Two-dimensional marine magnetotelluric (MT) observations are useful for offshore geologic studies, such as natural resource exploration, fault mapping, fluid estimation at subduction zones, and the delineation of the lithosphere-asthenosphere boundary beneath the seafloor. Earth structures are often assumed to be two dimensional, which allows MT data to be decomposed into a transverse electric (TE) mode and a transverse magnetic (TM) mode. The 2D assumption can effectively reduce acquisition and computational costs. However, offline 3D effects and other problems such as lack/failure of the compass on instruments are often encountered, making it difficult to decompose data into the TE and TM modes. In these cases, 2D inversion may be misleading or may not provide an acceptable misfit to the marine MT observations. Thus, we have developed a 2D determinant inversion to the marine MT method to mitigate these difficulties, implemented in the MARE2DEM code, and we tested its utility using synthetic examples and a field example. In the synthetic examples, the determinant inversion demonstrates an ability to overcome 3D effects caused by 3D anomalies and bathymetry. With confidence from the synthetic tests, we interpreted real data acquired in the Gulf of California, Mexico, where not only is the bathymetry 3D in nature, but the external compasses failed to record the orientation. The field data can not only be fit to a reasonable misfit with a determinant inversion, but the resolved conductive zones also have a good correlation with known faults. A comparison between the resistivity model from the field data and a seismic reflection section shows that a previously interpreted fault, the Wagner Fault, should be shifted 5 km toward the southwest and made slightly steeper. Thus, the implementation of the determinant inversion may provide a new approach for using problematic 2D data.

The marine magnetotelluric (MT) method has been used to investigate seafloor geology for hydrocarbon exploration (Constable et al., 1998; Hoversten et al., 2000; Key et al., 2006) and to understand the distribution of melt and water on earth, such as at midocean ridges (Key et al., 2013; Johansen et al., 2019; Wang et al., 2019a), hotspots (e.g., Nolasco et al., 1998), oceanic trenches, and subduction zones (e.g., Worzewski et al., 2011; Naif et al., 2013), as well as for other applications. Thus, marine MT data can not only assist in answering scientific questions, such as dynamics of the lithosphere-asthenosphere boundary and fluid distribution at subduction zones, but they can also satisfy industrial needs, such as in oil, groundwater, and geothermal reservoir exploration.

Although three-dimensionality is the default geometry for the subsurface structures of the earth, we often acquire 2D surveys rather than 3D surveys due to the high costs of the latter and the computational difficulties of 3D inversion. In the 2D case, we decompose marine MT data into a transverse electric (TE) mode, with electric current flowing approximately along the strike direction, and a transverse magnetic (TM) mode, with current flowing in a plane perpendicular to the strike direction. Unfortunately, difficulties sometimes prevent us from modeling the field data correctly in the TE and TM modes for two main reasons: (1) if the TE- and TM-mode decomposition is not straightforward in the presence of 3D distortions caused by, for example, small-scale heterogeneities in the seafloor, bathymetry, and large-scale effects from coastlines or (2) if the orientation of the instruments is not accurately recorded due to compass malfunction (or the lack of a compass). In contrast with marine MT, topography has a limited effect on MT observations on land and sites are always correctly oriented.

It may be hard to obtain useful results if the problems described above cannot effectively be addressed. Studies have been done for the suppression of 3D effects mainly based on land MT observations. TE-mode data are more influenced by 3D effects than TM-mode data, and the latter are more susceptible to static shifts. However, Berdichevsky et al. (1998) conclude that TE-mode data may be more robust to the 3D effects caused by resistive structures. Tensor decomposition is a standard approach to overcome distortions in land MT data (Groom and Bailey, 1989; Groom and Bahr, 1992; Chave and Torquil-Smith, 1994). DeGroot‐Hedlin (1991) proposes using regularized inversion that includes static shift to remove the influence of the distortion. In the marine environment, Baba and Chave (2005) use forward modeling to iteratively remove distortions caused by bathymetry. Moreover, a thin sheet model is often considered to remove mainly galvanic distortions in marine MT data (Price, 1949; Ranganayaki and Madden, 1980; Parker and Wheelock, 2012), but this is limited to low frequencies in which there is no inductive coupling between the ocean and the seafloor structure.

