and undefined Cenozoic  Mainly shale and sandstone  1180  2.2  0.48–1.6  4  Oceanic layer 2AB  Basalts and tuffs  880  1.8  0.4  5–6  Upper Cretaceous-Palaeocene  88 per cent shale, 12 per cent sandstone  1180  2.5  0.68–1.87  7  Lower Cretaceous  92 per cent shale, 3 per cent sandstone, 5 per cent limestone  1180  2.4  0.83–1.99  8  Pre-Cretaceous  80 per cent shale, 20 per cent sandstone  1180  3.3  1.12–2.2  5–8  Undivided Palaeocene and Cretaceous of the Røst Basin  87 per cent shale, 11 per cent sandstone, 2 per cent limestone  1180  2.5  1.4  Xx  Eroded material  Mainly sedimentary deposits with crystalline rocks  1180  3.0  1.4  9  Upper-crustal high-density crystalline rocks  Gabbro to anorthositic rocks, metamorphic rocks  880  2.9  0.4  10–11  Upper crust  Metasediments and/or granite and gneiss  880  3.2  1.5–2 (0.2–2.5)  12  Middle crust  Granitoids and/or gneiss  950  3.1  0.86 (0.1–2.5)  13  Lower crust  Metamorphic rocks  1050  3.0  0.32  14  High-density intra-crustal layer  Mafic granulites, gabbros  1050  3.0  0.32  15  Oceanic layer 3A  Sheeted dykes/gabbroic intrusions  1050  2.7  0.4  16–17  High-density lower-crustal layer and oceanic layer 3B  Gabbro and high-grade metamorphic rocks  1100  2.8–3.1  0.2  18  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 scale value kr [W m−1 K−1]  Radiogenic heat production S [μW m−3]  2.1–2.3  Naust  Mainly shale and sandstone  1180  2.3  0.59–2.0  2.4  Kai  Mainly shale and sandstone  1180  2.3  0.57–1.9  3  Brygge and undefined Cenozoic  Mainly shale and sandstone  1180  2.2  0.48–1.6  4  Oceanic layer 2AB  Basalts and tuffs  880  1.8  0.4  5–6  Upper Cretaceous-Palaeocene  88 per cent shale, 12 per cent sandstone  1180  2.5  0.68–1.87  7  Lower Cretaceous  92 per cent shale, 3 per cent sandstone, 5 per cent limestone  1180  2.4  0.83–1.99  8  Pre-Cretaceous  80 per cent shale, 20 per cent sandstone  1180  3.3  1.12–2.2  5–8  Undivided Palaeocene and Cretaceous of the Røst Basin  87 per cent shale, 11 per cent sandstone, 2 per cent limestone  1180  2.5  1.4  Xx  Eroded material  Mainly sedimentary deposits with crystalline rocks  1180  3.0  1.4  9  Upper-crustal high-density crystalline rocks  Gabbro to anorthositic rocks, metamorphic rocks  880  2.9  0.4  10–11  Upper crust  Metasediments and/or granite and gneiss  880  3.2  1.5–2 (0.2–2.5)  12  Middle crust  Granitoids and/or gneiss  950  3.1  0.86 (0.1–2.5)  13  Lower crust  Metamorphic rocks  1050  3.0  0.32  14  High-density intra-crustal layer  Mafic granulites, gabbros  1050  3.0  0.32  15  Oceanic layer 3A  Sheeted dykes/gabbroic intrusions  1050  2.7  0.4  16–17  High-density lower-crustal layer and oceanic layer 3B  Gabbro and high-grade metamorphic rocks  1100  2.8–3.1  0.2  18  Lithospheric upper mantle  Peridotite  1200  4.79  0.03  View Large The upper crystalline crust is characterized by the increased radiogenic heat production up to 2.2 μW m−3 within the SN-striking zone onshore in the middle of the southern part of the model area (Fig. 14a). Towards the north, a wide zone with an increased heat production (2 μW m−3) corresponds to the thickened low-density upper crustal layer inferred by Maystrenko et al. (2017). Both areas with an increased radiogenic heat can be represented by granite, granitic gneiss and/or granitoids with the increased content of the radiogenic elements, similar to the Precambrian Transscandinavian Igneous Belt granites which are characterized by an average radiogenic heat production of 2.6 μW m−3 (locally up to 4 μW m−3) according to Slagstad (2008). Within the southwestern part of the model area, the radiogenic heat production varies from 0.2 to 2.5 μW m−3 (Fig. 14a), indicating a possible lithological differentiation of the upper crust there. The middle crust is characterized by an average radiogenic heat production of c. 0.86 μW m−3 within the greater part of the study area (Fig. 14b) and slightly increased to 0.92 μW m−3 within the areas where the upper-crustal layer is absent (cf. Figs 14a and b). The same pattern of radiogenic heat production as in the case of the upper crust has been applied within the southwestern part of the model area (cf. Figs 14a and b). The thicknesses of the upper and middle crust within the southwestern part of the model area are mostly in the range 0.5–4 km and 1–5 km on average, respectively, with some local thickening and thinning. These relatively small thicknesses of the upper-middle crustal layers imply that the assigned radiogenic heat production does not drastically affect the modelled temperatures in that area compared to the mainland where the thickness of these layers is 12 km on average with local thickening up to more than 20 km. Therefore, even if our assumption of varying radiogenic heat production offshore may appears to be partially erroneous, the regional-scale pattern of the modelled temperature should not be affected by any notable extent. 6 RESULTS OF THE 3-D THERMAL MODELLING The 3-D conductive thermal pattern beneath the study area (Fig. 15) has been modelled by assigning thermal properties (Tables 5 and 6) to the layers of the 3-D structural model from Maystrenko et al. (2017), assigning thermal boundary conditions at the top and bottom of the 3-D model (e.g. Figs 6c, 8, 10 and 11; Tables 2–4) and including the thermal influence of the Cenozoic erosion and deposition (Fig. 7; Table 1). Table 6. Average radiogenic heat production of sedimentary rocks, derived from gamma ray logs, in the selected wells. Units of radiogenic heat production are μW m−3 (Fm. is formation and Gr. is group). Well  Naust Fm. (layers 2.1–2.3)  Kai Fm. (layer 2.4)  Hordaland Group (layer 3)  Rogaland-Shetland groups (layer 5–6)  Cromer Knoll Gr. (layer 7)  pre-Cretaceous (layer 8)  6507/5-1  1.2  0.9  0.7  0.75  0.93  1.13  6510/2-1 R  0.68  0.68  0.72  0.69  0.94  1.65  6610/7-2  0.86  0.86?  0.47  0.67  0.82  1.1  6707/10-1  0.54  0.54?  –  1.02  –  –  6607/5-1  2.02  1.92  –  1.88  2  –  6608/8-1  1.18  1.35  1.41  1.49  –  1.69  6610/2-1 S  0.88  0.88?  1.46  1.68  1.16  2.56  6706/6-1  1  0.57  1  1.2  –  –  6710/10-1  1.24  1.24?  1.6  1.5  –  –  Well  Naust Fm. (layers 2.1–2.3)  Kai Fm. (layer 2.4)  Hordaland Group (layer 3)  Rogaland-Shetland groups (layer 5–6)  Cromer Knoll Gr. (layer 7)  pre-Cretaceous (layer 8)  6507/5-1  1.2  0.9  0.7  0.75  0.93  1.13  6510/2-1 R  0.68  0.68  0.72  0.69  0.94  1.65  6610/7-2  0.86  0.86?  0.47  0.67  0.82  1.1  6707/10-1  0.54  0.54?  –  1.02  –  –  6607/5-1  2.02  1.92  –  1.88  2  –  6608/8-1  1.18  1.35  1.41  1.49  –  1.69  6610/2-1 S  0.88  0.88?  1.46  1.68  1.16  2.56  6706/6-1  1  0.57  1  1.2  –  –  6710/10-1  1.24  1.24?  1.6  1.5  –  –  View Large 6.1 Temperature within the upper part of the 3-D model The results of the 3-D thermal modelling for the upper part of the 3-D structural model are shown in Fig. 16 and are represented by the temperature maps of six horizontal model slices at depths below sea level of 2, 5, 7, 10, 15 and 18 km. It can be seen that the mainland is generally colder compared to the continental margin (Fig. 16). At a depth of 2 km below sea level, the Scandes Mountains are clearly reflected by the increased temperatures beneath the mainland (cf. Figs 2 and 16a). This is a result of the topographic effect due to the presence of the 1–1.5 km elevated Scandes Mountains compared to the rest of the mainland where the relief is smoother and deeper. The upper thermal boundary has been set at the Earth's surface and, therefore, the elevated relief of the Scandes Mountains adds an additional 1–1.5 km to the distance from the upper thermal boundary to the depths below sea level in Fig. 16. This topographic thermal effect of the Scandes Mountains is still clearly visible at a depth of 5 km and even deeper where it is smoothed by other thermal effects. In contrast, the thermal influence of the deep bathymetry offshore is reflected in the decreased temperature beneath the Lofoten Basin (Fig. 16) where the seafloor is located at depths of more than 2–3 km (Fig. 2). Actually, the white (blank) area in Fig. 16(a) outlines the bathymetry deeper than 2 km. The shape of this blank area is still clearly recognizable in terms of the lower temperatures at depths of 5 and 7 km (Figs 