# Electrical anisotropy in the presence of oceans—a sensitivity study

Electrical anisotropy in the presence of oceans—a sensitivity study Summary Electrical anisotropy in the presence of oceans is particularly relevant at continent–ocean subduction zones (e.g. Cascadian and Andean Margin), where seismic anisotropy has been found with trench-parallel or perpendicular fast direction. The identification of electrical anisotropy at such locations sheds new light on the relation between seismic and electrical anisotropies. At areas confined by two opposite oceans, for example the Pyrenean Area and Central America, we demonstrate that the superposed responses of both oceans generate a uniform and large phase split of the main phase tensor axes. The pattern of the tipper arrows is comparatively complicated and it is often difficult to associate their length and orientation to the coast effect. On the basis of simple forward models involving opposite oceans and anisotropic layers, we show that both structures generate similar responses. In the case of a deep anisotropic layer, the resistivity and phase split generated by the oceans alone will be increased or decreased depending on the azimuth of the conducting horizontal principal axes. The 3-D isotropic inversion of the anisotropic forward responses reproduces the input data reasonably well. The anisotropy is explained by large opposed conductors outside the station grid and by tube-like elongated conductors representing a macroscopic anisotropy. If the conductive direction is perpendicular to the shorelines, the anisotropy is not recovered by 3-D isotropic inversion. Electrical anisotropy, Geomagnetic induction, Magnetotellurics, Numerical modelling INTRODUCTION The primary goal of a magnetotelluric (MT) survey is the retrieval of the resistivity structure of the subsurface from natural time variations of the electromagnetic field components measured at the Earth's surface. Directional properties of the resistivity structure are of special interest as they can indicate geodynamic processes or be related to the strike of geological structures or preferential pathways of fluid and melt. In coastal regions, the oceans, as bodies of highly conductive sea water (∼0.25 Ω·m), represent the main conductive bodies at near-surface depth and thus have a large impact on electromagnetic induction studies, called the coast effect. This effect superposes the electromagnetic responses of the subsurface aggravating the identification of geological structures. A special case is constituted by opposite oceans. Their influence causes a rather homogenous phase split and rather small induction arrows at sites in between where the induced coast effects cancel each other out. A similar pattern of phase tensors and induction arrows is often associated with anisotropic conductivity structures (Bahr & Simpson 2002; Gatzemeier & Moorkamp 2005; Häuserer & Junge 2011; Löwer 2014). This resemblance makes the identification of anisotropic data characteristics very difficult in the presence of oceans. However, as electrical anisotropy might be related to and reflect geodynamic processes as subduction of oceanic lithosphere, it is crucial to distinguish between ocean and anisotropic responses. Seismic anisotropy has been found in most subduction zones (e.g. Cascadian and Andean Margin) with trench-parallel or perpendicular fast directions (Long & Silver 2008). The determination of electrical anisotropy at such locations can shed new light on the relation between seismic and electrical anisotropies (e.g. Gatzemeier & Moorkamp 2005; Hamilton et al. 2006). BACKGROUND First observed near the coast in Australia (Parkinson 1959) and Japan (Rikitake 1959), the coast effect causes large anomalous magnetic variations in coastal regions (Parkinson 1962). At long periods, it can be recognized up to several hundreds of kilometres inland and strongly depends on the shape of the coastline and the bathymetry of the adjacent ocean. Moreover, the resistivity structure beneath the oceans and continents plays an important role and can intensify, attenuate or deflect the influence of the oceans (e.g. Parkinson & Jones 1979; Mackie et al. 1988; Thiel et al. 2009; Brasse et al. 2009a; Thiel & Heinson 2010; Wannamaker et al. 2014). The impedance function and the tipper arrows are affected by the coast effect (Santos et al. 2001). The coast effect in MT studies is addressed by implementing the oceans as prior information into the 2-D or 3-D inversion and forward models (e.g. Becken et al. 2008; Tietze & Ritter 2013; Meqbel et al. 2014; González-Castillo et al. 2015) or by previously separating the coast effect from the transfer functions (e.g. Weaver & Agarwal 1991; Santos et al. 2001). If the oceans are not incorporated into the prior model, the inversion algorithm will implement highly conductive and local anomalies along the shorelines. The 2-D effect of two opposite oceans was studied by Dosso & Meng (1992) for vertical magnetic transfer functions (VTF) and Malleswari & Veeraswamy (2014) for impedance functions. Kanda & Ogawa (2014) conducted a 3-D MT study in NE Japan. They inverted VTF for the period range 16–256 s and included the Sea of Japan and parts of the adjacent Pacific Ocean as prior information into the 100 Ω·m background model. The forward response of the bathymetry model indicated that the coast effects produced by each ocean individually did not superpose for the observed period range. For the general 3-D isotropic case, the split of the phase tensor's principal axis is caused by horizontal conductivity gradients, involving non-zero tippers. For the 1-D case comprising an electrical anisotropic layer, the split results from the vertical conductivity change at the interface between the isotropic and anisotropic layers depending on the azimuth (Heise et al. 2006). The main phase values represent the contrast between the principal conductivities of the anisotropy and the conductivity of the isotropic layer. Due to the absence of lateral resistivity gradients, the phase split involves induction arrows of zero lengths. Isotropic inversion of theoretical anisotropic data was done in 2-D by Heise & Pous (2001) and in 3-D by Löwer & Junge (2017). Their inversion models exhibited alternating isotropic structures of high and low resistivities explaining the data reasonably well. Weidelt (1999) predicted that an arbitrary complex isotropic model is able to reproduce an intrinsic anisotropic resistivity distribution by macroscopic isotropic structures, provided that the model discretization is fine enough. An overview of anisotropic studies is given in Martí (2014). In this study, we focus on phase tensors (Caldwell et al. 2004) and tipper arrows (Wiese 1962), since they are not affected by near-surface resistivity inhomogeneities. We first study the effect of opposite oceans for two prominent ocean–continent–ocean regions: the Pyrenean area and Central America. For MT studies conducted in the Pyrenees, see example Pous et al. (1995), Ledo (1996), Ledo et al. (2000), Campanyà et al. (2011, 2012), Campanyà (2013) and Cembrowski (2017). MT studies in Mexico and Central America have been performed by, for example Elming & Rasmussen (1997), Jording et al. (2000), Jödicke et al. (2006), Brasse et al. (2009a,b) and Worzewski et al. (2011). Other examples of similar ocean–continent–ocean areas are from South East Asia, Japan and Italy. Furthermore, we show the similarity of ocean and anisotropic responses by comparing the data response of a simple ocean–continent–ocean model to the response of a 1-D model with an anisotropic layer. Additional models are constructed that involve both conductivity anomalies: opposite oceans and anisotropic layers. It will be shown that depending on the strike of the anisotropy, that is the most conducting horizontal direction, the phase split is increased or decreased. We perform 3-D isotropic inversions of the anisotropic forward responses and study the isotropic resistivity pattern of the originally anisotropic body reproducing the phase split. Our results reveal possible anisotropic features behind ostensible isotropic resistivity patterns and broaden the scope of geological interpretation. METHODOLOGY: 3-D FORWARD MODELING AND INCLUSION OF OCEANS Data were simulated using the MT3D software, which is briefly described in this section; for details see Löwer (2014). The MT3D code is written in MATLAB and accesses COMSOL Multiphysics 4.3 via the MATLAB-Comsol-Livelink. The forward responses for all stations and frequencies are calculated from several models, as the models depend on the target frequency and station location. The model volumes are described by three concentric half spheres embedded in a cuboid (Fig. 1a). The sizes of the cubic box (4) and the outermost sphere (3) depend on the respective skin depth (δmax) for the highest resistivity used in the constructed model. However, this value can be increased in order to consider the horizontal adjustment length when incorporating oceans into the model (Ranganayaki & Madden 1980; Simpson & Bahr 2005). The dimensions of the cubic box are 6δmax × 6δmax × 3δmax, the outermost sphere features a radius of 1.5δmax. The sizes of the two inner spheres (1, 2) can be chosen due to the requirements of the constructed resistivity distribution. A 3-D tetrahedral mesh is defined within the model volume with the highest grid resolution in the centre and coarsening towards the outermost boundaries with the element sizes and growth rates depending on the dimensions of the cubic box and concentric spheres. The numerical investigation area is positioned at the centre of the spheres, so that the highest grid resolution is achieved beneath that area. In this way, different models with about 250.000–400.000 mesh elements are generated. Figure 1. View largeDownload slide Example of a model volume for 1000 s. (a) The model volume is composed of concentric half spheres (1, 2, 3) embedded in a cubic box (4). The dimensions of the cubic box and of the half spheres are adapted to the resistivity distribution of the constructed model. The tetrahedral grid that continuously coarsens to the boundary of the model space is only shown at the boundaries. (b) Bathymetry model at z = 0 m for 1000 s of southwest Europe including parts of the Atlantic and the Mediterranean. The onshore resistivity and the resistivity outside of the half spheres are set to 500 Ω·m. Figure 1. View largeDownload slide Example of a model volume for 1000 s. (a) The model volume is composed of concentric half spheres (1, 2, 3) embedded in a cubic box (4). The dimensions of the cubic box and of the half spheres are adapted to the resistivity distribution of the constructed model. The tetrahedral grid that continuously coarsens to the boundary of the model space is only shown at the boundaries. (b) Bathymetry model at z = 0 m for 1000 s of southwest Europe including parts of the Atlantic and the Mediterranean. The onshore resistivity and the resistivity outside of the half spheres are set to 500 Ω·m. The resistivity model is constructed by assigning resistivity values to a prior defined fixed number of points (SP, support points) in the 3-D environment beneath and adjacent to the investigation area. For each model volume, the SP are linearly interpolated on the relevant finite elements (FE) grid of the three half spheres and a constant background resistivity is ascribed to the gridpoints outside of the outer sphere. The forward modeling, which also allows a 3-D anisotropic resistivity distribution, is performed separately for the different frequencies and regions applying the geometrical scheme mentioned above. This procedure allows a high numerical precision by a preferably low number of FE cells and low number of degrees of freedom. Since the vertical resolution of the FE grid decreases towards the outer boundaries, a simple SP scheme is applied for modeling the influence of the bathymetry (GEBCO, www.gebco.net). The scheme involves modeling the oceans as layers of constant depth to avoid modeling shallow oceans far away from the investigation area. Instead of using the true sea water conductivity (0.25 Ω·m), the modeled ocean resistivity is varied so that the conductance, that is the product of water depth and sea water conductivity, is maintained. It became apparent that two different ocean SP levels at 2 and 10 km depth were sufficient to model the shallow part near the coast and the deep ocean farther away. Fig. 1(b) shows the bathymetry resistivity model for a period of 1000 s with the investigated area in the centre of the half spheres. The resistivity distribution is illustrated in the x–y plane at the surface with the onshore resistivity and the resistivity outside of the concentric half spheres set to 500 Ω·m. The ocean depth near the study area was set to 2 km. The described ocean SP scheme enables the precise modeling of the spatially varying sea water influence and therefore allows an unprecedented study of its effect on MT data. In this study, we focus on phase tensors and tipper arrows (Wiese 