Determinant data have been effectively used to overcome 3D effects in 1D and 2D inversions for land MT data (Berdichevsky et al., 1980; Pedersen and Engels, 2005). The determinant is invariant under rotation and hence is not influenced by the orientation of the measuring coordinates (Eggers, 1982). For 2D resistivity variations, the determinant apparent resistivity gives the geometric mean of the parallel and perpendicular resistivities and could be interpreted as an average scalar resistivity for the medium by analogy with mixtures (Madden, 1976). Ranganayaki (1984) finds that, even in 3D situations, the determinant apparent resistivity and phase data give the geometric mean of parallel and perpendicular apparent resistivities and the sum of their phases. Park and Livelybrooks (1989) state that using determinant data is as good as using the arithmetic mean of the impedance tensor. Szarka and Menvielle (1997) show that determinant data as the rotational invariant are independent of the direction of the inducing electromagnetic field and those of the recording axes. Árnason (2015) shows that determinant data have the ability to overcome the static shift for land MT data. Different questions have also been answered with determinant inversion, such as the Lithoprobe Southeastern Canadian cordilleran transect (Jones et al., 1988), geothermal studies (Arango et al., 2009), limestone quarry evaluation (Bastani et al., 2013), fractured zones (Linde and Pedersen, 2004; Mehta et al., 2017), Fennoscandia resistivity structures (Cherevatova et al., 2015), and geohazard evaluation (Kalscheuer et al., 2013; Wang et al., 2016).

Here, we propose the use of 2D determinant inversion for marine MT data to mitigate 3D effects and other influences in data sets acquired with 2D profiles. Synthetic tests and a field example of a data set with compass malfunctions demonstrate the ability of the method to overcome the difficulty of decoupling TE- and TM-mode data and 3D effects in a complex marine environment.

The generation of marine MT signals is by natural phenomena, such as solar wind and global thunderstorm/lighting activities. The signals are generally considered as plane waves due to the long travel distances between the locations of these activities and the observations. The long-period time series of electromagnetic observations can be transformed into frequency-domain data, where the electric fields (Ex, Ey) and magnetic fields (Hx,Hy) are essentially connected through the frequency-dependent impedance tensor Z given as
[ExEy]=[ZxxZxyZyxZyy][HxHy],
(1)
in a Cartesian coordinate system in which x represents the strike direction, y is the profile direction, and z is the depth. The determinant impedance, a well-known data type in land MT studies (Berdichevsky et al., 1980; Jones et al., 1988; Pedersen and Engels, 2005), is defined as
Zdet=ZxxZyyZxyZyx.
(2)
In 2D media, the off-diagonal components Zxy and Zyx and the determinant impedance can be used to define apparent resistivities (ρxy/yx/det) and phases (ϕxy/yx/det) of the TE mode, TM mode, and a determinant mode, respectively, as
ρxy/yx/det=1μω|Zxy/yx/det|2,
(3)
ϕxy/yx/det=tan1(Im(Zxy/yx/det)/Re(Zxy/yx/det)),
(4)
where ω is the angular frequency and μ is the permeability.
When a rotation is needed to obtain the maximal values for Zxy and Zyx, the determinant of the rotated impedance, Zdet, will be the same as the determinant of the unrotated impedance (Eggers, 1982), Zdet, so that
Zdet=|cosθsinθsinθcosθ|Zdet|cosθsinθsinθcosθ|,
(5)
where θ is a rotation angle that rotates the observational profile perpendicular to the strike direction of a preferred geologic structure. The rotation needed for Zxy and Zyx is unnecessary for the determinant because the determinant of a rotation matrix is one. This can to some extent overcome 3D distortion and profile orientation issues, making data preparation relatively simple for 2D inversion.