16b and c), reflecting the steeply deepening sea bottom which corresponds to the upper thermal boundary and, therefore, pulls the influence of the low (c. 0 °C) deep-sea temperatures down to greater depths. The eastern part of the mainland is notably colder than the continental margin (Fig. 16). This difference in temperature between the mainland and the continental margin increases with depth (Fig. 16), mainly reflecting both a chimney effect of the relatively high thermally conductive, crystalline rocks exposed at the Earth's surface within the mainland, and a very deep location of the lower thermal boundary, represented by the base of the lithosphere, beneath the mainland (Figs 6c and 11). The next interesting aspect of the thermal pattern within the upper part of the 3-D model is related to the straight spatial relationship between areas with thick sedimentary infill and areas with increased temperatures within the Lofoten–Vesterålen margin and the Vøring Basin (cf. Figs 3, 4 and 16). This feature of temperature distribution is associated with the low thermal conductivity of the sedimentary cover which enhanced the heat storage within the areas with thickened sedimentary rocks. This thermal insulation effect is reflected by the higher modelled temperatures within the Ribban and Vestfjorden basins compared to the Lofoten Ridge which is located between these two basins. This effect is also very pronounced at depths of 15–18 km within the deep Någrind Syncline (Figs 16e and f). Moreover, superposition of (1) different temperature-increasing effects (thermal insulation by the thick sedimentary rocks within the Røst Basin and the Hel Graben; Fig. 4) and significant shallowing of the lower thermal boundary towards the oceanic domain (Figs 6c and 11), and (2) opposite temperature-decreasing effects [deep bathymetry (Fig. 2) and thick, less than 2.7 Ma old, sedimentary rocks within the Lofoten Basin (Figs 3a–c)] are responsible for an NE–SW-trending zone with increased temperature within the Røst Basin and the Hel Graben which is especially pronounced at depths of 10, 15 and 18 km (Figs 16d–f). This zone of increased temperature should have extended towards the oceanic Lofoten Basin, if the bathymetry had not been so deep and if the thickness of the young and, therefore, thermally not equilibrated Pleistocene sedimentary rocks had not been so great there. The major controlling factor of the modelled temperatures at the top of the crystalline basement (Fig. 17) is related to the geometry of the top-basement (Fig. 6a), clearly showing that the deeper top-basement corresponds to the highest modelled temperatures and vice versa. Thus, the highest temperatures have been modelled within the deepest parts of the Vøring Basin where the modelled temperatures are 400–450 °C on average (Fig. 17), whereas the Ribban and Vestfjorden basins are characterized by lower temperatures less than 300 °C on average with some local increase to more than 350 °C within the Vestfjorden Basin. The modelled temperatures on the mainland and the Lofoten–Vesterålen archipelago simply reproduce the present-day Earth´s surface temperature (cf. Figs 8 and 17) because the crystalline basement crops out at the Earth's surface there. 6.1.1 Modelled temperature versus measured temperature The obtained temperatures within the uppermost part of the 3-D model have been compared with measured temperatures in available wells which are shown in Fig. 18. Positions of the wells with only drill-stem test (DST) temperatures offshore and temperatures from well loggings onshore (Fig. 18a) are plotted separately from the locations of all available wells, including the wells with less reliable bottom-hole temperatures (BHT), in Fig. 18(b). Due to the fact that only a few wells with DST temperatures are available offshore and their restricted locations are close to each other (Fig. 18a), the BHT have been used particularly to check the calculated temperatures with the measured ones. However, it is important to note that BHT can be disturbed by circulation of the drilling fluid and, therefore, are less reliable compared to DST temperatures (temperature of fluids, thermally equilibrated with the host sedimentary rocks) and temperature logs (measured under thermal equilibrium conditions in the wells). In this case, a comparison between the observations and the results of the 3-D thermal modelling is provided separately for the wells with DST temperatures and temperature logs (Figs 18a and 19a; Table 7) and for the wells with BHT (Figs 18b and 19b; Table 8). Table 7. Difference between modelled temperatures and measured ones (measured values minus the modelled ones) from different wells located inside the detailed 3-D model area. Only the DST (drill-stem test) temperatures are used. No.  Temperature range of differences between modelled and measured temperatures  Percentage of values (per cent)  Number of values  4  from −5 to 5  92.3  12  5  from 5 to 10  7.7  1  No.  Temperature range of differences between modelled and measured temperatures  Percentage of values (per cent)  Number of values  4  from −5 to 5  92.3  12  5  from 5 to 10  7.7  1  View Large Table 8. Difference between modelled temperatures and measured ones (measured values minus the modelled ones) in available deep wells 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. No.  Temperature range of differences between modelled and measured temperatures  Percentage of values (per cent)  Number of values  3  from −20 to −10  1.9  1  4  from −10 to −5  17.0  9  5  from −5 to 5  50.9  27  6  from 5 to 10  17.0  9  7  from 10 to 20  13.2  7  No.  Temperature range of differences between modelled and measured temperatures  Percentage of values (per cent)  Number of values  3  from −20 to −10  1.9  1  4  from −10 to −5  17.0  9  5  from −5 to 5  50.9  27  6  from 5 to 10  17.0  9  7  from 10 to 20  13.2  7  View Large Comparison between the modelled and measured temperatures demonstrates that the greater part of the obtained temperatures is in reasonable agreement with the main tendency in distribution of the measured temperatures (Fig. 19). The latter is especially true when only DST and temperature logs are considered (Fig. 19a). Larger misfits are present when compared with the BHT estimations (Fig. 19b). To investigate the magnitude of these misfits in detail, an additional study has been carried out by plotting the difference between the measured and the modelled temperatures in tables (Tables 7 and 8) and the related maps (Fig. 18). According to Table 7 and Fig. 18(a), it is clear that most of the misfits (92.3 per cent) between the modelled and measured DST and well-log temperatures are in the range of ±5 °C with only one well showing a misfit of slightly higher than 5 °C. In contrast, if the wells with BHT are also considered in addition to the previous wells, only around 51 per cent of the misfits are in the range of ±5 °C and the misfits with a range of ±10 °C form almost 85 per cent of the total number of the used wells (Table 8). Consequently, the greater portion of the reasonable differences for this kind of regional-scale study lies in the range of ±10 °C, indicating that the major trend of the measured temperatures has been reasonably well reproduced during our 3-D thermal modelling. Misfits larger than ±10 °C are also present in Table 8. The spatial distribution of these larger misfits (Fig. 18b) demonstrates that the wells with large differences of ±20 °C are located close to the wells with the smaller differences of ±10 °C or even ±5 °C. However, there is almost no way to reduce such a large difference because the distance between the wells with different misfits is locally less than the 4 km horizontal resolution provided by our 3-D structural model. Any attempt to reduce the misfit in a particular well with a large misfit will automatically increase the misfit in the closely located well(s) and vice versa. Moreover, the local-scale thermal pattern for each particular well cannot be reproduced during our simulations without including a more detailed lithological section of these wells and surrounding areas. This is technically very difficult in the case of the regional-scale 3-D thermal modelling. Most of the large misfits are possibly caused by relatively local processes, such as fluid flow. In the case of intensive fluid flow, circulation of the heated or cooled fluids through the sedimentary rocks can play an important role in terms of convective or advective heat transfers in addition to the modelled regional-scale heat conduction. 