Efficient and Scalable Finite-Element Magnetotelluric Modeling on High-Order Meshes

In a previous paper (Heinson & Constable 1992) we discussed the effect of coastlines on sea-floor magnetotelluric (MT) data collected deep within the ocean basins. In order to quantify the geomagnetic coast effect we developed a model for oceanic upper mantle electrical conductivity independent of previous sea-floor MT interpretations, based on sea-floor controlled-source electromagnetic (CSEM) soundings, laboratory studies of mantle materials, and global geomagnetic-sounding estimates for lower mantle conductivity. We demonstrated that the coast effect of our model was large, was not manifest as severe anisotropy in the MT response if the ocean basins were bounded by coastlines on three or more sides, and that a qualitative agreement existed between the MT response of our simple coastline model and published sea-floor MT data. The implication of the latter is that by including the effect of the coastlines additional mechanisms for enhanced upper mantle conductivity, such as volatiles, carbon, melt, hydrogen and other factors, may not be required by the MT data. Tarits, Chave & Schultz (1993) question the validity of a large number of aspects of our work. Their principal conclusions are that (a) horizontal or vertical leakage paths between the ocean and other oceans or the mantle will substantially reduce the magnitude of the ocean-wide coast effect; (b) the principle of extrapolating laboratory electrical-conductivity measurements to mantle conditions is unreliable from uncertainties in the understanding of pressure, temperature and petrological states of the upper mantle; (c) published sea-floor MT data sets examined by us were of such vintage that any conclusions drawn were unreliable or incorrect; and (d) the conductivity profile compiled by Chave, Flosadottir & Cox (1990), based on 1-D interpretations of sea-floor MT and CSEM data that took no account of the coast effect, is consequently a more reliable estimator of mantle-conductivity structure than our model. While all aspects of Tarits et d’s comments were addressed to some extent in our original paper, we did not investigate all details fully either in the interests of conciseness, or because the impact on our conclusions was minimal. We will take this opportunity to delve further into some of these issues, but before considering the complications it will be useful to reiterate the motivation for our work. First, Oldenburg’s (1981) and Oldenburg, Whittal & Parker’s (1984) 1-D interpretations of three sea-floor MT data sets included a high-conductivity zone (HCZ) in the oceanic upper mantle that decreased in magnitude and deepened with increasing age. The existence of a HCZ has become a paradigm not only amongst the electromagnetic community but also with seismologists, petrologists and mineral physicists. Many entire papers are written on the subject, attempting to explain the disparities between laboratory measurements of olivine conductivity at upper mantle temperatures and the HCZ, correlating the HCZ with seismic low-velocity zones (LVZ), examining the temporal evolution of the HCZ, etc. The impact of Oldenburg’s work has been so large that it seemed appropriate to re-examine the basis of the HCZ and question whether it is indeed required by the data. Note that

<p><b>This thesis focuses on the use of magnetotelluric (MT) data from both the North Island and South Island of New Zealand to model Geomagnetically Induced Currents (GIC) in the New Zealand power network. The model results have been compared with those from a previously used thin-sheet (TS) conductance model and with measured GIC. </b></p> <p>Initially, a single station modelling approach using a uniform conductivity Earth model is used to model the measured GIC in a transformer at Islington (ISL). This model is further improved by separately modelling low and high frequency components of GIC and then combining these to give full GIC. The model reproduces most of the GIC variations and the correlation coefficient is >70% for major magnetic storms from 2002-2015. As the model reproduces an average response of the network towards geoelectric fields it underestimates the most of extreme GIC. The analysis of GIC from other substations suggests that measured GIC depend on local geoelectric fields and the substation configuration within the network which cannot be captured using a single station approach. These limitations of single station model are addressed using more realistic geoelectric fields based on magnetotelluric data and consideration of the full network. </p> <p>To compute geoelectric fields in the whole network the gaps between MT sites are filled using a Nearest Neighbor interpolation technique. As the northern part of the North Island has no MT data an equivalent circuit approach is followed to model GIC for only the lower part of the network. The MT model GIC are in the period range of 2-30 minutes, based on the available MT data period range. Both the MT and TS techniques are used to compute geoelectric fields and to model GIC for the St. Patrick’s Day storm of 2015 and a 20 November 2003 magnetic storm. Both the MT and TS methods show the same transformers as experiencing large GIC during both storms. The primary difference between the models is that amplitudes of high frequency components of the TS model are significantly smaller than for the MT model. In particular they do not produce large GIC during the sudden storm commencement (SSC) of the St. Patrick’s Day magnetic storm. For the 20 November 2003 storm the TS model effectively reproduces the low frequency components and extreme GIC. The model results show that the North Island power network could be at risk during adverse space weather conditions.</p> <p>Although the South Island has sparser MT data the same technique is used to model SI GIC during both the St. Patrick’s Day and 2003 magnetic storms. Results are compared with measured data from ISL, South Dunedin (SDN) and Halfway Bush (HWB) transformers. The MT model effectively reproduces the measured GIC variations particularly during SSC during the St. Patrick’s Day storm. The TS model gives a very small GIC magnitude during the SSC. During the 20 November 2003 storm both the MT and TS models reproduce strong amplitudes of low frequency components seen in the ISL measured data. </p> <p>Both the MT and TS models show a substantial scale difference between measured and model GIC both for ISL and HWB transformers that needs to be further explored either in terms of better geoelectric interpolation or power network parameters. Overall, the MT model appears much more promising for future GIC modelling, particularly during a sudden storm commencement and for abrupt GIC variations.</p>