We implemented the determinant inversion in MARE2DEM (Key, 2016), which is a well-structured academic code for inverting MT and controlled-source electromagnetic (CSEM) data into 2D resistivity models. Due to the architecture of MARE2DEM, a determinant data type can be used for MT-only inversion and joint inversion of MT and CSEM data. We use synthetic examples and a field example to show the value of using determinant inversion in marine MT. It is worth mentioning that the MARE2DEM implementation of 2D determinant inversion can also be used in land applications to overcome the influence of 3D topography.

Synthetic test with a simple model

After Pedersen and Engels (2005) proposed using determinant data in 2D inversion to overcome 3D effects, the method has started to be used in different applications on land. However, determinant inversion is still new in the marine MT method. A synthetic test with a simple model is used to show that determinant data are less affected by 3D structure and bathymetry, which are sometimes an inevitable difficulty in the interpretation of marine MT data along a 2D profile.

Three-dimensional forward modeling is carried out with a modified version of the 3D MT finite element (FE) code initially developed by Jahandari and Farquharson (2017). The new modification of the code is mainly the boundary condition generated with a layered model rather than a half-space model, which is required for marine MT modeling. A marine model without any anomaly is used to test the performance of the modification. Apparent resistivities are around the background resistivity value with a few data points beyond 6% of what they should be, and phases are approximately 45° with a few data points beyond 1° of what they should be for the off-diagonal components of the impedance tensor. A synthetic model with a conductive anomaly then is generated. The polygon file describing the synthetic model was generated with FacetModeller (Lelièvre et al., 2018). In the synthetic model (Figure 1), the seawater is 5 km thick and has conductivity of 3 S/m. The top of a conductive anomaly, 5 S/m, is buried at 20 km depth. The volume of the conductor is 100 × 100 × 50 km. The conductivity of the air and background media is 10−8 and 10−2 S/m, respectively. Synthetic observations are 1 m above the seafloor with 30 km spacing in the horizontal directions. The observations and the conductive anomaly are symmetric with respect to the z-axis. The synthetic model is discretized into 1,094,676 tetrahedra using TetGen (Si, 2015). The observation positions are located at the centers of small regular tetrahedra. The distance from the center to the vertex of the small tetrahedra is 1 m, which provides a fine discretization for the FE to have enough accuracy for the calculations (Figure 1). Profile L1, as marked in Figure 1, is selected for inversion. This profile is parallel to the x-direction and has a 10 km offset from the anomaly in the y-direction. Ten frequencies used in the modeling are logarithmically equally distributed between 10−2 and 10−5 Hz.

After the MT responses are calculated with the modified 3D MT code (Jahandari and Farquharson, 2017), the 2D MT inversion with determinant data was carried out with the modified version of MARE2DEM (Key, 2016; Wang et al., 2019b). The main modifications of MARE2DEM are the inclusion of a data type for the determinant and its sensitivity calculation. The synthetic observations were contaminated by Gaussian noise in the impedance tensor equivalent to a 10% error floor on the apparent resistivities and a 2.86° error floor on the phases, which simulates typical field observations. The impedance polar diagrams show the dimensionality of the synthetic data, and no preferred strike direction is displayed (Figure 2). We inverted 2D models along the profile L1 (Figure 1). The initial model used for inversion has a resistivity of 100 ohm-m and 18,850 elements. The inverted models along profile L1 showed that TE-mode inversion has less influence from the structure to the side of the profile than TM-mode inversion because electric current mostly flows along the x-direction rather than the y-direction due to the blocking of current flow by the resistive background with respect to the position of the profile. The TE- and TM-mode data inverted together and determinant data can detect the side anomaly (Figure 3). The determinant inversion has, however, a reasonable data fit and less influence from the 3D effects, which show as off-target artifacts (Figure 3). In all cases, the bottom of the conductor is blurred due to the poor resolution of MT data to the bottom of deep conductors (Kalscheuer et al., 2010). When we used the determinant data, which is equivalent to the geometric mean of TE- and TM-mode data (Madden, 1976; Ranganayaki, 1984), the inversion has less influence from the 3D effects than TM-mode inversion (Figure 3).