1962). Contrary to Caldwell et al. (2004), we do not display the phase tensor as an ellipse with Φmax and Φmin being the major and minor axes, but following the suggestion of Häuserer & Junge (2011), the phase tensor is plotted as orthogonal bars. Hereby, the length and the colour of each bar correspond to the values of Φmax = arctan(Φmax) and Φmin = arctan(Φmin). We find this representation more intuitive since in a 2-D case the arctan(Φmax) and arctan(Φmin) are the phase angles of the complex impedance elements Zxy and Zyx. Moreover, the tangent function has a singularity at ± π/2, and thus Φ is more conspicuous at high phases than at low values. Together with the angle α (tensor's dependence on the coordinate system), the direction of the major axis is given by α − β. In order to compare tipper arrows from different models, we display the difference between the real and imaginary parts (misfit induction vector). As an illustration of the misfit between two (e.g. predicted and observed) phase tensors, Heise et al. (2007, 2008) introduced the misfit tensor defined by $${\rm{\Delta }} = {\rm{I}} - \frac{1}{2}( {{{{\bf \Phi }}_{{\rm{obs}}}}^{ - 1}{{{\bf \Phi }}_{{\rm{pred}}}} + {{{\bf \Phi }}_{{\rm{pred}}}}{{{\bf \Phi }}_{{\rm{obs}}}}^{ - 1}} )$$. Booker (2014) suggested taking the absolute difference between the observed Φobs and the predicted Φpred phase tensor. In our study, we display the invariants of the phase tensor (Φmax, Φmin) and the direction of the major axis (α − β), and therefore we suggest showing their differences (Fig. 2). The differences between the maximum and minimum phases (ΔΦmax, ΔΦmin) are represented by horizontal and vertical black bars with their length illustrating the phase difference. The bars’ origin equals the origin of a unit circle which circumference (R) marks a phase difference of 10°, that is for a phase difference of 10° for ΔΦmax the length of the horizontal bar equals the radius of the circle. If the end of the bar is located inside the circle the misfit is < 10°, for bars crossing the circumference the misfit is > 10°. The colour of the 10° circle shows the clockwise difference between the orientation of the observed and the predicted phase tensor Δ(α − β). For differences Φobs/predmax − Φobs/predmin < 5°, we find the orientation hard to define (α is undefined for Φmax = Φmin) and therefore we choose a green colour denoting a 1-D like situation. The example in Fig. 2 shows the misfit/difference (Fig. 2b) between two phase tensors, pt1 and pt2 (Fig. 2a), which is −5° for the maximum phase, 15° for the minimum phase and 30° (clockwise) for the orientation. Figure 2. View largeDownload slide Example of phase tensor misfit/difference. The misfit (b) is evaluated by plotting the differences between the invariants of pt1 and pt2 (a). The horizontal and the vertical black bars represent the maximum and minimum phase misfits, respectively. The colour of the circle illustrates the difference between the orientations of the phase tensors. If one of the two phase tensors nearly shows a 1-D situation (Φmax < Φmin + 5°), the colour of the circle is green. Figure 2. View largeDownload slide Example of phase tensor misfit/difference. The misfit (b) is evaluated by plotting the differences between the invariants of pt1 and pt2 (a). The horizontal and the vertical black bars represent the maximum and minimum phase misfits, respectively. The colour of the circle illustrates the difference between the orientations of the phase tensors. If one of the two phase tensors nearly shows a 1-D situation (Φmax < Φmin + 5°), the colour of the circle is green. Coast effect Pyrenees The study area comprises the Pyrenean Chain and parts of its foreland basins (Fig. 3). To the east, the Pyrenees are bounded by the Mediterranean Sea with an average water depth of about 1400 m. To the west, the Pyrenees are bounded by the Bay of Biscay as a part of the Atlantic Ocean. The bay is characterized by a large continental shelf with shallow sea water to the northeast and a steep continental slope describing the transition to the deep Atlantic Ocean with depths beyond 4000 m. The shortest distance between both oceans is approximately 370 km. Theoretical transfer functions are calculated at 25 site locations (red dots) equally distributed throughout the area of interest with approximate site distances of about 80 km. Figure 3. View largeDownload slide The study area is the Pyrenean Chain and parts of its foreland basins. The Mediterranean and the Bay of Biscay bound the Pyrenees on both sides and make the Pyrenees an ideal area to study a combined coast effect of two oceans. The bathymetry of the oceans is colour coded to depth intervals of 500 m. Transfer functions are calculated at locations marked by red dots. Figure 3. View largeDownload slide The study area is the Pyrenean Chain and parts of its foreland basins. The Mediterranean and the Bay of Biscay bound the Pyrenees on both sides and make the Pyrenees an ideal area to study a combined coast effect of two oceans. The bathymetry of the oceans is colour coded to depth intervals of 500 m. Transfer functions are calculated at locations marked by red dots. The induction vectors for the bathymetry embedded in different homogeneous background resistivity models (100, 500 and 2000 Ω·m) are shown in Fig. 4 for 100, 1000 and 6250 s. For the period of 100 s (Figs 4a, d and g), the real induction vectors are almost orthogonal to the nearest coastlines naturally pointing away from areas of current concentrations. The imaginary tipper arrows are antiparallel to the real part for all sites and therefore suggest a 2-D structure. Due to the relatively small induction volume for this period, the effects of the oceans do not superimpose. However, the Mediterranean dominates as there is deeper water close to the shoreline. For the period of 1000 s and background resistivities of 500 and 2000 Ω·m (Figs 4e and h), 3-D effects become evident with the imaginary arrows oblique to the real arrows. In Figs 4(f) and (i) (6250 s) both coast effects are superimposed resulting in striking patterns. For the high background resistivity of 2000 Ω·m, the real arrows rotate to the east, influenced by the rather deep bathymetry of the Atlantic Ocean. The comparison of the results clearly shows that the coast effect grows with increasing resistivity and is strongly influenced by the distant bathymetry for long periods. Figure 4. View largeDownload slide Tipper arrows and skew values (coloured circles) showing the coast effect for different homogeneous background resistivities (100, 500 and 2000 Ω·m) for 100, 1000 and 6250 s. Red: real part. Blue: imaginary part. Evidently, the coast effect intensifies with increasing background resistivity and the effect of both oceans is superimposed at the long periods. Moreover, the Atlantic Ocean dominates the coast effect with increasing periods. Especially, the shape of the Bay of Biscay causes high skew values indicating a 3-D resistivity distribution for that area. Figure 4. View largeDownload slide Tipper arrows and skew values (coloured circles) showing the coast effect for different homogeneous background resistivities (100, 500 and 2000 Ω·m) for 100, 1000 and 6250 s. Red: real part. Blue: imaginary part. Evidently, the coast effect intensifies with increasing background resistivity and the effect of both oceans is superimposed at the long periods. Moreover, the Atlantic Ocean dominates the coast effect with increasing periods. Especially, the shape of the Bay of Biscay causes high skew values indicating a 3-D resistivity distribution for that area. The coloured circles in Fig. 4 represent the skew β values corresponding to the phase tensors in Fig. 5. The amount of β generally increases with increasing coast effect indicating the 3-D nature of the bathymetry. Especially, the sites to the south of the Bay of Biscay feature rather high skews β up to 7° for the model with 100 Ω·m background and 12° for the model with 500 Ω·m background. Contrary, the skews to the north of the study area exhibit small absolute values with |β| < 3°, although the obliquity of real and imaginary arrows for long periods (Figs 4f and i) clearly indicates a 3-D situation. Figure 5. View largeDownload slide (a)–(i) Phase tensors showing coast effect for different homogeneous background resistivities (100, 500 and 2000 Ω·m) for 100, 1000 and 6250 s. The coast effect results in a split of maximum and minimum phases with major axes oriented towards the oceans. The phase difference can be seen as a measure of the strength of the coast effect. The superimposed coast effect causes a very uniform phase tensor split and orientation. The differences of the rotational invariants of the phase tensors are illustrated in (j)–(l) between the 500 and the 100 Ω·m model and in (m)–(o) between the 2000 and the 500 Ω·m model. The radius of the circles denotes a phase difference of 10°. Figure 5. View largeDownload slide (a)–(i) Phase tensors showing coast effect for different homogeneous background resistivities (100, 500 and 2000 Ω·m) for 100, 1000 and 6250 s. The coast effect results in a split of maximum and minimum phases with major axes oriented towards the oceans. The phase difference can be seen as a measure of the strength of the coast effect. The superimposed coast effect causes a very uniform phase tensor split and orientation. The differences of the rotational invariants of the phase tensors are illustrated in (j)–(l) between the 500 and the 100 Ω·m model and in (m)–(o) between the 2000 and the 500 Ω·m model. The radius of the circles denotes a phase difference of 10°. Compared to the tipper arrows, the phase tensors show a rather simple behaviour (Figs 5a–i) as the coast effect splits the phase into a maximum (minimum) value greater (less) than 45°with the axis orientation roughly perpendicular (parallel) to the shoreline. The phase difference increases with decreasing distances to the oceans, similar to the length of the induction vector. Due to the position of the oceans flanking the orogen on both sides, the overall phase tensor orientation is very uniform for longer periods. Although the pattern is regionally uniform and thus would suggest a 2-D situation with clear strike direction for longer periods, the corresponding skews β in Fig. 4 show the strong asymmetry of the tensors and indicate the three-dimensionality of the resistivity distribution. The comparison of phase tensors is additionally illustrated with the method described in Fig. 2 (Figs 5j–o). Fig. 6 shows the period-dependent transfer functions (apparent resistivity, impedance phase, phase tensor, induction arrows and skews β) for the sites marked in Fig. 5(d). The station located south of the Bay of Biscay (Fig. 6a) illustrates a clear 3-D situation. With increasing periods the skew increases continuously from 0° to values exceeding 10° and simultaneously the real and imaginary arrows take an oblique direction. In contrast, the skews in the Central Pyrenees (Fig. 6b) remain below 1.5 and thus would indicate a non-3-D situation. However, for the long periods, the phase tensors’ major axes are not aligned with the tipper orientations and real and imaginary arrows are oblique. Figure 6. View largeDownload slide Transfer functions for the stations marked in Fig. 5(d) and the bathymetry model with a 500 Ω·m background resistivity. From top to bottom: apparent resistivities, impedance phases, phase tensors and induction vectors, and skew values. (a) Site south to the Bay of Biscay. (b) Site in the Central Pyrenees. Figure 6. View largeDownload slide Transfer functions for the stations marked in Fig. 5(d) and the bathymetry model with a 500 Ω·m background resistivity. From top to bottom: apparent resistivities, impedance phases, phase tensors and induction vectors, and skew values. (a) Site south to the Bay of Biscay. (b) Site in the Central Pyrenees. Comparison with Central America Central America and Mexico with the Pacific Ocean to the southwest and the Gulf of Mexico and the Caribbean Sea to the northeast is another prominent example of two opposite oceanic bodies (Fig. 7). The adjacent Pacific Ocean is characterized by the Middle America Trench. It is a major subduction zone and is situated about 100 km away from the coast of Central America. It runs roughly parallel to the coastline and marks the transition from the shallow shelf water (< 1 km depth) to the deep Pacific Ocean (> 3 km depth). The eastern coastline is more complicated compared to the western shoreline with a strongly varying bathymetry in the Gulf of Mexico and the Caribbean Sea. Theoretical VTF and phase tensors are calculated for 57 site locations (red circles) for a model with the oceans incorporated in a 500 Ω·m half-space. The results are shown in Fig. 8 for 100, 1000 and 6250 s. For the short periods, the coast effect is restricted within an area near the coastlines with tipper arrows and maximum phases oriented perpendicular to the nearest shorelines (Figs 8a and d). It evidently depends on the water depth close to the adjacent shoreline and it is strongest for