6.2 Temperature within the lower part of the 3-D model The modelled temperatures within the lower part of the 3-D model are shown in Fig. 20 by using the temperature maps for four horizontal slices through the 3-D thermal model at depths below sea level of 25, 40, 80 and 100 km. From these maps (Fig. 20), it is even more obvious that the areas beneath the mainland are characterized by lower temperatures compared with the continental margin and the oceanic domain. This is due to the fact that the thermal influence of the lower thermal boundary configuration (Figs 6c and 11) becomes more evident at great depths where the distance to the base of the lithosphere becomes shorter. The deepening of the lower thermal boundary beneath the mainland causes a decrease in temperatures there, whereas the shallowing of the lithosphere–asthenosphere boundary beneath the oceanic domain results in increased modelled temperatures (cf. Figs 6c, 11 and 20). Moreover, the shape of the low-velocity/low-density mantle is reflected by the increased modelled temperatures as a result of the pre-defined 250 °C thermal anomaly at the depth of 100 km projected to the lower thermal boundary, assuming that the low seismic shear wave velocities (e.g. Pilidou et al. 2005; Hejrani et al. 2017) and inferred low densities (Maystrenko et al. 2017) within this atypical mantle are at least partially related to its enhanced temperature in addition to possible compositional variations. In addition to the deep-seated temperature-controlling factors, the near-surface thermal influence is still recognizable at a depth of 25 km. Decreased temperatures within the Lofoten Basin compared with the Røst Basin and the Utrøst Ridge (Fig. 20a) are due to the deep bathymetry and the deposition of the Pleistocene sedimentary rocks, which are thermally not equilibrated. In contrast, the modelled thermal trend is already strongly controlled by the shape of the lower thermal boundary at a depth of 40 km (cf. Figs 6c and 20b). At depths of 80 and 100 km, the white (blank) area corresponds to sublithospheric mantle, that is, located beneath the lower thermal boundary. Therefore, the configuration of the lower thermal boundary, represented by the lithosphere–asthenosphere boundary, has a major impact on the modelled temperature distribution within the deep part of the 3-D model. The calculated temperatures at the Moho discontinuity level (Fig. 21) partially reflect its geometry (Fig. 6b). The key factor controlling the modelled temperature at the Moho is not only its depth position but also the distance between the Moho and the lower thermal boundary, that is the thickness of the lithospheric mantle. Therefore, both Moho depth and the thickness of the lithospheric mantle mainly control the distribution of the modelled temperature at the Moho. In addition, one of the secondary factors is related to a higher radiogenic heat production of the crystalline crust compared to the lithospheric mantle rocks (more than 10 times lower on average) (Table 5). Therefore, the thickness of the crust plays an important role as well. The interaction between these factors can be recognized in the temperature map in Fig. 21 where two maxima of the modelled temperature have different origins. The first temperature maximum (up to more than 800 °C) is located beneath the mainland in the south of the model area where the Moho topography is at its deepest (46–48 km depth on average; Fig. 6b). Therefore, this maximum of the modelled temperature is mainly caused by the depth position of the Moho and partially by the thickening of the internally more heat-productive crystalline crust. The second temperature maximum (up to 800 °C) is located beneath the Lofoten–Vesterålen archipelago (Fig. 21) where the Moho is about 10 km shallower than the previous temperature maximum. However, the lithosphere–asthenosphere boundary is about 25 km deeper beneath the first temperature maximum, indicating that the distance between the Moho and the lower thermal boundary is 25 km more in that location compared with the thinner lithospheric mantle beneath the Lofoten–Vesterålen archipelago. Therefore, the reduced distance from the Moho to the deep heat emanating from the Earth's interior beneath the Lofoten–Vesterålen archipelago plays an important role in addition to the relatively deep position of the Moho there. The rest of the modelled temperatures at the Moho level reflects the dominance of the Moho topography as the controlling factor. Fig. 22 shows the present-day depth to the 1300 °C isotherm which represents the base of the thermal lithosphere. There is a clearly visible uplift of the lithosphere–asthenosphere boundary within the low-velocity/low-density zone of the upper mantle. This uplift reflects the thermal anomaly (+250 °C at 150 km depth) which has been set to at least partially take into account the presence of the low-velocity/low-density zone within the upper mantle. The uplift of the lithosphere–asthenosphere boundary is around 15 km on average compared to the input, present-day, lithosphere–asthenosphere boundary in Fig. 6(c), reaching more than 25 km in the east and being very smoothed in the northwest where it varies from 5 to 10 km. However, the precise amplitude of the uplift is tentative due to uncertainties in transformation of the low-velocity, upper-mantle anomaly into a temperature anomaly (Cammarano et al.2003; Lee 2003; Afonso et al. 2010). 6.3 Vertical slices through the 3-D model Three vertical 2-D slices (Fig. 23) through the 3-D thermal model (Fig. 15) have been selected to illustrate cross-sectional views of the modelled temperatures. The locations of these cross-sections have been chosen to be at the same location as the crustal sections described in Maystrenko et al. (2017). These slices allow us to see the vertical distribution of the modelled temperatures (Fig. 23), in addition to the horizontal ones, shown in Figs 16 and 20. The increased temperature within the low-velocity/low-density mantle is displayed along all three vertical slices in Fig. 23. A zone with increased temperature within the anomalous mantle is especially pronounced near the lithosphere–asthenosphere boundary along the vertical slice 2 (Fig. 23b) which crosses this low-velocity/low-density zone almost in the middle (Fig. 2). In contrast, the vertical slices 1 and 3 cross the marginal parts of the anomalous mantle (Fig. 2) and, therefore, the related increase of temperature is smoother compared with the one in slice 2 (cf. Figs 23a–c). The thermal anomaly within the low-velocity/low-density mantle becomes very smooth at shallow depths where it is almost unrecognizable. A remarkable feature along the vertical slices is the absence of the straightforward correlation between an uplift of the modelled isotherms and the shallow Moho (Fig. 19). This is mostly due to the fact that the lower thermal boundary at the base of the lithosphere is shallow within the western part of the model area. In addition, the thermal influence of the positive thermal anomaly within the anomalous mantle is superimposed on the thermal trend controlled by the configuration of the lower thermal boundary. The thermal influence of the shallowing lithosphere–asthenosphere boundary is more pronounced along slice 3 which crosses the oceanic domain to the west (Fig. 23c). It confirms that the thermal influence of the early Cenozoic continental breakup, reflected by the shallowing base of the lithosphere, is still clearly recognizable within the western part of the Lofoten–Vesterålen margin segment in terms of increased temperatures. The modelled regional-scale thermal pattern is also affected by the insulation effect of the thick low-thermally conductive sedimentary rocks which is particularly obvious along slice 1 where the modelled isotherms are slightly uplifted beneath the Vøring Basin. 