If we switch the TE- and TM-mode data to simulate an incorrect decomposition of the two modes, our inversions showed that for profile L1, the inversions with switched data mode cannot correctly recover the model (Figure 4 and 4) because the profile has 3D effects from the anomaly. Indeed, the TM inversion of TE data does a good job (Figure 4), similar to what Key et al. (2006) observe for their “cross-line electric” inversion. Whether one uses the switched mode or the correct mode, the determinant data are the same as shown in equation 5 (Figures 3 and 4), so that the corresponding inversion is stable. Thus, the determinant inversion can overcome a problem caused by difficult decomposition of TE and TM modes caused by failed compasses when the 3D distortion is not strong.

Synthetic test with a “Hawaiian” model

This example is a simplified version of the Hawaiian plume, which has a complex structure combined with bathymetry (Ballmer et al., 2013; Rychert et al., 2013). The plume shape and melt migration conduit of the plume are still elusive geophysical targets. By using this example, the MT method can be evaluated for its potential to resolve the relevant information at great depth. Again, the polygon file for the synthetic model was generated with FacetModeller (Lelièvre et al., 2018) and the forward modeling is carried out with the 3D MT FE code (Jahandari and Farquharson, 2017). In the synthetic model (Figure 5 and 5), the seawater is 4 km thick with conductivity of 3 S/m, and the thickness decreases to 0 km at the boundary of the island due to the inclusion of artificial bathymetry. A transition layer between the seawater and lithosphere is 6–10 km thick, varying with the bathymetry, with conductivity of 10−2 S/m. The lithosphere is 90 km thick with conductivity of 10−4 S/m. The asthenosphere has conductivity of 10−2 S/m at the depth of 100–400 km, where its conductivity increases to 1 S/m at greater depths. The plume conductivity is 0.1 S/m in the lithosphere and 1 S/m in the asthenosphere. The conductivity of the air and background media is 10−8 and 10−2 S/m, respectively. We know that this is a much-simplified version of the true geology, but it serves to test our method. The synthetic model is discretized into 944,251 tetrahedra using TetGen (Si, 2015). The same discretization strategy as for the previous example is used at the positions of the observations to ensure good enough accuracy for the calculations (Figure 5 and 5). Profile L1 is selected for inversion (Figure 5). Seven frequencies used in the modeling are logarithmically equally distributed between 10−3 and 10−5 Hz. Due to the complexity of the impedances at 10−2 to 10−3 Hz, they were not used in this synthetic test.

After the MT responses are calculated with the 3D MT FE code, the synthetic observations were contaminated by Gaussian noise equivalent to 10% error on apparent resistivities and 2.86° error on phases. The impedance polar diagrams of the data show that bathymetry causes features associated with 2D and 3D dimensionality (Figure 6). We inverted 2D models along the profile L1 with the modified MARE2DEM code. The initial model used for the inversion has resistivity of 100 ohm-m and 21,480 elements. The TE-mode inversion has a large misfit, especially at the stations close to the plume edge, and the corresponding model is also different from the real one (Figure 7). The TM-mode inversion has a small misfit, but deep structures are not resolved (Figure 7). The joint mode inversion also did not resolve the real model due to strong 3D distortion in the TE-mode data (Figure 7). The determinant inversion recovers the plume anomaly (Figure 7). Interestingly, the deep asthenosphere is seen in the model, but the position of the conduit is, however, not resolved. This is not entirely a surprise because subvertical pipes are difficult to image with MT data.