sites along the coast of the Pacific Ocean. Significant non-zero skews β are present close to the bays. Towards longer periods, the effect of the deep part of the Pacific Ocean dominates with real and imaginary arrows still being antiparallel near the Pacific coast (Fig. 8b). Most of the phase tensors major axes are oriented southeastwards as a result of the superimposed coast effect of the Pacific and the Gulf of Mexico as well as the Pacific and the Caribbean Sea. To the south of Yucatán, there is an area where the effects of all three oceanic bodies are compensated producing small tippers, phase splits and absolute skew values. For the period of 6250 s, the phase tensors appear very uniform in phase split and orientation. The VTF for this period show the strong influence of the Pacific Ocean with real tipper arrows exceeding the value of 1. Note that even though the colinearity of tipper arrows as well as the uniformity of phase tensors near the Pacific Coast indicate a 2-D situation, the high absolute skew values exceeding 3° for many sites clearly suggest a 3-D situation. Exemplarily, Fig. 9 shows the period-dependent transfer functions for (a) a station close to the Pacific Ocean and (b) a station situated in Belize close to the Caribbean Sea. The exact station locations are marked in Fig. 8(d). Tipper arrows and phase tensors for the site near the Pacific coast suggest a rather 2-D behaviour with very consistent orientations, though the absolute skew values are higher than |3| for longer periods. The strong influence of the Pacific Oceans results in real tipper arrows with a length of more than 1 for longer periods and antiparallel imaginary arrows for all observed periods. An interesting pattern can be observed for the other station, where the skew β has a maximum of 8° at about 800 s and decreases below 3° for longer periods. Figure 7. View largeDownload slide Central America and Mexico is another prominent example of a landmass embedded by large oceans. It is bounded by the Pacific Ocean to the southeast and the Caribbean Sea and the Gulf of Mexico to the northwest. The bathymetry of the oceans is illustrated by colours. Red dots represent the locations at which theoretical transfer functions are calculated. Figure 7. View largeDownload slide Central America and Mexico is another prominent example of a landmass embedded by large oceans. It is bounded by the Pacific Ocean to the southeast and the Caribbean Sea and the Gulf of Mexico to the northwest. The bathymetry of the oceans is illustrated by colours. Red dots represent the locations at which theoretical transfer functions are calculated. Figure 8. View largeDownload slide Coast effect study for Central America and parts of Mexico for 100, 1000 and 6250 s. (a)–(c) Real (red) and imaginary (blue) tipper arrows and skew values (coloured circles). For shorter periods, the arrows are oriented perpendicular to the coastlines. With increasing period, the coast effect of Pacific Ocean dominates. (d)–(f) Phase tensors. The maximum phase of the phase tensors is oriented towards the nearest coastlines for short periods. Phase tensors feature a very uniform orientation and phase split for the long periods. Figure 8. View largeDownload slide Coast effect study for Central America and parts of Mexico for 100, 1000 and 6250 s. (a)–(c) Real (red) and imaginary (blue) tipper arrows and skew values (coloured circles). For shorter periods, the arrows are oriented perpendicular to the coastlines. With increasing period, the coast effect of Pacific Ocean dominates. (d)–(f) Phase tensors. The maximum phase of the phase tensors is oriented towards the nearest coastlines for short periods. Phase tensors feature a very uniform orientation and phase split for the long periods. Figure 9. View largeDownload slide Transfer functions for the stations marked in Fig. 9(d). From top to bottom: apparent resistivities, impedance phases, phase tensors and induction vectors, and skew values. (a) Site close to the Pacific Ocean. Note the tipper scale of 0.4 and real arrows increasing up to 1.4. (b) Site located in Belize. Figure 9. View largeDownload slide Transfer functions for the stations marked in Fig. 9(d). From top to bottom: apparent resistivities, impedance phases, phase tensors and induction vectors, and skew values. (a) Site close to the Pacific Ocean. Note the tipper scale of 0.4 and real arrows increasing up to 1.4. (b) Site located in Belize. The comparison of both coast effect studies shows an equivalent behaviour for the short periods when the different ocean effects do not overlap. The phase tensors’ major axes and tippers are oriented orthogonal to the coastlines with real and imaginary arrows being antiparallel. Towards longer periods, the individual coast effects are superimposed and the phase tensors become very uniform showing similar patterns for both studies. They feature a strong phase split all over the area and the orientation of the maximum phase direction is towards the regional water distribution on both sites. Whereas the coast effect on phase tensors is increased by two opposite oceanic bodies, the combined effect on tipper arrows is more complicated and locations exist where the induced vertical magnetic field reverses sign and the ocean effects cancel each other out. It becomes evident that the combined tipper arrows at long periods strongly depend on the distribution of the deep sea water and the position of the oceanic bodies. Comparison with observations Coast effect studies yield important information for the inversion and modeling of an observed data set. A data example from the Pyrenean Mountain Chain illustrates the importance of coast effect studies (Cembrowski 2017, Fig. 10). The observed phase tensors reveal a large phase split with orientations of the major axes being very similar to the synthetic coast effect study (Fig. 5). The degree of observed phase split indicates a strong coast effect and thus high resistivities for the Pyrenean lithosphere (≥ 500 Ω·m). For an inversion study, the large phase split would suggest the use of a very resistive starting model to strongly weight the implemented oceans. Interestingly, the high amount of phase difference in the observation is not fully reproduced by the synthetic ocean modeling, suggesting an additional geological origin. The careful prior comparison of synthetic coast effect data and observed data helps to find an adequate starting model for the inversion runs. Figure 10. View largeDownload slide Observed real (red) and imaginary (blue) tipper vectors (left) as well as phase tensors (right) from the Pyrenean mountain chain between France and Spain (Cembrowski 2017). The phase tensors show a uniform phase split as observable in the synthetic coast effect study. Note the difference in phase scaling compared to Figs 5(a)–(i). Figure 10. View largeDownload slide Observed real (red) and imaginary (blue) tipper vectors (left) as well as phase tensors (right) from the Pyrenean mountain chain between France and Spain (Cembrowski 2017). The phase tensors show a uniform phase split as observable in the synthetic coast effect study. Note the difference in phase scaling compared to Figs 5(a)–(i). Moreover, the visual comparison of observed and synthetic tipper vectors reveals the existence of a conductive, local anomaly to the north of the very eastern profile. The conductor causes a local southward orientation of the real part of the observed tipper vectors. In general, a northwards orientation of the real parts can be observed, most likely comparable to the superposed coast effect in Fig. 4(f). Studying the lithosphere beneath Japan, Kanda & Ogawa (2014) nicely compared observed and synthetic tipper vectors from a 100 Ω·m background bathymetry model. The model was also used as a starting model in the inversion of VTF. Compared to the synthetic tipper vectors, the observed tipper vectors indicated a stronger coast effect and thus a higher initial resistivity. Moreover, a general northward trend of real tipper vectors (Parkinson convention) observed for long periods might have partly been explained by the superposed coast effects, and not by geology alone. Their final inversion model features high conductive and local anomalies (< 0.1 Ω·m) at the shorelines that might be artefacts. Using a more resistive starting model will possibly result in moderate resistivities. ANISOTROPY AND COAST EFFECT Forward Modeling Study The uniform phase split in the presence of two opposite oceans strongly resembles the phase split observable for anisotropic structures that laterally extend over a wide area (e.g. Gatzemeier & Moorkamp 2005; Häuserer & Junge 2011; Löwer 2014). The uniform phase behaviour often involves small tippers due to small lateral conductivity gradients. Our bathymetry studies reveal that similar data characteristics are present at areas where the oceanic effects cancel each other out. Besides, areas exist with unexpected and often laterally homogeneous tipper patterns. Such homogeneous patterns are also observed by Löwer & Junge (2017) above 3-D anisotropic structures. The similarities encourage the consideration and study of anisotropic structures in the presence of conducting oceans. A simple ocean–continent–ocean model is constructed (Fig. 11—Model 1). The oceans are represented by two opposite conductive bodies (0.5 Ω·m) with a separating distance of 300 km embedded in a homogenous 100 Ω·m half-space. They feature a depth of 1 km close to the area of investigation and a depth of 8 km elsewhere. Forward responses are calculated between 10 and 6250 s for 63 stations distributed along seven profiles in between the two conductive bodies. Due to the resistivity distribution of Model 1 with the electromagnetic strike in x-direction, the transfer functions (TFs) exhibit a definitive 2-D behaviour. The responses can therefore be separated into the TE (Zxy) and TM (Zyx) mode with the electric field being parallel and orthogonal to the coast line, respectively. For this case, the maximum and minimum phase values of the phase tensor directly depict the impedance phases of the off-diagonal impedance elements. The observable phase and resistivity split are caused by the lateral resistivity gradient between oceans and background. At y = 0, the individual coast effects cancel each other out and tippers are zero. Figure 11. View largeDownload slide Transfer functions for a simple ocean model. Top: the model consists of two oceanic bodies with a distance of 300 km. The parallel profiles with nine stations each are located in between the oceanic bodies. Bottom left: apparent resistivities, impedance phases and tippers (y-component) are calculated for the station (x = 0 km and y = −50 km) marked with a red colour (top left). Bottom right: map plot of phase tensors and tipper arrows for 2500 s. Figure 11. View largeDownload slide Transfer functions for a simple ocean model. Top: the model consists of two oceanic bodies with a distance of 300 km. The parallel profiles with nine stations each are located in between the oceanic bodies. Bottom left: apparent resistivities, impedance phases and tippers (y-component) are calculated for the station (x = 0 km and y = −50 km) marked with a red colour (top left). Bottom right: map plot of phase tensors and tipper arrows for 2500 s. Three additional models are constructed comprising anisotropic half-spaces starting at a depth of 100 km (Fig. 12). The respective anisotropy ratios are 25 and are in accordance with mantle anisotropy ratios (3–100) that have been observed by various studies (e.g. Mareschal et al. 1995; Simpson 2001; Bahr & Simpson 2002; Gatzemeier & Moorkamp 2005). Model 2 has a 1-D resistivity distribution that is composed of two layers (Fig. 12, left). The top layer is isotropic with 100 Ω·m. Below, the anisotropic half-space starts at 100 km and features 20 Ω·m in x-direction and 500 Ω·m in y-direction. The vertical direction is conductive for all models. As the horizontal principle axes of the anisotropy coincide with the coordinate axes, the responses of the off-diagonal impedances describe two different models: the xy-component depicts a conductivity increase at 100 km and the apparent resistivity decreases with the corresponding phase being > 45°. Contrary the yx-component describes the resistivity increase from 100 to 500 Ω·m at 100 km and the apparent resistivities are increasing for longer periods and phases are below 45°. As lateral resistivity gradients do not exist for Model 2, tippers are zero. For comparison the responses of Model 1 (Fig. 11) are illustrated as grey lines, showing a similar split of apparent resistivities and phases. Figure 12. View largeDownload slide Transfer functions for different anisotropic models. Top: the different models are illustrated as depth profiles at x = 0 km. Bottom: apparent resistivities, impedance phases and tippers (y-component) are displayed for the station marked by red colour (top). Additionally, the forward responses of Model 1 (grey lines) and the responses of the final inversion models (open circles, cf. Fig. 14) are plotted. Figure 12. View largeDownload slide Transfer functions for different anisotropic models. Top: the different models are illustrated as depth profiles at x = 0 km. Bottom: apparent resistivities, impedance phases and tippers (y-component) are displayed for the station marked by red colour (top). Additionally, the forward responses of Model 1 (grey lines) and the responses of the final inversion models (open circles, cf. Fig. 14) are plotted. Model 3 (Fig. 12, middle) comprises the oceanic bodies of Model 1 and the anisotropy of Model 2. Thus, compared to Model 2, an increase of apparent resistivity and phase split is observable. The intensified phase split is caused by the lateral conductivity gradient along the shores. As the tipper depends on lateral changes of current concentration, it is influenced by the vertical conductivity contrast at the shore line as well as by the vertical distribution of the current component parallel to the coast. This explains the slight difference of the tipper length for Models 3 and 4. In Model 4 (Fig. 12, right), the horizontal principle axes of the anisotropy are interchanged, resulting in a decrease of apparent resistivity and phase split and thus a decrease of the coast effect compared to Model 1, whereas the tipper vectors remain similar. 