6.4 Thermal effect caused by the erosional and depositional processes The transient 3-D thermal modelling shows that the modelled temperatures beneath the reconstructed eroded rocks (Fig. 7) gradually decreased through the Cenozoic (Fig. 24), reaching the highest values at the end of the Cretaceous (Fig. 24a) when the thickness of the eroded material was greatest and consequently the base of the reconstructed rocks was at its maximal burial depth (Fig. 7a). At the end of the Cretaceous, the modelled temperatures beneath the reconstructed rocks could have reached up to 90 °C within the northeastern part of the Vestfjorden Basin and more than 80 °C near Andøya and farther west in the southern part of the Lofoten Ridge (Fig. 24a). The modelled temperatures at the base of the eroded rocks decreased as a result of the Cenozoic uplift and erosion, indicating a progressive cooling of the Lofoten–Vesterålen margin and adjacent areas. Decrease in the modelled temperatures is directly proportional to the estimated amount of the material eroded during each time interval (cf. Figs 7 and 24). The thermal effects of the simultaneous erosion and deposition have been estimated by calculating the temperature difference between the results of the 3-D thermal modelling when taking into account or not taking into account the erosion and subsequent deposition. In other words, the calculated temperatures of the model without consideration of the erosion and deposition during the modelling workflow have been subtracted from the modelled temperatures in the case of the model with erosion and deposition. The resulting differences are shown in terms of temperature maps in Fig. 25, showing that a positive thermal anomaly should exist within the areas where the sedimentary and/or crystalline rocks were eroded, whereas the negative values appear to be present in the Vøring and Lofoten basins showing the most important Cenozoic depocentres. Thermal anomalies in Fig. 25 are shown at different depths, indicating that these anomalies are very smooth towards the thermal equilibrium at shallow depths (e.g. 2 km in Fig. 25a), whereas the erosion/deposition-related anomalies are characterized by high amplitudes at greater depths (Figs 25c and d). At a depth of 2 km, the positive anomaly near the Lofoten Ridge is only around 7 °C and the negative one within the Vøring Basin is about −14 °C. In contrast, the erosion-caused positive thermal anomaly within the Vestfjorden Basin is up to 17, 24 and 27 °C and the negative thermal anomaly within the Vøring Basin is almost −33, −47 and −40 °C at 5, 10 and 25 km depth, respectively. The same is true for the negative temperature anomaly modelled beneath the Lofoten Basin where the amplitudes vary with depth from −33 °C at 5 km depth to almost −64 °C at 25 km depth. Our results support the previous 2-D modelling by Pascal & Midttømme (2006) who concluded that the thermal state of the southeastern part of our study area was likely affected by strong modifications due to glacial erosion and deposition during the Quaternary. According to the calculated 3-D temperature cube, the differences between the modelled temperature with and without the thermal effect caused by erosion and deposition or, in other words, the obtained erosion-related positive thermal anomaly reaches its maximum of more than +27 °C at depths of 17–22 km beneath the eastern part of the Vestfjorden Basin. The deposition-related negative anomaly is situated within the northeastern part of the Vøring Basin, showing a minimal value of c. −48 °C at 12–14 km depth. The most prominent negative anomaly is characterized by a minimum of c. −70 °C at 17–20 km depth beneath the oceanic Lofoten Basin. These zones of maxima and minima of the obtained thermal anomalies are mainly associated with the areas where relatively rapid erosion and deposition took place during late Cenozoic time in the Pleistocene, reflecting the thermal effect of heat advection by solid rocks due to vertical movements of these rocks in addition to heat conduction between the upper and lower thermal boundaries. Moreover, the above-described erosion/deposition-related thermal disturbances beneath the Vestfjorden and Vøring basins are still recognizable at more than 60 km depth within the continental margin. On the other hand, the negative thermal anomaly is already very smooth at 55 km depth beneath the Lofoten Basin. The amplitudes of the positive and negative thermal anomalies are mainly controlled by the distances to the upper and lower thermal boundaries because the system reaches a thermal equilibrium faster at shorter distances to the boundary condition. Therefore, the maximum amplitude of these thermal anomalies must be located at some distance from the thermal boundaries. In addition, thermal properties (mainly thermal diffusivity) of rocks play an important role in the distribution of thermally non-equilibrated zones within the 3-D thermal model both vertically and laterally. In other words, erosion or deposition, respectively, decreases or increases the distance between the thermal boundaries, and the conductive thermal field of the 3-D model needs time to reach a thermal equilibrium under these new conditions and also the required equilibration time increases away from the thermal boundaries depending on the thermal properties of rocks. 7 DISCUSSION The regional configuration of the modelled erosion/deposition-induced zones with non-equilibrated temperatures within the study area is dependent on several factors. The most important parameters are the reconstructed thicknesses of the eroded rocks, the local influence of fluid flow, the palaeoclimatic scenario, configuration of the lower thermal boundary, subhorizontal heat advection by solid rocks and the rate of erosion and deposition. One of the most critical factors is the reliability of the reconstructed thickness of the eroded rocks (Fig. 7a), the offshore part of which is based on the published map of NPD (2010) and Eig (2012) and, therefore, is strongly dependent on these input data. In order to validate the reconstructed erosion locally on Andøya, the vitrinite reflectance data of Bjorøy et al. (1980) have been used independently. The comparison shows that if a new kinetic vitrinite reflectance model ‘basin%Ro’ by Nielsen et al. (2017) is used, the estimated maximum burial temperature is around 80 °C on average for the rocks containing the vitrinite reflectance of 0.45%Ro. In the case of our study, the modelled temperature at the base of the total reconstructed thickness of the eroded rocks within the eastern parts of Andøya is also around 80 °C (Fig. 24a). Therefore, this fits very well between the vitrinite reflectance-based and the modelled temperatures. Such similar independent results support our final total thickness estimation of the eroded material within at least the eastern part of Andøya where the rock samples of Cretaceous and Jurassic age were collected and studied by Bjorøy et al. (1980). In addition, our own results demonstrate a gradual decrease of temperature at the present-day surface beneath the eroded succession during the Cenozoic (Fig. 7). This variation coincides with the general trend of decreasing temperatures through the Cenozoic, predicted by independent results of the apatite fission-track analyses onshore (Hendriks & Andriessen 2002; Hendriks et al.2010; Davids et al.2013). However, precise comparison of our modelled temperatures at different time intervals of the Cenozoic with the Cenozoic temperatures according to the apatite fission track analyses is difficult due to the different resolutions of the methods. Based on our total reconstructed thickness of the eroded material at the end of the Cretaceous (Fig. 7a), the main depocentre was localized over the adjacent offshore areas to the Lofoten–Vesterålen archipelago and shows the thickness maxima within the Vestfjorden and near Andøya. This is partially supported by the recent studies on the vertical motions caused by fluvial and glacial erosion with an AFT analysis by Medvedev & Hartz (2015) who have also obtained the thickest eroded succession within NW Vestfjorden and adjacent smaller fjords. However, our own estimation of the erosion within the western part of the Lofoten–Vesterålen