If we switch the TE- and TM-mode data to simulate an incorrect decomposition of the two modes, the results show that inversions with the switched data mode cannot recover the model (the relevant figure is not shown). Because the plume is 3D and combined with a bathymetric structure, the TE and TM modes cannot be effectively used in this example, even without orientation problems. However, regardless of whether one uses the switched mode or the correct mode, the determinant data are the same and the determinant inversion is stable. Hence, we show that the determinant inversion can partially overcome the 3D effects caused by 3D anomalies and bathymetry.

The Gulf of California, Mexico

The Gulf of California (GC), Mexico, considered as an extension of the Pacific Ocean (Figure 8), is an oblique extensional rift system along the Pacific and North America plate boundary (Larson et al., 1972). Previous studies suggest that the creation of the GC began around 12 million years ago with the formation of a proto-Gulf during the Neogene (Martín-Barajas, 2000). At that time, the peninsula block started to separate from the continent with relative movement westward. This continental break was consequently a process of extension, and a series of related tectonic movements led to the development of significant transform faults at the boundary between the Pacific and North American plates during the Pliocene, creating the San Andreas Fault system (Stock and Hodges, 1989). By the end of the proto-Gulf (6 million years ago), the Pacific and North American plate motion became localized. Then, the Baja California microplate was entirely transferred to the Pacific plate and the present GC formed (Oskin et al., 2001; González-Escobar et al., 2014).

The study area spans the transition between the Wagner Basin (WB) and the Consag Basin (CB) situated in the northern GC (NGC) (Figure 8). These two basins are filled with 6–7 km of sediments and are also colocated with fault zones, such as the Wagner Fault (WF) and the Consag Fault (CF) in the NGC. Despite the considerable accumulation of sediments, some faults reach the seafloor, creating a permeable area predisposed to allow fluid outflow within the faults. This may lead to a conductive feature of the fault zone. Based on seismic reflection profiles in the NGC, the acoustic basement is located at depths greater than 7 km (González‐Escobar et al., 2009; Martín‐Barajas et al., 2013).

To investigate the fault system in the NGC, 15 marine MT instruments were deployed along two crossed profiles (Avilés-Esquivel et al., 2020; Montiel-Álvarez et al., 2020), approximately 100 km long, with spacing of 7–15 km at the seafloor (Figure 8). The deepest bathymetry is approximately 220 m in the WB (Figure 8). Profile 1 is used in this study (the white triangles in Figure 8), even though two stations are not useful due to acquisition issues. The data acquisition duration was 18 days. The time series were processed by a multistation transfer function estimation code (Egbert, 1997), giving data from 0.125 to 5960 s (28 frequencies logarithmically equally distributed). Unfortunately, the compass of the MT instruments did not function properly, so that the orientations of the receivers at the seafloor were estimated using crosscorrelations of the magnetic field measured at the Piñon Flat Observatory (350 km away), Southern California, with rotated magnetic fields recorded at the MT receivers. Different techniques were used to correct the orientations, such as orthogonal Procrustes rotation analysis (OPRA), crosscorrelation with the remote station, and rotating the stations to the crossline of the profile, but all were difficult to fit using 2D inversion of the decomposed TE/TM data. This suggests that there is 3D distortion in the data besides the compass problem.