3-D isotropic inversion study In recent years, the application of 3-D inversion on MT array data has become a standard process. Codes for inverting for 3-D anisotropic resistivities are not yet available and thus 3-D forward modeling routines are the method of choice to test for intrinsic anisotropy (Löwer & Junge 2017). It is still an open question if certain resistivity patterns derived from the 3-D isotropic inversion may be replaced by simple anisotropic bodies. To recognize such patterns, we perform 3-D inversions of the responses from the forward calculations of Model 2–4 with ModEM (Kelbert et al. 2014). The joint inversion of impedances and VTFs is done for the 63 stations shown in Fig. 11. An error of 3 per cent is ascribed to each impedance component individually. Additionally, an error floor of 3 per cent of |Zxy · Zyx|1/2  is attributed to small diagonal elements. A constant value of 0.02 is used for the error bounds of the VTFs. The inner study area is discretized with a 9 km grid consisting of 23 × 34 (x- and y-directions) cells. Outside, the cell widths increase by a factor of 1.2 towards the outer boundaries. In vertical direction, the thickness of the first layer is 0.3 km and increases by a factor of 1.1 for subsequent layers. As static shift problems do not occur in our study, 0.3 km for the uppermost layer yields a sufficient resolution. The discretization results in a grid of 61 × 70 × 61 (x-, y- and z-directions) cells. A homogeneous half-space of 100 Ω·m is used as a starting model. For the inversions of responses from Models 3 and 4, the oceanic bodies are additionally incorporated as prior information and are fixed during the inversion. The spatial smoothing is set to 0.2, resulting in a spreading of bulk resistivity values into adjacent cells (Murphy & Egbert 2017). The final inversion models are displayed in Fig. 14, illustrated as different depth slices and cross-sections at x = 0 km and y = 0 km. The respective normalized root-mean-square misfit (nrms) for Models 2, 3 and 4 are 0.68, 1.44 and 0.97, respectively. The overall nrms does not make any specifications about frequency, location or TF-dependent misfit. Hence, Fig. 12 additionally shows the predicted off-diagonal responses of the final inversion models as open circles. The apparent resistivities and impedance phases of the inversion responses reproduce the input data reasonably well. However, the small systematic phase and tipper misfit for Model 3 results in a higher rms than for the other inversions. Figure 14. View largeDownload slide Final resistivity inversion models of the forward responses of Models 2, 3 and 4. Black lines mark the position of the oceanic bodies and the electrical anisotropy layer. Figure 14. View largeDownload slide Final resistivity inversion models of the forward responses of Models 2, 3 and 4. Black lines mark the position of the oceanic bodies and the electrical anisotropy layer. Fig. 13 shows map plots of predicted phase tensors and tippers for 2500 s (left) and the corresponding phase tensor (middle) and tipper misfits (right) between forward and predicted responses. Phase tensors are well predicted for Models 2 and 4. As already observed for the comparison of impedance data, the observed phase split of phase tensors is largest for Model 3. The predicted tippers reveal the three-dimensionality of the inversion responses for the northern and southern stations of all models. The vectorial differences between modeled and predicted tippers (right) show that systematic misfits occur for all models. Obviously, the fit of the impedances dominates the fit of the tippers in the inversion. The predicted tippers are not parallel as for the modeled data in Fig. 11, as obviously the combined prediction of impedances and tippers requires a 3-D resistivity distribution. Figure 13. View largeDownload slide Evaluation of inversion responses. Left: map plot of inversion model responses. Phase tensors and tippers are displayed for 2500 s. Middle: phase tensor misfit between forward and inversion responses. The circle has a radius equivalent to a misfit of 5°. Right: tipper misfit between forward and inversion responses. Figure 13. View largeDownload slide Evaluation of inversion responses. Left: map plot of inversion model responses. Phase tensors and tippers are displayed for 2500 s. Middle: phase tensor misfit between forward and inversion responses. The circle has a radius equivalent to a misfit of 5°. Right: tipper misfit between forward and inversion responses. The final resistivity models of the inversions illustrate how the inversion routine attempts to explain anisotropic data (Fig. 14). The inversion model 2 (left) is dominated by two conductive structures located to the east and west of the station grid in a depth of around 80 100 km. As opposed oceans, they produce a rather uniform phase split at all sites. Two elongated tube-like conductors (∼2 Ω·m) are extended in the direction of the conductive principle axes of the anisotropy at around 70 km depth. These structures cause an additional phase split and compensate the tippers produced by the anomalies outside the station grid. They represent a macroscopic anisotropy, since they cannot be resolved separately by the data. The large phase split of the responses from Model 3 can only partly be explained by the oceans implemented in the starting model. As in the inversion result of Model 2, an additional split is realized by conductive tubes (∼20 Ω·m) at around 70 km. The large anomalies of Model 2 outside the station grid are shifted beneath the grid, since the implementation of the oceans decreases the model sensitivities. The inversion of data from Model 4 with interchanged horizontal anisotropic resistivities results in a comparably conductive background (Fig. 14, right). The higher conductance attenuates the coast effect and decreases the apparent resistivity and phase split. Moreover, resistive structures are incorporated below the shorelines. Conductive tubes in the direction of the good conductive anisotropy axis are not observable. DISCUSSION AND CONCLUSIONS We have performed 3-D bathymetry forward modeling of areas where landmasses are bounded by opposite oceans. For the Pyrenean area and Central America, we showed that for shorter periods the coast effect is restricted within areas close to the oceans and the orientations of tipper arrows and phase tensors essentially depend on the geometry of the coastline. Whereas for shorter periods an individual effect of the respective ocean can be observed, the influence is superimposed for longer periods. The phase tensor behaviour becomes very uniform with a strong phase split and the maximum phases oriented towards the opposed oceans. The comparison between both study areas shows that the pattern of the tipper arrows is rather complicated and depends on the distribution of the deep sea water and the mutual position of the opposite oceans. At certain areas, the oceanic influences cancel each other out and result in almost zero tippers or render it difficult to associate length and orientation to the coast effect. Prior studies of the coast effect provide important information on the nature of observed data sets. Assessing the synthetic coast effect responses for different background models helps to avoid misinterpreting data patterns caused by complicated coast effects. The comparison of synthetic and observed ocean effect yields information about the lithospheric conductance and facilitates the selection of an appropriate starting model for the inversion. Our coast effect studies aim at regional MT arrays rather than local studies. Thus this work makes an important contribution to the MT community, since arrays of MT stations (e.g. EarthScopeUSArray in the United States or SinoProbe in China) have become the standard method in magnetotelluric exploration. Furthermore, we demonstrated that the impedance response of an anisotropic layer at depth very much resembles the response of opposite oceans with both models causing a split of phases and of resistivities. The responses depend on the ocean depth, the distance between both oceans, the background resistivity and the resistivities of the anisotropic layer. The effect of oceans and anisotropy is shown for models with opposite oceans and anisotropic half-spaces at 100 km depth with the conductive horizontal direction being orthogonal and parallel to the coastlines, respectively. In both cases, the tipper responses are very similar, since the vertical magnetic field is only generated due to the lateral conductivity gradient between sea and land. Contrary, the phase and resistivity behaviour strongly depend on the direction of the conductive horizontal anisotropy axes. We performed 3-D isotropic inversions of the anisotropic forward data for 63 stations distributed along seven profiles. The inversion explains the input data well. Conspicuous systematic misfits are only observed for Model 3 where ocean response and anisotropy generate a large phase and apparent resistivity split. We do not consider the systematic misfits as an absolute diagnostic for electrical anisotropy. In fact, they seem to occur in inversion studies of synthetic data when the model parametrization cannot fully resolve the data variability, independent of whether the synthetic input data are isotropic or anisotropic. The isotropic inversion replaces the anisotropic layer by parallel tube-like conductive anomalies representing a macroscopic anisotropy and by conductors outside the station grid. The result resembles the studies from Heise & Pous (2001) and Löwer & Junge (2017), where electrical anisotropy is explained by alternating isotropic structures of high and low resistivities beneath the station grid. Contrary to the 3-D model of Löwer & Junge (2017), the anisotropic model in this study is 1-D and conductive anomalies are also implemented outside the station grid. The inversion of Model 3 with opposite oceans also results in conductive tubes. However, they are one order of magnitude less conductive than those observed for Model 2. Contrary, the inversion of TF from Model 4 does not show the anisotropic model characteristics. In essence, mantle anisotropy in the presence of opposed oceans is hard to be recovered by 3-D isotropic inversion, when the conductive direction is perpendicular to the shorelines. The inversion results depend on the station grid and model parametrization. A high spatial model smoothness as well as oversized model cells do not allow for lateral alternating contrasting isotropic structures that represent macroscopic anisotropy. Moreover, test inversion runs with only three profiles consisting of 27 stations did not reveal alternating structures, but solely conductors outside the station grid, complicating the identification of anisotropy. The results showed that the stations should cover an area with a width at least twice the depth of the anisotropic layer to recover macroscopic anisotropy. According to our studies, we recommend to carefully check inversion models for resistivity anomalies outside the station grid and for alternating resistivity structures that may represent macroscopic anisotropy. Sensitivity studies of these structures can help to better understand their effect on TFs. 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Published by Oxford University Press on behalf of The Royal Astronomical Society. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Geophysical Journal International Oxford University Press

# Electrical anisotropy in the presence of oceans—a sensitivity study

, Volume 213 (2) – May 1, 2018
15 pages

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© The Author(s) 2018. Published by Oxford University Press on behalf of The Royal Astronomical Society.