archipelago and the adjacent offshore areas is larger compared with that reconstructed by Medvedev & Hartz (2015). It is, however, important to note that Medvedev & Hartz (2015) have already indicated that the exhumation of the outermost (western) Lofoten islands was significantly underestimated in their study and this, therefore, indirectly supports our higher values for the reconstructed thickness there. For completeness, we would like to mention that the restored thickness maximum of the Cenozoic deposits as modelled by Goledowski et al. (2013) is in close proximity to the present-day high elevation of the Scandes Mountains in the study area. Goledowski et al. (2013) also calculated palaeotemperatures of more than 60–70 °C at the present-day surface beneath this thick reconstructed Cenozoic matrix. However, our estimates do not fit the trend of the reconstructed erosion proposed in Goledowski et al. (2013). In addition, results of inverse modelling of the fission-track data by Hendriks & Andriessen (2002) do not really support a stronger uplift of the high-elevated area on the mainland in relation to the adjacent Lofoten–Vesterålen archipelago (e.g. Hendriks et al.2010; Davids et al.2013), at least within the northern part of the study area. Nevertheless, the limited number of the studied samples does not exclude the possibility proposed by Goledowski et al. (2013). The next important disturbing factor is related to possible fluid flow through both the sedimentary and the crystalline rocks within the study area. It has already been mentioned above that some of the large misfits between the modelled and observed temperatures in the wells offshore may indicate a local disturbance of the regional conductive thermal field by additional convective and/or advective heat transfer caused by the circulation of fluids (mainly groundwater) through the Mesozoic–Cenozoic sedimentary rocks. Theoretically, the conditions are especially favourable for the fluid flow through the less consolidated uppermost part of the sedimentary cover represented by the young sedimentary rocks of the Naust Formation within the Lofoten–Vesterålen margin and the Vøring Basin and its analogues within the Lofoten Basin. The possibility of significant fluid flow is supported by the ocean drilling program (ODP Site 642) which is located farther south on the Vøring Plateau. This well shows evidence of a relatively strong fluid inflow (Channell et al.2005). Therefore, the modelled temperatures can be theoretically disturbed by the fluid circulation through very porous sedimentary rocks which are expected to be present within the uppermost Cenozoic sedimentary successions. Moreover, the theoretical differentiation between upper and middle crystalline crust into blocks with different radiogenic heat production (Fig. 14) can alternatively be indicative for the temperatures enforced by the fluid flow within the sedimentary cover in places with the assigned increased radiogenic heat production and vice versa. Furthermore, the results of 2-D modelling of coupled groundwater flow and heat transfer (Maystrenko et al.2015a) point to a possibility of groundwater flow through the crystalline rocks onshore, implying that the modelled erosion-induced positive thermal anomaly can, in reality, be significantly reduced and/or even locally enhanced by a differently cooled and/or heated groundwater, respectively. The influence of the groundwater flow could have been especially strong during the melting of the ice sheets. The resulting cold water could advectively cool the subsurface by flowing through the faults and cracks that were reactivated during tectonic the related isostatic uplift. Possible undulations of the inferred palaeotemperatures at the Earth's surface and on the seafloor (Figs 8 and 10; Tables 2–4) can also affect the calculated thermal anomalies at shallow depths (mainly within 2 km from the upper thermal boundary). It is obvious that the palaeoclimatic scenario employed here is rather simplified for the greater part of the Cenozoic prior to the Weichselian glacial period c. 110 000 yr ago (Table 4). In addition, the relatively detailed palaeotemperature distribution during the Weichselian glaciation (Fig. 10) is partially uncertain and could have varied significantly. The main uncertainties are also related to some parts of the study area which were periodically free of ice and seawater. Therefore, the modelled temperature, especially near the coastline within the areas with shallow bathymetry, can possibly be affected by the uncertainties in the Weichselian palaeoclimatic conditions within those areas. The next uncertainty concerns the changes of rock porosities due to variations in the shallow palaeobathymetry (shallower than 700 m) and the shape of the ice sheet on the continental shelf. The influence of the present-day bathymetry on the continental shelf is indirectly included by the depth-dependent porosity according to exponential functions of increasing densities with depth in Maystrenko et al. (2017) because these empirical functions are based on the offshore well data and also taking into account the bathymetry. Moreover, the changes in deep bathymetry (deeper than 700 m) within the oceanic lithospheric domain have been included in the workflow of the modelling through the Cenozoic by considering the deepening of the seafloor with time due to cooling of the oceanic lithosphere (e.g. Stein & Stein 1992). Unfortunately, the changes in the shallow bathymetry within the present-day continental shelf cannot be properly quantified, but these changes were not more than 140 m during the last 120 000 yr (Hasenclever et al.2017) and were also not significant during the greater part of the Cenozoic that is reflected by more or less continuous sedimentation. The areas with reconstructed eroded material (Fig. 7) are most likely characterized by the very low sea level and/or were above sea level for a large part of the Cenozoic. The thickness of the ice sheet during the last glaciation could have reached more than 1 km onshore (Siegert et al.2001) where glaciers covered the crystalline rocks and remaining sedimentary rocks, which were already affected by compaction at more than 1 km palaeoburial depth at the end of the Cretaceous (cf. Figs 7a and f), thus implying that the load of the ice sheet could not have drastically changed the compaction parameters of the underlying substrate. The present-day offshore areas were mostly free of ice during the last glaciation (Olsen et al.2013; Fig. 9) and the thickness of the ice sheet was comparable with bathymetry during time intervals when the ice sheet expanded on the present-day continental shelf and replaced the seawater (Siegert et al.2001). Based on the statements above, fluctuations of the sea level and the ice sheet load did not significantly affect the porosities of the underlying rocks and, therefore, their influence can be neglected on the continental shelf and the mainland in our regional-scale study. Figure 9. View largeDownload slide Ice cover variations during the Weichselian glacial period according to Olsen et al. (2013). The magenta frame corresponds to the 3-D structural/thermal model. Figure 9. View largeDownload slide Ice cover variations during the Weichselian glacial period according to Olsen et al. (2013). The magenta frame corresponds to the 3-D structural/thermal model. Figure 10. View largeDownload slide Average palaeotemperatures at the Earth’s surface and the seafloor during the Weichselian glacial period within the area covered by the 3-D structural/thermal model. Figure 10. View largeDownload slide Average palaeotemperatures at the Earth’s surface and the seafloor during the Weichselian glacial period within the area covered by the 3-D structural/thermal model. In addition, the configuration of the lower thermal boundary (Figs 6c and 11) is also partially uncertain, especially for the time steps 55 and 18 Ma ago and within the low-velocity/low-density zone within the upper mantle. It is obvious that the thermal influence of the younger oceanic lithosphere was stronger compared to that of the present-day, but the magnitude of this difference related to breakup is still difficult to estimate