The approximately decomposed TE- and TM-mode data were used for inversions with MARE2DEM. These data show mainly 2D features but also some 3D distortions at long periods at stations S3–S6 (Figure 9). The initial half-space model with resistivity of 1 ohm-m was discretized into 15,871 triangles. An error floor of 5% on the apparent resistivities and 1.43° on the phase was applied to the processing error estimates. The difficulty of using the incompletely decomposed TE- and TM-mode data in inversion is that the inversions do not converge well (Figure 1010), especially for TE-mode data (Figure 10), which have more influence from 3D effects than TM-mode data (Figure 10). The lowest obtainable root-mean-square (rms) misfit of the TE-mode inversion and joint mode inversion is 2.91 and 2.62, respectively. Even though the TM-mode inversion has a reasonable misfit (rms is 1.54), the model is very different from the TE-mode inversion. Hence, the determinant inversion is used to overcome the difficulties of the TE- and TM-mode decomposition and potential 3D effects (Figure 10) along with any residual errors in orientation. Because determinant data are less sensitive to the orientation of the instruments and 3D distortions than TE- and TM-mode data, the inversion converges to a reasonable misfit (rms is 1.12). The conductive zone A in the determinant data resistivity model is clearly shown at 2–20 km in depth (Figure 10). The position of conductive zone A corresponds with a known fractured zone marked as WF in Figure 8. A fracture zone colocated with, or close to, conductive zones is most likely due to seawater in permeable zones. In general, the known faults marked as arrows show correlation with conductive zones in the resistivity model, such as CF, WF, the Cerro Prieto Fault (CPF), and the Amado Fault (AMF) (Figures 8 and 10). Conductive zone B is not directly connected to any known fault due to the depth limit, approximately 5–6 km, of the previous seismic study (Aragón-Arreola and Martín-Barajas, 2007; González‐Escobar et al., 2009; Martín‐Barajas et al., 2013).

To determine if the inverted model is reliable, skin depths, data sensitivity tests, a synthetic test, and the sensitivity matrix are all used to evaluate the model. The white dashed lines in Figure 10 represent the skin depth calculated with the method of Huang (2005), which is reported to show that the structures above this depth are reliable. However, this is not useful if the inversion has not converged to a good fit (such as Figure 10 and 10). Increasing the resistivity of anomalies A and B (Figure 10) to 100 ohm-m increases the rms from 1.12 to 5.57 and 2.31, respectively. Thus, the data are sensitive to both anomalies, especially to anomaly A, due to good data coverage. A simplified model abstracted from Figure 10 is also used for a synthetic test to examine the reliability in resolving the anomaly A (Figure 10). Even though the resolution is very low at the locations without data coverage, the anomaly A is recovered in the synthetic test (Figure 10). The sensitivity matrix with respect to a model is also used to evaluate the inverted models. Total sensitivities were computed as sums over all data points of the absolute values of sensitivities normalized by data uncertainty and cell area following Schwalenberg et al. (2002). The sensitivities for the TE-mode inversion are mainly concentrated at shallow depth (Figure 11). The sensitivities associated with the TM-mode inversion and joint mode inversion have better depth coverage than the TE-mode inversion (Figure 11 and 11). The joint inversion shows a high sensitivity at depth, but the data misfits are high (Figures 10 and 11). However, the sensitivities from the determinant inversion, with a reasonable rms, extend to greater depths compared with TE- and TM-mode inversions, suggesting that the determinant inversion model is more reliable than the ones of TE- and/or TM-mode inversions. The high sensitivities of conductive zones A and B (Figure 10) support the interpretation of the two conductive zones.

The interpreted seismic section from Aragón-Arreola and Martín-Barajas (2007) is superimposed on top of a part of the determinant resistivity model (Figure 12). The resistivity model is cut to fit the seismic reflection section. The two-way traveltime of 5 s corresponds to approximately 6 km in depth (Aragón-Arreola and Martín-Barajas, 2007). Good correlations between the conductive zones and the seismic structures are shown (Figure 12). The resistivity model shows that conductive sediments reach approximately 6 km in depth (Figure 10), which matches the information from previous studies (Aragón-Arreola and Martín-Barajas, 2007). Faults AMF, CPF, and WF correspond to conductive zones. The WF interpreted in the seismic section is shifted toward the northeast compared to a conductive zone in the resistivity model (Figure 12). With careful comparison between the uninterpreted seismic section and resistivity model (Figure 12), the interpretation of WF in the seismic section can be shifted to the southwest to colocate with the resolved conductive zone, suggesting that the previous interpretation of WF should be updated. The position of WF should be shifted southwest approximately 5 km, and the dip should be steeper as shown in Figure 12. The Adair Fault (ADF) is not clear in the resistivity model, probably due to its small scale. The correlation between the reflection structures and resistivity model shows the determinant data inversion overcomes 3D distortions and compass malfunction, from which the TE- and TM-mode data suffer.