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0956-540X
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### Abstract

Summary Electrical anisotropy in the presence of oceans is particularly relevant at continent–ocean subduction zones (e.g. Cascadian and Andean Margin), where seismic anisotropy has been found with trench-parallel or perpendicular fast direction. The identification of electrical anisotropy at such locations sheds new light on the relation between seismic and electrical anisotropies. At areas confined by two opposite oceans, for example the Pyrenean Area and Central America, we demonstrate that the superposed responses of both oceans generate a uniform and large phase split of the main phase tensor axes. The pattern of the tipper arrows is comparatively complicated and it is often difficult to associate their length and orientation to the coast effect. On the basis of simple forward models involving opposite oceans and anisotropic layers, we show that both structures generate similar responses. In the case of a deep anisotropic layer, the resistivity and phase split generated by the oceans alone will be increased or decreased depending on the azimuth of the conducting horizontal principal axes. The 3-D isotropic inversion of the anisotropic forward responses reproduces the input data reasonably well. The anisotropy is explained by large opposed conductors outside the station grid and by tube-like elongated conductors representing a macroscopic anisotropy. If the conductive direction is perpendicular to the shorelines, the anisotropy is not recovered by 3-D isotropic inversion. Electrical anisotropy, Geomagnetic induction, Magnetotellurics, Numerical modelling INTRODUCTION The primary goal of a magnetotelluric (MT) survey is the retrieval of the resistivity structure of the subsurface from natural time variations of the electromagnetic field components measured at the Earth's surface. Directional properties of the resistivity structure are of special interest as they can indicate geodynamic processes or be related to the strike of geological structures or preferential pathways of fluid and melt. In coastal regions, the oceans, as bodies of highly conductive sea water (∼0.25 Ω·m), represent the main conductive bodies at near-surface depth and thus have a large impact on electromagnetic induction studies, called the coast effect. This effect superposes the electromagnetic responses of the subsurface aggravating the identification of geological structures. A special case is constituted by opposite oceans. Their influence causes a rather homogenous phase split and rather small induction arrows at sites in between where the induced coast effects cancel each other out. A similar pattern of phase tensors and induction arrows is often associated with anisotropic conductivity structures (Bahr & Simpson 2002; Gatzemeier & Moorkamp 2005; Häuserer & Junge 2011; Löwer 2014). This resemblance makes the identification of anisotropic data characteristics very difficult in the presence of oceans. However, as electrical anisotropy might be related to and reflect geodynamic processes as subduction of oceanic lithosphere, it is crucial to distinguish between ocean and anisotropic responses. Seismic anisotropy has been found in most subduction zones (e.g. Cascadian and Andean Margin) with trench-parallel or perpendicular fast directions (Long & Silver 2008). The determination of electrical anisotropy at such locations can shed new light on the relation between seismic and electrical anisotropies (e.g. Gatzemeier & Moorkamp 2005; Hamilton et al. 2006). BACKGROUND First observed near the coast in Australia (Parkinson 1959) and Japan (Rikitake 1959), the coast effect causes large anomalous magnetic variations in coastal regions (Parkinson 1962). At long periods, it can be recognized up to several hundreds of kilometres inland and strongly depends on the shape of the coastline and the bathymetry of the adjacent ocean. Moreover, the resistivity structure beneath the oceans and continents plays an important role and can intensify, attenuate or deflect the influence of the oceans (e.g. Parkinson & Jones 1979; Mackie et al. 1988; Thiel et al. 2009; Brasse et al. 2009a; Thiel & Heinson 2010; Wannamaker et al. 2014). The impedance function and the tipper arrows are affected by the coast effect (Santos et al. 2001). The coast effect in MT studies is addressed by implementing the oceans as prior information into the 2-D or 3-D inversion and forward models (e.g. Becken et al. 2008; Tietze & Ritter 2013; Meqbel et al. 2014; González-Castillo et al. 2015) or by previously separating the coast effect from the transfer functions (e.g. Weaver & Agarwal 1991; Santos et al. 2001). If the oceans are not incorporated into the prior model, the inversion algorithm will implement highly conductive and local anomalies along the shorelines. The 2-D effect of two opposite oceans was studied by Dosso & Meng (1992) for vertical magnetic transfer functions (VTF) and Malleswari & Veeraswamy (2014) for impedance functions. Kanda & Ogawa (2014) conducted a 3-D MT study in NE Japan. They inverted VTF for the period range 16–256 s and included the Sea of Japan and parts of the adjacent Pacific Ocean as prior information into the 100 Ω·m background model. The forward response of the bathymetry model indicated that the coast effects produced by each ocean individually did not superpose for the observed period range. For the general 3-D isotropic case, the split of the phase tensor's principal axis is caused by horizontal conductivity gradients, involving non-zero tippers. For the 1-D case comprising an electrical anisotropic layer, the split results from the vertical conductivity change at the interface between the isotropic and anisotropic layers depending on the azimuth (Heise et al. 2006). The main phase values represent the contrast between the principal conductivities of the anisotropy and the conductivity of the isotropic layer. Due to the absence of lateral resistivity gradients, the phase split involves induction arrows of zero lengths. Isotropic inversion of theoretical anisotropic data was done in 2-D by Heise & Pous (2001) and in 3-D by Löwer & Junge (2017). Their inversion models exhibited alternating isotropic structures of high and low resistivities explaining the data reasonably well. Weidelt (1999) predicted that an arbitrary complex isotropic model is able to reproduce an intrinsic anisotropic resistivity distribution by macroscopic isotropic structures, provided that the model discretization is fine enough. An overview of anisotropic studies is given in Martí (2014). In this study, we focus on phase tensors (Caldwell et al. 2004) and tipper arrows (Wiese 1962), since they are not affected by near-surface resistivity inhomogeneities. We first study the effect of opposite oceans for two prominent ocean–continent–ocean regions: the Pyrenean area and Central America. For MT studies conducted in the Pyrenees, see example Pous et al. (1995), Ledo (1996), Ledo et al. (2000), Campanyà et al. (2011, 2012), Campanyà (2013) and Cembrowski (2017). MT studies in Mexico and Central America have been performed by, for example Elming & Rasmussen (1997), Jording et al. (2000), Jödicke et al. (2006), Brasse et al. (2009a,b) and Worzewski et al. (2011). Other examples of similar ocean–continent–ocean areas are from South East Asia, Japan and Italy. Furthermore, we show the similarity of ocean and anisotropic responses by comparing the data response of a simple ocean–continent–ocean model to the response of a 1-D model with an anisotropic layer. Additional models are constructed that involve both conductivity anomalies: opposite oceans and anisotropic layers. It will be shown that depending on the strike of the anisotropy, that is the most conducting horizontal direction, the phase split is increased or decreased. We perform 3-D isotropic inversions of the anisotropic forward responses and study the isotropic resistivity pattern of the originally anisotropic body reproducing the phase split. Our results reveal possible anisotropic features behind ostensible isotropic resistivity patterns and broaden the scope of geological interpretation. METHODOLOGY: 3-D FORWARD MODELING AND INCLUSION OF OCEANS Data were simulated using the MT3D software, which is briefly described in this section; for details see Löwer (2014). The MT3D code is written in MATLAB and accesses COMSOL Multiphysics 4.3 via the MATLAB-Comsol-Livelink. The forward responses for all stations and frequencies are calculated from several models, as the models depend on the target frequency and station location. The model volumes are described by three concentric half spheres embedded in a cuboid (Fig. 1a). The sizes of the cubic box (4) and the outermost sphere (3) depend on the respective skin depth (δmax) for the highest resistivity used in the constructed model. However, this value can be increased in order to consider the horizontal adjustment length when incorporating oceans into the model (Ranganayaki & Madden 1980; Simpson & Bahr 2005). The dimensions of the cubic box are 6δmax × 6δmax × 3δmax, the outermost sphere features a radius of 1.5δmax. The sizes of the two inner spheres (1, 2) can be chosen due to the requirements of the constructed resistivity distribution. A 3-D tetrahedral mesh is defined within the model volume with the highest grid resolution in the centre and coarsening towards the outermost boundaries with the element sizes and growth rates depending on the dimensions of the cubic box and concentric spheres. The numerical investigation area is positioned at the centre of the spheres, so that the highest grid resolution is achieved beneath that area. In this way, different models with about 250.000–400.000 mesh elements are generated. Figure 1. View largeDownload slide Example of a model volume for 1000 s. (a) The model volume is composed of concentric half spheres (1, 2, 3) embedded in a cubic box (4). The dimensions of the cubic box and of the half spheres are adapted to the resistivity distribution of the constructed model. The tetrahedral grid that continuously coarsens to the boundary of the model space is only shown at the boundaries. (b) Bathymetry model at z = 0 m for 1000 s of southwest Europe including parts of the Atlantic and the Mediterranean. The onshore resistivity and the resistivity outside of the half spheres are set to 500 Ω·m. Figure 1. View largeDownload slide Example of a model volume for 1000 s. (a) The model volume is composed of concentric half spheres (1, 2, 3) embedded in a cubic box (4). The dimensions of the cubic box and of the half spheres are adapted to the resistivity distribution of the constructed model. The tetrahedral grid that continuously coarsens to the boundary of the model space is only shown at the boundaries. (b) Bathymetry model at z = 0 m for 1000 s of southwest Europe including parts of the Atlantic and the Mediterranean. The onshore resistivity and the resistivity outside of the half spheres are set to 500 Ω·m. The resistivity model is constructed by assigning resistivity values to a prior defined fixed number of points (SP, support points) in the 3-D environment beneath and adjacent to the investigation area. For each model volume, the SP are linearly interpolated on the relevant finite elements (FE) grid of the three half spheres and a constant background resistivity is ascribed to the gridpoints outside of the outer sphere. The forward modeling, which also allows a 3-D anisotropic resistivity distribution, is performed separately for the different frequencies and regions applying the geometrical scheme mentioned above. This procedure allows a high numerical precision by a preferably low number of FE cells and low number of degrees of freedom. Since the vertical resolution of the FE grid decreases towards the outer boundaries, a simple SP scheme is applied for modeling the influence of the bathymetry (GEBCO, www.gebco.net). The scheme involves modeling the oceans as layers of constant depth to avoid modeling shallow oceans far away from the investigation area. Instead of using the true sea water conductivity (0.25 Ω·m), the modeled ocean resistivity is varied so that the conductance, that is the product of water depth and sea water conductivity, is maintained. It became apparent that two different ocean SP levels at 2 and 10 km depth were sufficient to model the shallow part near the coast and the deep ocean farther away. Fig. 1(b) shows the bathymetry resistivity model for a period of 1000 s with the investigated area in the centre of the half spheres. The resistivity distribution is illustrated in the x–y plane at the surface with the onshore resistivity and the resistivity outside of the concentric half spheres set to 500 Ω·m. The ocean depth near the study area was set to 2 km. The described ocean SP scheme enables the precise modeling of the spatially varying sea water influence and therefore allows an unprecedented study of its effect on MT