precisely. The same is true for the predefined +250 °C thermal anomaly at 150 km depth projected to the lower thermal boundary which must be theoretically present within the low-density/velocity mantle, but again the precise amplitude of this anomaly is uncertain. Moreover, the geometry of the lithosphere–asthenosphere boundary itself is somewhat speculative within the anomalous mantle area of the continental margin which also contributes to the uncertainties in the modelled temperatures with depth towards the lower thermal boundary. According to Maystrenko et al. (2014), two possible cases with ± 20 km depth to the lithosphere–asthenosphere boundary in relation to the preferred depth at 120 km have been examined in terms of thermal influences of these probable depth variations of the base of the lithosphere. The thermal influence of the examined depths of the lower thermal boundary decreases towards the Earth's surface. Deviations of the modelled temperature reach ∼4 per cent at 6 km depth for the 20 km deeper base of the lithosphere and ∼12 per cent for the 20 km shallower one. This sensitivity test indicates that an influence of the lower thermal boundary at the shallower depths is important because the distance between the lower and upper boundaries becomes smaller. According to Leroy et al. (2008), the conductive thermal evolution of continental passive margins during 80 million years after the breakup is characterized by a thermal thinning of the unstretched continental lithosphere and by a thermal thickening in the stretched continental lithosphere. The thermal thickening of the stretched lithosphere is considered to arise by deepening of the base of the lithosphere during the post-breakup time beneath the oceanic domain and in its close vicinity. In contrast, thermal thinning of the unstretched lithosphere beneath the present-day mainland has not been included into the workflow due to a presence of the upper-mantle low-velocity/low-density zone effect which could be superimposed or even control the thermal history of the study area beneath the continental domain. Moreover, the thickness of the lithosphere beneath the mainland is more than 120 km, implying that small thermal perturbations at and beyond this depth should not strongly affect our results within the upper part of the model. Figure 11. View largeDownload slide Inferred depths to the lithosphere–asthenosphere boundary corresponding to the 1300 °C isotherm after the continental breakup 55 Ma ago (a) and at the end of the Brygge interval 18 Ma ago (b). The shaded area corresponds to an area where a positive thermal anomaly has been introduced at the base of the lithosphere. COB, continent-ocean boundary; HG, Hel Graben; LV/LDM, low-velocity/low-density mantle; NH, Nyk High; NR, Nordland Ridge; NS, Någrind Syncline; TB, Træna Basin; TP, Trøndelag Platform; UH, Utgard High; VB, Vøring Basin. Figure 11. View largeDownload slide Inferred depths to the lithosphere–asthenosphere boundary corresponding to the 1300 °C isotherm after the continental breakup 55 Ma ago (a) and at the end of the Brygge interval 18 Ma ago (b). The shaded area corresponds to an area where a positive thermal anomaly has been introduced at the base of the lithosphere. COB, continent-ocean boundary; HG, Hel Graben; LV/LDM, low-velocity/low-density mantle; NH, Nyk High; NR, Nordland Ridge; NS, Någrind Syncline; TB, Træna Basin; TP, Trøndelag Platform; UH, Utgard High; VB, Vøring Basin. Figure 12. View largeDownload slide Example of a plot showing stratigraphy, total natural gamma and calculated radiogenic heat production for one of the wells (well 6507/5-1) used to calculate the radiogenic heat production of sedimentary infill (the stratigraphy and gamma-ray log are from NPD (2017)). Figure 12. View largeDownload slide Example of a plot showing stratigraphy, total natural gamma and calculated radiogenic heat production for one of the wells (well 6507/5-1) used to calculate the radiogenic heat production of sedimentary infill (the stratigraphy and gamma-ray log are from NPD (2017)). Figure 13. View largeDownload slide Radiogenic heat production of the sedimentary layers, based on the well data: the Naust (Middle Miocene-Pleistocene) formation (a), the Kai Formation (b), Brygge (Eocene-lower Miocene) Formation (c), the Upper Cretaceous-Palaeocene (d), the Lower Cretaceous (e) and the pre-Cretaceous (f). Black circles indicate locations of the wells used to derive the radiogenic heat production. COB, continent-ocean boundary; TP, Trøndelag Platform; VB, Vøring Basin. Figure 13. View largeDownload slide Radiogenic heat production of the sedimentary layers, based on the well data: the Naust (Middle Miocene-Pleistocene) formation (a), the Kai Formation (b), Brygge (Eocene-lower Miocene) Formation (c), the Upper Cretaceous-Palaeocene (d), the Lower Cretaceous (e) and the pre-Cretaceous (f). Black circles indicate locations of the wells used to derive the radiogenic heat production. COB, continent-ocean boundary; TP, Trøndelag Platform; VB, Vøring Basin. Figure 14. View largeDownload slide Radiogenic heat production of the upper crystalline crust (a; layers 10–11) and the middle crystalline crust (b; layer 12). COB, continent-ocean boundary; HG, Hel Graben; NH, Nyk High; NR, Nordland Ridge; NS, Någrind Syncline; TB, Træna Basin; TP, Trøndelag Platform; UH, Utgard High; VB, Vøring Basin. Figure 14. View largeDownload slide Radiogenic heat production of the upper crystalline crust (a; layers 10–11) and the middle crystalline crust (b; layer 12). COB, continent-ocean boundary; HG, Hel Graben; NH, Nyk High; NR, Nordland Ridge; NS, Någrind Syncline; TB, Træna Basin; TP, Trøndelag Platform; UH, Utgard High; VB, Vøring Basin. Figure 15. View largeDownload slide The lithosphere-scale 3-D thermal model of the Lofoten–Vesterålen segment of the Mid-Norwegian continental margin and adjacent areas. Exaggerated slightly more than three times vertically. Figure 15. View largeDownload slide The lithosphere-scale 3-D thermal model of the Lofoten–Vesterålen segment of the Mid-Norwegian continental margin and adjacent areas. Exaggerated slightly more than three times vertically. The results of the 3-D thermal modelling show that the Bivrost Lineament divides the modelled thermal pattern within the study area into two parts with the generally higher temperatures northeast of this lineament within the Lofoten–Vesterålen margin segment and the lower temperatures in the southwest within the Vøring Basin (Figs 16 and 20). The Bivrost Lineament is a deep-seated fault zone, along which sedimentary, crustal and mantle blocks with different lithologies and thicknesses are juxtaposed (Mokhtari & Pegrum 1992; Olesen et al.2002; Maystrenko et al.2017). Therefore, the assigned thermal properties also differ along the lineament, contributing to a thermal differentiation between the Lofoten–Vesterålen and Vøring margin segments. On the other hand, this regularity in temperature distribution within the deep part of the model is mainly controlled by a spatial coincidence between the Bivrost Lineament and the southwestern limit of the low-velocity/low-density upper-mantle anomaly (e.g. Fig. 22), which outlines the predefined positive thermal anomaly at the lower thermal boundary. Besides, the erosion-induced positive thermal anomaly within the Lofoten–Vesterålen margin segment (the Lofoten Ridge, Ribban and Vestfjorden basins) and the accompanying negative anomaly within the northeastern part of the Vøring Basin significantly affect the temperature distribution in the upper part of the model (Fig. 25) and are also responsible for the higher modelled temperatures northeast of the Bivrost Lineament and the lower ones southwest of this lineament. Unfortunately, there are only a few available wells with measured temperatures northeast of the Bivrost Lineament (Fig. 18) and, therefore, our results cannot be unquestionably verified there. On the other hand, the obtained misfit between the measured and modelled temperatures is acceptable in the available wells (Fig. 18b), supporting at least partially our results. Figure 16. View largeDownload slide Maps with modelled temperatures at the present day within the upper part of the 3-D thermal model (Fig. 15), represented by the temperature horizontal slices for the depths (below sea level) of 2 km (a), 5 km (b), 7 km (c), 10 km (d), 15 km (e) and 18 km (f). The black dashed line corresponds to the present-day shelf edge and the white area in panel (a) corresponds to the area where the sea bottom is located deeper than 2 km. COB, continent-ocean boundary; HG, Hel Graben; NH, Nyk High; NR, Nordland Ridge; NS, Någrind Syncline; TB, Træna Basin; TP, Trøndelag Platform; UH, Utgard High; VB, Vøring Basin. Figure 16. View largeDownload slide Maps with modelled temperatures at the present day within the upper part of the 3-D thermal model (Fig. 15), represented by the temperature horizontal slices for the depths (below sea level) of 2 km (a), 5 km (b), 7 km (c), 10 km (d), 15 km (e) and 18 km (f). The black dashed line corresponds to the present-day shelf edge and the white area in panel (a) corresponds to the area where the sea bottom is located deeper than 2 km. COB, continent-ocean boundary; HG, Hel Graben; NH, Nyk High; NR, Nordland Ridge; NS, Någrind Syncline; TB, Træna Basin; TP, Trøndelag Platform; UH, Utgard High; VB, Vøring Basin. Figure 17. View largeDownload slide Modelled present-day temperatures at the top of the crystalline basement. The black dashed line corresponds to the present-day shelf edge. COB, continent-ocean boundary; HG, Hel Graben; NH, Nyk High; NR, Nordland Ridge; NS, Någrind Syncline; TB, Træna Basin; TP, Trøndelag Platform; UH, Utgard High; VB, Vøring Basin. Figure 17. View largeDownload slide Modelled present-day temperatures at the top of the crystalline basement. The black dashed line corresponds to the present-day shelf edge. COB, continent-ocean boundary; HG, Hel Graben; NH, Nyk High; NR, Nordland Ridge; NS, Någrind Syncline; TB, Træna Basin; TP, Trøndelag Platform; UH, Utgard High; VB, Vøring Basin. Figure 18. View largeDownload slide Locations of the available wells with the measured temperatures and spatial distribution of the temperature variations (measured temperatures minus the modelled ones) within the 3-D model area. (a) Wells with drill-stem test (DST) temperatures offshore and temperature logs onshore and (b) wells with less reliable bottom-hole temperatures (BHT) together with temperatures in the wells in Fig. 18(a). Black dashed line corresponds to the present-day shelf edge. Figure 18. View largeDownload slide Locations of the available wells with the measured temperatures and spatial distribution of the temperature variations (measured temperatures minus the modelled ones) within the 3-D model area. (a) Wells with drill-stem test (DST) temperatures offshore and temperature logs onshore and (b) wells with less reliable bottom-hole temperatures (BHT) together with temperatures in the wells in Fig. 18(a). Black dashed line corresponds to the present-day shelf edge. Figure 19. View largeDownload slide Comparison of the modelled (blue dots) and the observed (red dots) temperatures for the available wells with only drill-stem test (DST) temperatures and temperature logs (a) and bottom-hole temperatures (BHT) together with temperatures in Figs 18(a) and 19(a). Figure 19. View largeDownload slide Comparison of the modelled (blue dots) and the observed (red dots) temperatures for the available wells with only drill-stem test (DST) temperatures and temperature logs (a) and bottom-hole temperatures (BHT) together with temperatures in Figs 18(a) and 19(a). Figure 20. View largeDownload slide Maps with modelled temperatures at the present day within the lower part of the 3-D thermal model (Fig. 15), represented by the temperature horizontal slices below sea level for the depths of 25 km (a), 40 km (b), 80 km (c) and 100 km (d). The white areas correspond to the asthenosphere. COB, continent-ocean boundary; HG, Hel Graben; LV/LDM, low-velocity/low-density mantle; NH, Nyk High; NR, Nordland Ridge; NS, Någrind Syncline; TB, Træna Basin; TP, Trøndelag Platform; UH, Utgard High; VB, Vøring Basin. Figure 20. View largeDownload slide Maps with modelled temperatures at the present day within the lower part of the 3-D thermal model (Fig. 15), represented by the temperature horizontal slices below sea level for the depths of 25 km (a), 40 km (b), 80 km (c) and 100 km (d). The white areas correspond to the asthenosphere. COB, continent-ocean boundary; HG, Hel Graben; LV/LDM, low-velocity/low-density mantle; NH, Nyk High; NR, Nordland Ridge; NS, Någrind Syncline; TB, Træna Basin; TP, Trøndelag Platform; UH, Utgard High; VB, Vøring Basin. Figure 21. View largeDownload slide Modelled present-day temperatures at the Moho. COB, continent-ocean boundary; HG, Hel Graben; LV/LDM, low-velocity/low-density mantle; NH, Nyk High; NR, Nordland Ridge; NS, Någrind Syncline; TB, Træna Basin; TP, Trøndelag Platform; UH, Utgard High; VB, Vøring Basin. Figure 21. View largeDownload slide Modelled present-day temperatures at the Moho. COB, continent-ocean boundary; HG, Hel Graben; LV/LDM, low-velocity/low-density mantle; NH, Nyk High; NR, Nordland Ridge; NS, Någrind Syncline; TB, Træna Basin; TP, Trøndelag Platform; UH, Utgard High; VB, Vøring Basin. Figure 22. View largeDownload slide Depth to the calculated 1300 °C isotherm at the present day, representing the present-day thermal lithosphere–asthenosphere boundary. COB, continent-ocean boundary; HG, Hel Graben; LV/LDM, low-velocity/low-density mantle; NH, Nyk High; NR, Nordland Ridge; NS, Någrind Syncline; TB, Træna Basin; TP, Trøndelag Platform; UH, Utgard High; VB, Vøring Basin. Figure 22. View largeDownload slide Depth to the calculated 1300 °C isotherm at the present day, representing the present-day thermal lithosphere–asthenosphere boundary. COB, continent-ocean boundary; HG, Hel Graben; LV/LDM, low-velocity/low-density mantle; NH, Nyk High; NR, Nordland Ridge; NS, Någrind Syncline; TB, Træna Basin; TP, Trøndelag Platform; UH, Utgard High; VB, Vøring Basin. Figure 23. View largeDownload slide Present-day distribution of the modelled temperatures along three selected 2-D vertical slices through the 3-D thermal model (for the location see Fig. 2). LAB, lithosphere–asthenosphere boundary; TCB, top of the crystalline basement. Figure 23. View largeDownload slide Present-day distribution of the modelled temperatures along three selected 2-D vertical slices through the 3-D thermal model (for the location see Fig. 2). LAB, lithosphere–asthenosphere boundary; TCB, top of the crystalline basement. Figure 24. View largeDownload slide Temperatures at the base of the eroded sediments: at the end of the Cretaceous (a), at the end of the Palaeocene (b), at the end of the Brygge (c), at the end of the Kai (d), at the end of the Naust N (e) and at the end of the Naust A (f). The black dashed line corresponds to the present-day shelf edge. COB, continent-ocean boundary; HG, Hel Graben; NH, Nyk High; NR, Nordland Ridge; NS, Någrind Syncline; TB, Træna Basin; TP, Trøndelag Platform; UH, Utgard High; VB, Vøring Basin. Figure 24. View largeDownload slide Temperatures at the base of the eroded sediments: at the end of the Cretaceous (a), at the end of the Palaeocene (b), at the end of the Brygge (c), at the end of the Kai (d), at the end of the Naust N (e) and at the end of the Naust A (f). The black dashed line corresponds to the present-day shelf edge. COB, continent-ocean boundary; HG, Hel Graben; NH, Nyk High; NR, Nordland Ridge; NS, Någrind Syncline; TB, Træna Basin; TP, Trøndelag Platform; UH, Utgard High; VB, Vøring Basin. Vertical heat advection by solid rocks (e.g. Mancktelow & Grasemann 1997; Stüwe 2007) has been considered during the 3-D thermal modelling by thickness changes of the eroded and deposited material at different steps of the 3-D thermal modelling when the position of the upper thermal boundary has been changed accordingly. However, a subhorisontal heat advection by solid rocks could complicate the obtained thermal pattern in Fig. 25. The subhorisontal heat advection by solid rocks could be especially important within the Lofoten Basin where the Pleistocene and older, large-scale, submarine slides have been documented by interpretation of the reflection seismic lines (Fiedler & Faleide 1996; Hjelstuen et al.2007). According to Hjelstuen et al. (2007), the thickness