Determinant data and inversion have not been introduced in marine MT studies before. Hence, with the implementation of the idea in MARE2DEM, the 2D determinant inversion is a publicly available new tool for marine EM geophysicists. Based on the synthetic and field examples, using determinant data can overcome 3D distortions and other difficulties. This advantage is useful when the TE- and TM-mode decomposition is not achievable, as shown in the synthetic tests (Figure 5) and the case study at GC (Figure 10). The introduction of 2D determinant inversion in marine MT can improve the interpretation of some data sets, especially those collected with a 2D acquisition geometry on the rough seafloor, which are difficult to handle with TE- and TM-mode inversions. Unlike TE- and TM-mode inversions with incompletely decomposed data, determinant inversion can converge to a reasonable model. Determinant data are rotationally invariant and are, in fact, independent of the direction of the inducing electromagnetic field and those of the recording axes (Szarka and Menvielle, 1997). Using 2D determinant inversion, the synthetic example of the 3D Hawaiian model shows that the marine MT method has the ability to resolve the general features of a conductive plume head, but it cannot resolve the conduit, which acts as a passage for the migration of melt from asthenosphere to lithosphere. One should bear in mind that the 2D determinant inversion has limits when facing complex 3D structures. In that case, 3D inversion is the best choice. However, 3D inversion with the inclusion of realistic bathymetry is not yet well-developed. A reasonable option is the bathymetry removal before 3D inversion with structured model discretization (Baba and Chave, 2005; Baba et al., 2017), but this is not always possible for large-scale coastal effects (Wang et al., 2019a). Also, Parker and Wheelock (2012) demonstrate that 3D bathymetry and coastlines cause 3D distortions in MT data even in the case of 1D subsurface resistivity structure. In such a case, the 2D determinant inversion is a useful function.

Model evaluation is an important step in inversions. Once a reasonable model is obtained, a couple of schemes can be used to evaluate the model resolution, as has been emphasized in a few studies (Candansayar and Tezkan, 2008; Kalscheuer et al., 2010, 2013; Wang et al., 2019b; Ren and Kalscheuer, 2020). In the field example, the skin depth of Huang (2005) is one method used to check the reliability of the inverted model. Based on Spies (1989), the effective investigation depth can be 1.5 times that of the skin depth. Thus, the investigation depth used in this study is conservative. A premise of using skin depth is that the misfit of the inversion predictions to the data should be reasonable. Otherwise, it is not useful to examine the skin depth, such as for the models in Figure 10 and 10. The two models have a deeper skin depth than the maximal model depth, but the data have large misfits. This also demonstrates that the skin depth should not be the only tool used for model reliability estimation. The sensitivity matrix of the inversion models is another tool used to check the reliability of the inversions (Schwalenberg et al., 2002). In the field example, the sensitivities of the TE-mode data are concentrated at a shallow depth, whereas the sensitivities for the TM-mode data are relatively high at a great depth. The determinant data are, however, more sensitive to the deep structures compared with the TE- and TM-mode data due to suppression of 3D effects, suggesting the idea that the determinant inversion converges better and resolves more reasonable structures than the other two modes (Figure 10). Besides, data sensitivity analyses and a synthetic test also are used to evaluate the anomalies resolved in the determinant inversion (Figure 1010). Generally speaking, the interesting anomalies, especially the anomaly A, are reliable. The location without data coverage shows artifacts, which should be considered in the interpretation. Even though the inversion fits the data and the features are “resolved,” this does not mean that the inversion fully represents the true geology. Thus, a priori information and other geophysical data should be used to evaluate the inversion results, as we used in the GC field example.