data. In this study, we focus on phase tensors and tipper arrows (Wiese 1962). Contrary to Caldwell et al. (2004), we do not display the phase tensor as an ellipse with Φmax and Φmin being the major and minor axes, but following the suggestion of Häuserer & Junge (2011), the phase tensor is plotted as orthogonal bars. Hereby, the length and the colour of each bar correspond to the values of Φmax = arctan(Φmax) and Φmin = arctan(Φmin). We find this representation more intuitive since in a 2-D case the arctan(Φmax) and arctan(Φmin) are the phase angles of the complex impedance elements Zxy and Zyx. Moreover, the tangent function has a singularity at ± π/2, and thus Φ is more conspicuous at high phases than at low values. Together with the angle α (tensor's dependence on the coordinate system), the direction of the major axis is given by α − β. In order to compare tipper arrows from different models, we display the difference between the real and imaginary parts (misfit induction vector). As an illustration of the misfit between two (e.g. predicted and observed) phase tensors, Heise et al. (2007, 2008) introduced the misfit tensor defined by $${\rm{\Delta }} = {\rm{I}} - \frac{1}{2}( {{{{\bf \Phi }}_{{\rm{obs}}}}^{ - 1}{{{\bf \Phi }}_{{\rm{pred}}}} + {{{\bf \Phi }}_{{\rm{pred}}}}{{{\bf \Phi }}_{{\rm{obs}}}}^{ - 1}} )$$. Booker (2014) suggested taking the absolute difference between the observed Φobs and the predicted Φpred phase tensor. In our study, we display the invariants of the phase tensor (Φmax, Φmin) and the direction of the major axis (α − β), and therefore we suggest showing their differences (Fig. 2). The differences between the maximum and minimum phases (ΔΦmax, ΔΦmin) are represented by horizontal and vertical black bars with their length illustrating the phase difference. The bars’ origin equals the origin of a unit circle which circumference (R) marks a phase difference of 10°, that is for a phase difference of 10° for ΔΦmax the length of the horizontal bar equals the radius of the circle. If the end of the bar is located inside the circle the misfit is < 10°, for bars crossing the circumference the misfit is > 10°. The colour of the 10° circle shows the clockwise difference between the orientation of the observed and the predicted phase tensor Δ(α − β). For differences Φobs/predmax − Φobs/predmin < 5°, we find the orientation hard to define (α is undefined for Φmax = Φmin) and therefore we choose a green colour denoting a 1-D like situation. The example in Fig. 2 shows the misfit/difference (Fig. 2b) between two phase tensors, pt1 and pt2 (Fig. 2a), which is −5° for the maximum phase, 15° for the minimum phase and 30° (clockwise) for the orientation. Figure 2. View largeDownload slide Example of phase tensor misfit/difference. The misfit (b) is evaluated by plotting the differences between the invariants of pt1 and pt2 (a). The horizontal and the vertical black bars represent the maximum and minimum phase misfits, respectively. The colour of the circle illustrates the difference between the orientations of the phase tensors. If one of the two phase tensors nearly shows a 1-D situation (Φmax < Φmin + 5°), the colour of the circle is green. Figure 2. View largeDownload slide Example of phase tensor misfit/difference. The misfit (b) is evaluated by plotting the differences between the invariants of pt1 and pt2 (a). The horizontal and the vertical black bars represent the maximum and minimum phase misfits, respectively. The colour of the circle illustrates the difference between the orientations of the phase tensors. If one of the two phase tensors nearly shows a 1-D situation (Φmax < Φmin + 5°), the colour of the circle is green. Coast effect Pyrenees The study area comprises the Pyrenean Chain and parts of its foreland basins (Fig. 3). To the east, the Pyrenees are bounded by the Mediterranean Sea with an average water depth of about 1400 m. To the west, the Pyrenees are bounded by the Bay of Biscay as a part of the Atlantic Ocean. The bay is characterized by a large continental shelf with shallow sea water to the northeast and a steep continental slope describing the transition to the deep Atlantic Ocean with depths beyond 4000 m. The shortest distance between both oceans is approximately 370 km. Theoretical transfer functions are calculated at 25 site locations (red dots) equally distributed throughout the area of interest with approximate site distances of about 80 km. Figure 3. View largeDownload slide The study area is the Pyrenean Chain and parts of its foreland basins. The Mediterranean and the Bay of Biscay bound the Pyrenees on both sides and make the Pyrenees an ideal area to study a combined coast effect of two oceans. The bathymetry of the oceans is colour coded to depth intervals of 500 m. Transfer functions are calculated at locations marked by red dots. Figure 3. View largeDownload slide The study area is the Pyrenean Chain and parts of its foreland basins. The Mediterranean and the Bay of Biscay bound the Pyrenees on both sides and make the Pyrenees an ideal area to study a combined coast effect of two oceans. The bathymetry of the oceans is colour coded to depth intervals of 500 m. Transfer functions are calculated at locations marked by red dots. The induction vectors for the bathymetry embedded in different homogeneous background resistivity models (100, 500 and 2000 Ω·m) are shown in Fig. 4 for 100, 1000 and 6250 s. For the period of 100 s (Figs 4a, d and g), the real induction vectors are almost orthogonal to the nearest coastlines naturally pointing away from areas of current concentrations. The imaginary tipper arrows are antiparallel to the real part for all sites and therefore suggest a 2-D structure. Due to the relatively small induction volume for this period, the effects of the oceans do not superimpose. However, the Mediterranean dominates as there is deeper water close to the shoreline. For the period of 1000 s and background resistivities of 500 and 2000 Ω·m (Figs 4e and h), 3-D effects become evident with the imaginary arrows oblique to the real arrows. In Figs 4(f) and (i) (6250 s) both coast effects are superimposed resulting in striking patterns. For the high background resistivity of 2000 Ω·m, the real arrows rotate to the east, influenced by the rather deep bathymetry of the Atlantic Ocean. The comparison of the results clearly shows that the coast effect grows with increasing resistivity and is strongly influenced by the distant bathymetry for long periods. Figure 4. View largeDownload slide Tipper arrows and skew values (coloured circles) showing the coast effect for different homogeneous background resistivities (100, 500 and 2000 Ω·m) for 100, 1000 and 6250 s. Red: real part. Blue: imaginary part. Evidently, the coast effect intensifies with increasing background resistivity and the effect of both oceans is superimposed at the long periods. Moreover, the Atlantic Ocean dominates the coast effect with increasing periods. Especially, the shape of the Bay of Biscay causes high skew values indicating a 3-D resistivity distribution for that area. Figure 4. View largeDownload slide Tipper arrows and skew values (coloured circles) showing the coast effect for different homogeneous background resistivities (100, 500 and 2000 Ω·m) for 100, 1000 and 6250 s. Red: real part. Blue: imaginary part. Evidently, the coast effect intensifies with increasing background resistivity and the effect of both oceans is superimposed at the long periods. Moreover, the Atlantic Ocean dominates the coast effect with increasing periods. Especially, the shape of the Bay of Biscay causes high skew values indicating a 3-D resistivity distribution for that area. The coloured circles in Fig. 4 represent the skew β values corresponding to the phase tensors in Fig. 5. The amount of β generally increases with increasing coast effect indicating the 3-D nature of the bathymetry. Especially, the sites to the south of the Bay of Biscay feature rather high skews β up to 7° for the model with 100 Ω·m background and 12° for the model with 500 Ω·m background. Contrary, the skews to the north of the study area exhibit small absolute values with |β| < 3°, although the obliquity of real and imaginary arrows for long periods (Figs 4f and i) clearly indicates a 3-D situation. Figure 5. View largeDownload slide (a)–(i) Phase tensors showing coast effect for different homogeneous background resistivities (100, 500 and 2000 Ω·m) for 100, 1000 and 6250 s. The coast effect results in a split of maximum and minimum phases with major axes oriented towards the oceans. The phase difference can be seen as a measure of the strength of the coast effect. The superimposed coast effect causes a very uniform phase tensor split and orientation. The differences of the rotational invariants of the phase tensors are illustrated in (j)–(l) between the 500 and the 100 Ω·m model and in (m)–(o) between the 2000 and the 500 Ω·m model. The radius of the circles denotes a phase difference of 10°. Figure 5. View largeDownload slide (a)–(i) Phase tensors showing coast effect for different homogeneous background resistivities (100, 500 and 2000 Ω·m) for 100, 1000 and 6250 s. The coast effect results in a split of maximum and minimum phases with major axes oriented towards the oceans. The phase difference can be seen as a measure of the strength of the coast effect. The superimposed coast effect causes a very uniform phase tensor split and orientation. The differences of the rotational invariants of the phase tensors are illustrated in (j)–(l) between the 500 and the 100 Ω·m model and in (m)–(o) between the 2000 and the 500 Ω·m model. The radius of the circles denotes a phase difference of 10°. Compared to the tipper arrows, the phase tensors show a rather simple behaviour (Figs 5a–i) as the coast effect splits the phase into a maximum (minimum) value greater (less) than 45°with the axis orientation roughly perpendicular (parallel) to the shoreline. The phase difference increases with decreasing distances to the oceans, similar to the length of the induction vector. Due to the position of the oceans flanking the orogen on both sides, the overall phase tensor orientation is very uniform for longer periods. Although the pattern is regionally uniform and thus would suggest a 2-D situation with clear strike direction for longer periods, the corresponding skews β in Fig. 4 show the strong asymmetry of the tensors and indicate the three-dimensionality of the resistivity distribution. The comparison of phase tensors is additionally illustrated with the method described in Fig. 2 (Figs 5j–o). Fig. 6 shows the period-dependent transfer functions (apparent resistivity, impedance phase, phase tensor, induction arrows and skews β) for the sites marked in Fig. 5(d). The station located south of the Bay of Biscay (Fig. 6a) illustrates a clear 3-D situation. With increasing periods the skew increases continuously from 0° to values exceeding 10° and simultaneously the real and imaginary arrows take an oblique direction. In contrast, the skews in the Central Pyrenees (Fig. 6b) remain below 1.5 and thus would indicate a non-3-D situation. However, for the long periods, the phase tensors’ major axes are not aligned with the tipper orientations and real and imaginary arrows are oblique. Figure 6. View largeDownload slide Transfer functions for the stations marked in Fig. 5(d) and the bathymetry model with a 500 Ω·m background resistivity. From top to bottom: apparent resistivities, impedance phases, phase tensors and induction vectors, and skew values. (a) Site south to the Bay of Biscay. (b) Site in the Central Pyrenees. Figure 6. View largeDownload slide Transfer functions for the stations marked in Fig. 5(d) and the bathymetry model with a 500 Ω·m background resistivity. From top to bottom: apparent resistivities, impedance phases, phase tensors and induction vectors, and skew values. (a) Site south to the Bay of Biscay. (b) Site in the Central Pyrenees. Comparison with Central America Central America and Mexico with the Pacific Ocean to the southwest and the Gulf of Mexico and the Caribbean Sea to the northeast is another prominent example of two opposite oceanic bodies (Fig. 7). The adjacent Pacific Ocean is characterized by the Middle America Trench. It is a major subduction zone and is situated about 100 km away from the coast of Central America. It runs roughly parallel to the coastline and marks the transition from the shallow shelf water (< 1 km depth) to the deep Pacific Ocean (> 3 km depth). The eastern coastline is more complicated compared to the western shoreline with a strongly varying bathymetry in the Gulf of Mexico and the Caribbean Sea. Theoretical VTF and phase tensors are calculated for 57 site locations (red circles) for a model with the oceans incorporated in a 500 Ω·m half-space. The results are shown in Fig. 8 for 100, 1000 and 6250 s. For the short periods, the coast effect is restricted within an area near the coastlines with tipper arrows and maximum phases