of the Pleistocene mega-slides can be more than 300–400 m within the area of the Lofoten Basin covered by our 3-D model. In this case, the temperature at the bottom of the mega-slides could be higher than the adopted temperature at the seafloor during the 3-D modelling. These mega-slides originated from the SW Barents Sea (Hjelstuen et al.2007) where a positive temperature anomaly due to Cenozoic erosion could have already been significant during the sliding events (e.g. Cavanagh et al.2006). Besides, the sedimentary rocks of the mega-slides could also have been affected by Quaternary glaciations which acted in the opposite direction to the Cenozoic erosion, decreasing temperature within the sedimentary cover down to around 2 km depth (Fjeldskaar & Amantov 2018). Therefore, the sedimentary rocks of the late Cenozoic mega-slides were not in thermal equilibrium prior to sliding which makes it problematic in estimating the influence of heat. To include the heat advection during the sliding events, the additional detailed 3-D thermal modelling must be performed within the SW Barents Sea, outside of our study area, which is not in the scope of the present study. In any case, the expected thermal effect of solid-rock, subhorisontal, heat advection may reach a maximum of +10–20 °C if the influence of the glacial events is neglected. However, a decrease of subsurface temperature during the last glaciations within the SW Barents Sea could even theoretically have enhanced the modelled negative thermal anomaly within the Lofoten Basin in Fig. 25. Besides, medium- and small-scale submarine slides are present at the shelf edge within the model area (Hjelstuen et al.2007; Rise et al.2013), but their rather local thermal effect has been neglected during this regional-scale study. Figure 25. View largeDownload slide Thermal anomalies due to erosion and deposition during the Cenozoic, calculated as a difference between the modelled temperatures with the thermal effect of erosion/deposition and the modelled temperatures without this effect. The black dashed line corresponds to the present-day shelf edge and the white area in Fig. 25(a) corresponds to the area where the sea bottom is located deeper than 2 km. COB, continent-ocean boundary; HG, Hel Graben; NH, Nyk High; NR, Nordland Ridge; NS, Någrind Syncline; TB, Træna Basin; TP, Trøndelag Platform; UH, Utgard High; VB, Vøring Basin. Figure 25. View largeDownload slide Thermal anomalies due to erosion and deposition during the Cenozoic, calculated as a difference between the modelled temperatures with the thermal effect of erosion/deposition and the modelled temperatures without this effect. The black dashed line corresponds to the present-day shelf edge and the white area in Fig. 25(a) corresponds to the area where the sea bottom is located deeper than 2 km. COB, continent-ocean boundary; HG, Hel Graben; NH, Nyk High; NR, Nordland Ridge; NS, Någrind Syncline; TB, Træna Basin; TP, Trøndelag Platform; UH, Utgard High; VB, Vøring Basin. In fact, the amplitudes of the calculated, erosion-/deposition-induced, thermal anomalies would be higher, if gradual real-time erosion and deposition had been considered instead of removing or adding packages of rocks through several time-restricted steps as we have done. This is due to the fact that gradual erosion or deposition is extended in time compared to moving packages of rocks at the beginning of each step. Therefore, rocks in places of gradual erosion or deposition are less thermally equilibrated than rocks in places where a package of rocks was added or removed. Unfortunately, the gradual erosion and deposition cannot be modelled by the available modules of the used software. In this case, the obtained positive and negative thermal anomalies should be slightly higher or lower, respectively, if the gradual erosion and deposition had been applied during the thermal modelling. In order to consider in more detail the relationship between erosion/deposition and thermal reequilibration at deeper crustal and mantle levels, a fully coupled, thermomechanical, 3-D modelling approach should be used. For instance, Cacace & Scheck-Wenderoth (2016) have shown that the detailed temporal evolution of the lithospheric strength, which controls the subsidence history, is strongly coupled to the temporal thermal configuration of the lithosphere. Moreover, crustal faulting has played an important role in both structural and thermal configuration of the continental margins (e.g. Clift et al. 2002; Geoffroy et al.2015), implying that movements of the crustal blocks along the major faults could represent a significant heat advection by solid rocks. Therefore, our results of the transient 3-D thermal modelling are a good starting point to create a dynamical thermomechanical model for the Lofoten–Vesterålen continental margin and adjacent areas, allowing us to minimize all the uncertainties mentioned above. 8 CONCLUSIONS The obtained results of the time-dependent 3-D conductive thermal modelling for the Lofoten–Vesterålen margin, the northeastern Vøring Basin and adjacent areas demonstrate that the present-day subsurface temperature is characterized by the presence of thermally non-equilibrated zones clearly influenced by the Cenozoic erosion and deposition within the study area. The erosion-induced positive thermal anomaly has its maximum of more than +27 °C at depths of 17–22 km beneath the eastern part of the Vestfjorden Basin where erosion has been particularly strong during the last 2.7 million years. The accompanying negative anomaly within the northeastern part of the Vøring Basin has minimal values of around −48 °C at 12–14 km depth and is mainly the result of the relatively rapid deposition of the Naust Formation during the Pleistocene. Moreover, the most intensive deposition-related negative anomaly is almost −70 °C at 17–20 km depth beneath the oceanic Lofoten Basin where the rapid Pleistocene deposition was accompanied by submarine mega-sliding of the sedimentary rocks sourced from the Barents Sea. Besides, the thermal influence of the early Cenozoic lithospheric thinning and the continental breakup with formation of new oceanic lithosphere is still recognizable within the western part of the Lofoten–Vesterålen region in terms of the increasing temperatures towards the oceanic domain recorded within the obtained 3-D thermal model. In addition to heat conduction, convective and/or advective heat transfer by fluids is indicated by large misfits between the modelled and measured temperatures within some local wells which are located relatively close to the majority of the wells with much better fits, implying that the modelled erosion/deposition-related thermal anomalies could also be theoretically affected by the groundwater flow. Acknowledgements This study has been supported in the framework of the NEONOR2 project by the Norwegian Research Council, the Geological Survey of Norway, the Norwegian Petroleum Directorate, the Norwegian Mapping Authority, Aker BP, DEA Norge, DONG Norge, E.ON Norge, Lundin Norway, Maersk Oil Norway, Norske Shell, Norwegian Energy Company (Noreco), Repsol Exploration Norge, Statoil and VNG Norge. Special thanks go to Mauro Cacace from the Helmholtz Centre Potsdam, GFZ German Research Centre for Geosciences for his help with the code for creating the 3-D mesh of the geometrically complex layers. We are grateful to Alexander Minakov and an anonymous reviewer for their very helpful comments which improved our manuscript. Our gratitude also goes to David Roberts for improvement of the English. REFERENCES Afonso J.C., Ranalli G., Fernandez M., 2005. Thermal expansivity and elastic properties of the lithospheric mantle: results from mineral physics of composites, Phys. Earth planet. 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TI - 3-D thermal effect of late Cenozoic erosion and deposition within the Lofoten–Vesterålen segment of the Mid-Norwegian continental margin
JF - Geophysical Journal International
DO - 10.1093/gji/ggy013
DA - 2018-05-01
UR - https://www.deepdyve.com/lp/oxford-university-press/3-d-thermal-effect-of-late-cenozoic-erosion-and-deposition-within-the-MYhonIC6iN
SP - 885
EP - 918
VL - 213
IS - 2
DP - DeepDyve
ER -