The field study presented here provides useful information not evident from previous studies (Aragón-Arreola and Martín-Barajas, 2007; González‐Escobar et al., 2009; Martín‐Barajas et al., 2013). The NGC has approximately 6 km thick sediments, which shows as a low resistivity feature. The fault zones propagate through the sediments and have complex features. Because the faults are inferred to be permeable, it is highly likely that the faults are filled with seawater, so that most of the fault zones, such as CF, WF, CPF, and AMF, are conductive and can be resolved using MT data. These conductive fault systems are similar to those observed along the coast of the Baltic Sea (Mehta et al., 2017; Wang et al., 2019b) and at the Middle America Trench (Naif et al., 2015). Inevitably, the exploration depth of the seismic profile is limited due to the width of the GC. Because the seismic reflection profile only extended to 5–6 km depth, it is not possible to resolve the dip of the faults at great depth, such as WF. However, the marine MT method provides more information about some of the traced faults at deeper depths.

The marine MT method is a useful tool for offshore studies, including natural resource exploration, undersea fault mapping, and investigations of midocean ridges, hotspots, oceanic trenches, and subduction zones. The determinant inversion has been successfully implemented in MARE2DEM, which can invert marine MT determinant data or jointly invert them with CSEM data. The modified MARE2DEM also can be used for land applications of determinant inversion with proper consideration of topography.

With synthetic and field examples, the advantages of using determinant inversion in marine MT have been shown. When the modes of MT data are mixed for whatever reasons, or when the 3D effects are hard to ignore but not very strong, a determinant inversion can effectively overcome these difficulties. In the synthetic test of a Hawaiian plume, the determinant inversion shows that the marine MT method has the potential to resolve the position of the plume and the geometry of the plume head. The determinant inversion in the field example at the GC resolved conductive zones, which generally correspond well with known faults. The TE- and TM-mode inversions cannot, however, provide equivalent results. The field example also shows that the WF should be shifted 5 km southwest and that there is another potential fault that is too deep to be detected by previous seismic reflection data due to the complexity of the GC. This provides new information for our understanding of the geologic evolution of the GC.

Although 3D inversion with bathymetry included would be the best option for marine MT data, currently publicly available codes do not handle large-scale bathymetry and coastal effects well and they also require that the instrument orientation be known. Thus, 2D determinant inversion can play an important role in marine MT data interpretation.

This paper is intended to memorialize L. B. Pedersen. The research was supported by National Science Foundation under grant OCE-1536400. Data were collected under the CONACyT CeMIEGeo program, and we thank A. G. Fernández for his leadership of this program. Four anonymous reviewers and the editors X. Hu, J. Blanch, and J. Shragge are appreciated for the constructive comments. P. Lelievre, C. Galley, and X. Lu are appreciated for guiding the use of FacetModeller. S. Wang thanks the Cecil & Ida Green Foundation and the Seafloor Electromagnetic Methods Consortium at Scripps Institution of Oceanography for postdoctoral support.

Data used in the field example are available at http://marineemlab.ucsd.edu. The modified MARE2DEM is available to anyone under the condition of acknowledging the contributions of K. Key for the original MARE2DEM.

DATA AND MISFITS

The data fits of inversions are shown in the Appendix  A. Figures 1, 2, 3, and 4 are for the inversions in Figure 33. Figures 5, 6, and 7 are for the inversions in Figure 44. Figures 8, 9, 10, and 11 are for the inversions in Figure 77. Figures 12, 13, 14, 15, and 16 are for the inversions in Figure 1010 and 10, respectively. In general, the inversions have reasonable data fits.

Biographies and photographs of the authors are not available.

Freely available online through the SEG open-access option.