oriented perpendicular to the nearest shorelines (Figs 8a and d). It evidently depends on the water depth close to the adjacent shoreline and it is strongest for sites along the coast of the Pacific Ocean. Significant non-zero skews β are present close to the bays. Towards longer periods, the effect of the deep part of the Pacific Ocean dominates with real and imaginary arrows still being antiparallel near the Pacific coast (Fig. 8b). Most of the phase tensors major axes are oriented southeastwards as a result of the superimposed coast effect of the Pacific and the Gulf of Mexico as well as the Pacific and the Caribbean Sea. To the south of Yucatán, there is an area where the effects of all three oceanic bodies are compensated producing small tippers, phase splits and absolute skew values. For the period of 6250 s, the phase tensors appear very uniform in phase split and orientation. The VTF for this period show the strong influence of the Pacific Ocean with real tipper arrows exceeding the value of 1. Note that even though the colinearity of tipper arrows as well as the uniformity of phase tensors near the Pacific Coast indicate a 2-D situation, the high absolute skew values exceeding 3° for many sites clearly suggest a 3-D situation. Exemplarily, Fig. 9 shows the period-dependent transfer functions for (a) a station close to the Pacific Ocean and (b) a station situated in Belize close to the Caribbean Sea. The exact station locations are marked in Fig. 8(d). Tipper arrows and phase tensors for the site near the Pacific coast suggest a rather 2-D behaviour with very consistent orientations, though the absolute skew values are higher than |3| for longer periods. The strong influence of the Pacific Oceans results in real tipper arrows with a length of more than 1 for longer periods and antiparallel imaginary arrows for all observed periods. An interesting pattern can be observed for the other station, where the skew β has a maximum of 8° at about 800 s and decreases below 3° for longer periods. Figure 7. View largeDownload slide Central America and Mexico is another prominent example of a landmass embedded by large oceans. It is bounded by the Pacific Ocean to the southeast and the Caribbean Sea and the Gulf of Mexico to the northwest. The bathymetry of the oceans is illustrated by colours. Red dots represent the locations at which theoretical transfer functions are calculated. Figure 7. View largeDownload slide Central America and Mexico is another prominent example of a landmass embedded by large oceans. It is bounded by the Pacific Ocean to the southeast and the Caribbean Sea and the Gulf of Mexico to the northwest. The bathymetry of the oceans is illustrated by colours. Red dots represent the locations at which theoretical transfer functions are calculated. Figure 8. View largeDownload slide Coast effect study for Central America and parts of Mexico for 100, 1000 and 6250 s. (a)–(c) Real (red) and imaginary (blue) tipper arrows and skew values (coloured circles). For shorter periods, the arrows are oriented perpendicular to the coastlines. With increasing period, the coast effect of Pacific Ocean dominates. (d)–(f) Phase tensors. The maximum phase of the phase tensors is oriented towards the nearest coastlines for short periods. Phase tensors feature a very uniform orientation and phase split for the long periods. Figure 8. View largeDownload slide Coast effect study for Central America and parts of Mexico for 100, 1000 and 6250 s. (a)–(c) Real (red) and imaginary (blue) tipper arrows and skew values (coloured circles). For shorter periods, the arrows are oriented perpendicular to the coastlines. With increasing period, the coast effect of Pacific Ocean dominates. (d)–(f) Phase tensors. The maximum phase of the phase tensors is oriented towards the nearest coastlines for short periods. Phase tensors feature a very uniform orientation and phase split for the long periods. Figure 9. View largeDownload slide Transfer functions for the stations marked in Fig. 9(d). From top to bottom: apparent resistivities, impedance phases, phase tensors and induction vectors, and skew values. (a) Site close to the Pacific Ocean. Note the tipper scale of 0.4 and real arrows increasing up to 1.4. (b) Site located in Belize. Figure 9. View largeDownload slide Transfer functions for the stations marked in Fig. 9(d). From top to bottom: apparent resistivities, impedance phases, phase tensors and induction vectors, and skew values. (a) Site close to the Pacific Ocean. Note the tipper scale of 0.4 and real arrows increasing up to 1.4. (b) Site located in Belize. The comparison of both coast effect studies shows an equivalent behaviour for the short periods when the different ocean effects do not overlap. The phase tensors’ major axes and tippers are oriented orthogonal to the coastlines with real and imaginary arrows being antiparallel. Towards longer periods, the individual coast effects are superimposed and the phase tensors become very uniform showing similar patterns for both studies. They feature a strong phase split all over the area and the orientation of the maximum phase direction is towards the regional water distribution on both sites. Whereas the coast effect on phase tensors is increased by two opposite oceanic bodies, the combined effect on tipper arrows is more complicated and locations exist where the induced vertical magnetic field reverses sign and the ocean effects cancel each other out. It becomes evident that the combined tipper arrows at long periods strongly depend on the distribution of the deep sea water and the position of the oceanic bodies. Comparison with observations Coast effect studies yield important information for the inversion and modeling of an observed data set. A data example from the Pyrenean Mountain Chain illustrates the importance of coast effect studies (Cembrowski 2017, Fig. 10). The observed phase tensors reveal a large phase split with orientations of the major axes being very similar to the synthetic coast effect study (Fig. 5). The degree of observed phase split indicates a strong coast effect and thus high resistivities for the Pyrenean lithosphere (≥ 500 Ω·m). For an inversion study, the large phase split would suggest the use of a very resistive starting model to strongly weight the implemented oceans. Interestingly, the high amount of phase difference in the observation is not fully reproduced by the synthetic ocean modeling, suggesting an additional geological origin. The careful prior comparison of synthetic coast effect data and observed data helps to find an adequate starting model for the inversion runs. Figure 10. View largeDownload slide Observed real (red) and imaginary (blue) tipper vectors (left) as well as phase tensors (right) from the Pyrenean mountain chain between France and Spain (Cembrowski 2017). The phase tensors show a uniform phase split as observable in the synthetic coast effect study. Note the difference in phase scaling compared to Figs 5(a)–(i). Figure 10. View largeDownload slide Observed real (red) and imaginary (blue) tipper vectors (left) as well as phase tensors (right) from the Pyrenean mountain chain between France and Spain (Cembrowski 2017). The phase tensors show a uniform phase split as observable in the synthetic coast effect study. Note the difference in phase scaling compared to Figs 5(a)–(i). Moreover, the visual comparison of observed and synthetic tipper vectors reveals the existence of a conductive, local anomaly to the north of the very eastern profile. The conductor causes a local southward orientation of the real part of the observed tipper vectors. In general, a northwards orientation of the real parts can be observed, most likely comparable to the superposed coast effect in Fig. 4(f). Studying the lithosphere beneath Japan, Kanda & Ogawa (2014) nicely compared observed and synthetic tipper vectors from a 100 Ω·m background bathymetry model. The model was also used as a starting model in the inversion of VTF. Compared to the synthetic tipper vectors, the observed tipper vectors indicated a stronger coast effect and thus a higher initial resistivity. Moreover, a general northward trend of real tipper vectors (Parkinson convention) observed for long periods might have partly been explained by the superposed coast effects, and not by geology alone. Their final inversion model features high conductive and local anomalies (< 0.1 Ω·m) at the shorelines that might be artefacts. Using a more resistive starting model will possibly result in moderate resistivities. ANISOTROPY AND COAST EFFECT Forward Modeling Study The uniform phase split in the presence of two opposite oceans strongly resembles the phase split observable for anisotropic structures that laterally extend over a wide area (e.g. Gatzemeier & Moorkamp 2005; Häuserer & Junge 2011; Löwer 2014). The uniform phase behaviour often involves small tippers due to small lateral conductivity gradients. Our bathymetry studies reveal that similar data characteristics are present at areas where the oceanic effects cancel each other out. Besides, areas exist with unexpected and often laterally homogeneous tipper patterns. Such homogeneous patterns are also observed by Löwer & Junge (2017) above 3-D anisotropic structures. The similarities encourage the consideration and study of anisotropic structures in the presence of conducting oceans. A simple ocean–continent–ocean model is constructed (Fig. 11—Model 1). The oceans are represented by two opposite conductive bodies (0.5 Ω·m) with a separating distance of 300 km embedded in a homogenous 100 Ω·m half-space. They feature a depth of 1 km close to the area of investigation and a depth of 8 km elsewhere. Forward responses are calculated between 10 and 6250 s for 63 stations distributed along seven profiles in between the two conductive bodies. Due to the resistivity distribution of Model 1 with the electromagnetic strike in x-direction, the transfer functions (TFs) exhibit a definitive 2-D behaviour. The responses can therefore be separated into the TE (Zxy) and TM (Zyx) mode with the electric field being parallel and orthogonal to the coast line, respectively. For this case, the maximum and minimum phase values of the phase tensor directly depict the impedance phases of the off-diagonal impedance elements. The observable phase and resistivity split are caused by the lateral resistivity gradient between oceans and background. At y = 0, the individual coast effects cancel each other out and tippers are zero. Figure 11. View largeDownload slide Transfer functions for a simple ocean model. Top: the model consists of two oceanic bodies with a distance of 300 km. The parallel profiles with nine stations each are located in between the oceanic bodies. Bottom left: apparent resistivities, impedance phases and tippers (y-component) are calculated for the station (x = 0 km and y = −50 km) marked with a red colour (top left). Bottom right: map plot of phase tensors and tipper arrows for 2500 s. Figure 11. View largeDownload slide Transfer functions for a simple ocean model. Top: the model consists of two oceanic bodies with a distance of 300 km. The parallel profiles with nine stations each are located in between the oceanic bodies. Bottom left: apparent resistivities, impedance phases and tippers (y-component) are calculated for the station (x = 0 km and y = −50 km) marked with a red colour (top left). Bottom right: map plot of phase tensors and tipper arrows for 2500 s. Three additional models are constructed comprising anisotropic half-spaces starting at a depth of 100 km (Fig. 12). The respective anisotropy ratios are 25 and are in accordance with mantle anisotropy ratios (3–100) that have been observed by various studies (e.g. Mareschal et al. 1995; Simpson 2001; Bahr & Simpson 2002; Gatzemeier & Moorkamp 2005). Model 2 has a 1-D resistivity distribution that is composed of two layers (Fig. 12, left). The top layer is isotropic with 100 Ω·m. Below, the anisotropic half-space starts at 100 km and features 20 Ω·m in x-direction and 500 Ω·m in y-direction. The vertical direction is conductive for all models. As the horizontal principle axes of the anisotropy coincide with the coordinate axes, the responses of the off-diagonal impedances describe two different models: the xy-component depicts a conductivity increase at 100 km and the apparent resistivity decreases with the corresponding phase being > 45°. Contrary the yx-component describes the resistivity increase from 100 to 500 Ω·m at 100 km and the apparent resistivities are increasing for longer periods and phases are below 45°. As lateral resistivity gradients do not exist for Model 2, tippers are zero. For comparison the responses of Model 1 (Fig. 11) are illustrated as grey lines, showing a similar split of apparent resistivities and phases. Figure 12. View largeDownload slide Transfer functions for different anisotropic models. Top: the different models are illustrated as depth profiles at x = 0 km. Bottom: apparent resistivities, impedance phases and tippers (y-component) are displayed for the station marked by red colour (top). Additionally, the forward responses of Model 1 (grey lines) and the responses of the final inversion models (open circles, cf. Fig. 14) are plotted. Figure 12. View largeDownload slide Transfer functions for different anisotropic models. Top: the different models are illustrated as depth profiles at x = 0 km. Bottom: apparent resistivities, impedance phases and tippers (y-component) are displayed for the station marked by red colour (top). Additionally, the forward responses of Model 1 (grey lines) and the responses of the final inversion models (open circles, cf. Fig. 14) are plotted. Model 3 (Fig. 12, middle) comprises the oceanic bodies of Model 1 and the anisotropy of Model 2. Thus, compared to Model 2, an increase of apparent resistivity and phase split is observable. The intensified phase split is caused by the lateral conductivity gradient along the shores. As the tipper depends on lateral changes of current concentration, it is influenced by the vertical conductivity contrast at the shore line as well as by the vertical distribution of the current component parallel to the coast. This explains the slight difference of the tipper length for Models 3 and 4. In Model 4 (Fig. 12, right), the horizontal principle axes of the anisotropy are interchanged, resulting in a decrease of apparent resistivity and phase split and thus a decrease of the coast effect compared to Model 1, whereas the tipper vectors remain similar. 3-D isotropic inversion study In recent years, the application of 3-D inversion on MT array data has become a standard process. Codes for inverting for 3-D anisotropic resistivities are not yet available and thus 3-D forward modeling routines are the method of choice to test for intrinsic anisotropy (Löwer & Junge 2017). It is still an open question if certain resistivity patterns derived from the 3-D isotropic inversion may be replaced by simple anisotropic bodies. To recognize such patterns, we perform 3-D inversions of the responses from the forward calculations of Model 2–4 with ModEM (Kelbert et al. 2014). The joint inversion of impedances and VTFs is done for the 63 stations shown in Fig. 11. An error of 3 per cent is ascribed to each impedance component individually. Additionally, an error floor of 3 per cent of |Zxy · Zyx|1/2  is attributed to small diagonal elements. A constant value of 0.02 is used for the error bounds of the VTFs. The inner study area is discretized with a 9 km grid consisting of 23 × 34 (x- and y-directions) cells. Outside, the cell widths increase by a factor of 1.2 towards the outer boundaries. In vertical direction, the thickness of the first layer is 0.3 km and increases by a factor of 1.1 for subsequent layers. As static shift problems do not occur in our study, 0.3 km for the uppermost layer yields a sufficient resolution. The discretization results in a grid of 61 × 70 × 61 (x-, y- and z-directions) cells. A homogeneous half-space of 100 Ω·m is used as a starting model. For the inversions of responses from Models 3 and 4, the oceanic bodies are additionally incorporated as prior information and are fixed during the inversion. The spatial smoothing is set to 0.2, resulting in a spreading of bulk resistivity values into adjacent cells (Murphy & Egbert 2017). The final inversion models are displayed in Fig. 14, illustrated as different depth slices and cross-sections at x = 0 km and y = 0 km. The respective normalized root-mean-square misfit (nrms) for Models 2, 3 and 4 are 0.68, 1.44 and 0.97, respectively. The overall nrms does not make any specifications about frequency, location or TF-dependent misfit. Hence, Fig. 12 additionally shows the predicted off-diagonal responses of the final inversion models as open circles. The apparent resistivities and impedance phases of the inversion responses reproduce the input data reasonably well. However, the small systematic phase and tipper misfit for Model 3 results in a higher rms than for the other inversions. Figure 14. View largeDownload slide Final resistivity inversion models of the forward responses of Models 2, 3 and 4. Black lines mark the position of the oceanic bodies and the electrical anisotropy layer. Figure 14. View largeDownload slide Final resistivity inversion models of the forward responses of Models 2, 3 and 4. Black lines mark the position of the oceanic bodies and the electrical anisotropy layer. Fig. 13 shows map plots of predicted phase tensors and tippers for 2500 s (left) and the corresponding phase tensor (middle) and tipper misfits (right) between forward and predicted responses. Phase tensors are well predicted for Models 2 and 4. As already observed for the comparison of impedance data, the observed phase split of phase tensors is largest for Model 3. The predicted tippers reveal the three-dimensionality of the inversion responses for the northern and southern stations of all models. The vectorial differences between modeled and predicted tippers (right) show that systematic misfits occur for all models. Obviously, the fit of the impedances dominates the fit of the tippers in the inversion. The predicted tippers are not parallel as for the modeled data in Fig. 11, as obviously the combined prediction of impedances and tippers requires a 3-D resistivity distribution. Figure 13. View largeDownload slide Evaluation of inversion responses. Left: map plot of inversion model responses. Phase tensors and tippers are displayed for 2500 s. Middle: phase tensor misfit between forward and inversion responses. The circle has a radius equivalent to a misfit of 5°. Right: tipper misfit between forward and inversion responses. Figure 13. View largeDownload slide Evaluation of inversion responses. Left: map plot of inversion model responses. Phase tensors and tippers are displayed for 2500 s. Middle: phase tensor misfit between forward and inversion responses. The circle has a radius equivalent to a misfit of 5°. Right: tipper misfit between forward and inversion responses. The final resistivity models of the inversions illustrate how the inversion routine attempts to explain anisotropic data (Fig. 14). The inversion model 2 (left) is dominated by two conductive structures located to the east and west of the station grid in a depth of around 80 100 km. As opposed oceans, they produce a rather uniform phase split at all sites. Two elongated tube-like conductors (∼2 Ω·m) are extended in the direction of the conductive principle axes of the anisotropy at around 70 km depth. These structures cause an additional phase split and compensate the tippers produced by the anomalies outside the station grid. They represent a macroscopic anisotropy, since they cannot be resolved separately by the data. The large phase split of the responses from Model 3 can only partly be explained by the oceans implemented in the starting model. As in the inversion result of Model 2, an additional split is realized by conductive tubes (∼20 Ω·m) at around 70 km. The large anomalies of Model 2 outside the station grid are shifted beneath the grid, since the implementation of the oceans decreases the model sensitivities. The inversion of data from Model 4 with interchanged horizontal anisotropic resistivities results in a comparably conductive background (Fig. 14, right). The higher conductance attenuates the coast effect and decreases the apparent resistivity and phase split. Moreover, resistive structures are incorporated below the shorelines. Conductive tubes in the direction of the good conductive anisotropy axis are not observable. DISCUSSION AND CONCLUSIONS We have performed 3-D bathymetry forward modeling of areas where landmasses are bounded by opposite oceans. For the Pyrenean area and Central America, we showed that for shorter periods the coast effect is restricted within areas close to the oceans and the orientations of tipper arrows and phase tensors essentially depend on the geometry of the coastline. Whereas for shorter periods an individual effect of the respective ocean can be observed, the influence is superimposed for longer periods. The phase tensor behaviour becomes very uniform with a strong phase split and the maximum phases oriented towards the opposed oceans. The comparison between both study areas shows that the pattern of the tipper arrows is rather complicated and depends on the distribution of the deep sea water and the mutual position of the opposite oceans. At certain areas, the oceanic influences cancel each other out and result in almost zero tippers or render it difficult to associate length and orientation to the coast effect. Prior studies of the coast effect provide important information on the nature of observed data sets. Assessing the synthetic coast effect responses for different background models helps to avoid misinterpreting data patterns caused by complicated coast effects. The comparison of synthetic and observed ocean effect yields information about the lithospheric conductance and facilitates the selection of an appropriate starting model for the inversion. Our coast effect studies aim at regional MT arrays rather than local studies. Thus this work makes an important contribution to the MT community, since arrays of MT stations (e.g. EarthScopeUSArray in the United States or SinoProbe in China) have become the standard method in magnetotelluric exploration. Furthermore, we demonstrated that the impedance response of an anisotropic layer at depth very much resembles the response of opposite oceans with both models causing a split of phases and of resistivities. The responses depend on the ocean depth, the distance between both oceans, the background resistivity and the resistivities of the anisotropic layer. The effect of oceans and anisotropy is shown for models with opposite oceans and anisotropic half-spaces at 100 km depth with the conductive horizontal direction being orthogonal and parallel to the coastlines, respectively. In both cases, the tipper responses are very similar, since the vertical magnetic field is only generated due to the lateral conductivity gradient between sea and land. Contrary, the phase and resistivity behaviour strongly depend on the direction of the conductive horizontal anisotropy axes. We performed 3-D isotropic inversions of the anisotropic forward data for 63 stations distributed along seven profiles. The inversion explains the input data well. Conspicuous systematic misfits are only observed for Model 3 where ocean response and anisotropy generate a large phase and apparent resistivity split. We do not consider the systematic misfits as an absolute diagnostic for electrical anisotropy. In fact, they seem to occur in inversion studies of synthetic data when the model parametrization cannot fully resolve the data variability, independent of whether the synthetic input data are isotropic or anisotropic. The isotropic inversion replaces the anisotropic layer by parallel tube-like conductive anomalies representing a macroscopic anisotropy and by conductors outside the station grid. The result resembles the studies from Heise & Pous (2001) and Löwer & Junge (2017), where electrical anisotropy is explained by alternating isotropic structures of high and low resistivities beneath the station grid. Contrary to the 3-D model of Löwer & Junge (2017), the anisotropic model in this study is 1-D and conductive anomalies are also implemented outside the station grid. The inversion of Model 3 with opposite oceans also results in conductive tubes. However, they are one order of magnitude less conductive than those observed for Model 2. Contrary, the inversion of TF from Model 4 does not show the anisotropic model characteristics. In essence, mantle anisotropy in the presence of opposed oceans is hard to be recovered by 3-D isotropic inversion, when the conductive direction is perpendicular to the shorelines. The inversion results depend on the station grid and model parametrization. A high spatial model smoothness as well as oversized model cells do not allow for lateral alternating contrasting isotropic structures that represent macroscopic anisotropy. Moreover, test inversion runs with only three profiles consisting of 27 stations did not reveal alternating structures, but solely conductors outside the station grid, complicating the identification of anisotropy. The results showed that the stations should cover an area with a width at least twice the depth of the anisotropic layer to recover macroscopic anisotropy. According to our studies, we recommend to carefully check inversion models for resistivity anomalies outside the station grid and for alternating resistivity structures that may represent macroscopic anisotropy. Sensitivity studies of these structures can help to better understand their effect on TFs. 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Published by Oxford University Press on behalf of The Royal Astronomical Society.

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