<p><b>This thesis focuses on the use of magnetotelluric (MT) data from both the North Island and South Island of New Zealand to model Geomagnetically Induced Currents (GIC) in the New Zealand power network. The model results have been compared with those from a previously used thin-sheet (TS) conductance model and with measured GIC. </b></p> <p>Initially, a single station modelling approach using a uniform conductivity Earth model is used to model the measured GIC in a transformer at Islington (ISL). This model is further improved by separately modelling low and high frequency components of GIC and then combining these to give full GIC. The model reproduces most of the GIC variations and the correlation coefficient is >70% for major magnetic storms from 2002-2015. As the model reproduces an average response of the network towards geoelectric fields it underestimates the most of extreme GIC. The analysis of GIC from other substations suggests that measured GIC depend on local geoelectric fields and the substation configuration within the network which cannot be captured using a single station approach. These limitations of single station model are addressed using more realistic geoelectric fields based on magnetotelluric data and consideration of the full network. </p> <p>To compute geoelectric fields in the whole network the gaps between MT sites are filled using a Nearest Neighbor interpolation technique. As the northern part of the North Island has no MT data an equivalent circuit approach is followed to model GIC for only the lower part of the network. The MT model GIC are in the period range of 2-30 minutes, based on the available MT data period range. Both the MT and TS techniques are used to compute geoelectric fields and to model GIC for the St. Patrick’s Day storm of 2015 and a 20 November 2003 magnetic storm. Both the MT and TS methods show the same transformers as experiencing large GIC during both storms. The primary difference between the models is that amplitudes of high frequency components of the TS model are significantly smaller than for the MT model. In particular they do not produce large GIC during the sudden storm commencement (SSC) of the St. Patrick’s Day magnetic storm. For the 20 November 2003 storm the TS model effectively reproduces the low frequency components and extreme GIC. The model results show that the North Island power network could be at risk during adverse space weather conditions.</p> <p>Although the South Island has sparser MT data the same technique is used to model SI GIC during both the St. Patrick’s Day and 2003 magnetic storms. Results are compared with measured data from ISL, South Dunedin (SDN) and Halfway Bush (HWB) transformers. The MT model effectively reproduces the measured GIC variations particularly during SSC during the St. Patrick’s Day storm. The TS model gives a very small GIC magnitude during the SSC. During the 20 November 2003 storm both the MT and TS models reproduce strong amplitudes of low frequency components seen in the ISL measured data. </p> <p>Both the MT and TS models show a substantial scale difference between measured and model GIC both for ISL and HWB transformers that needs to be further explored either in terms of better geoelectric interpolation or power network parameters. Overall, the MT model appears much more promising for future GIC modelling, particularly during a sudden storm commencement and for abrupt GIC variations.</p>

자연 전자기장을 이용하여 지하 매질의 전기적 구조를 규명하는 자기지전류(magnetotelluric; MT) 탐사의 정확한 해석을 위해서는 특정 전기적 구조에 대한 정확한 수치적 반응을 구할 수 있는 3차원 모델링이 필수적이다. 특히, 매질내에 전기적 이방성이 있을 때는 MT 반응이 달라지므로 전기적 이방성의 영향을 고려한 MT 탐사 모델링이 필요하다. 특히, MT 탐사기법을 이용한 지열저류층의 모니터링과 같이 MT 반응의 작은 변화를 분석해야 하는 시간경과 자료의 해석의 경우, 대상 지역에 이방성이 존재할 경우 이를 고려할 수 있는 정확한 모델링이 필수적이다. 이 연구에서는 기존의 등방성만을 고려하던 유한차분법 MT 모델링 알고리듬을 수직 혹은 수평 횡등방성 이방성을 고려할 수 있도록 개선하였다. 개발한 알고리듬을 박리층 모델을 이용하여 검증한 후, 수직횡등방성 이방성이 MT 반응에 미치는 영향에 대해서 분석하였다. 향후에는 수평 횡등방성 이방성이 MT 반응에 미치는 영향에 대해서도 분석하고자 하며, 알고리듬을 더욱 발전시켜 경사 횡등방성 이방성까지 고려할 수 있도록 발전시키고자 한다. Magnetotelluric (MT) survey investigates electrical structure of subsurface by measuring natural electromagnetic fields on the earth surface. For the accurate interpretation of MT data, the precise three-dimensional (3-D) modeling algorithm is prerequisite. Since MT responses are affected by electrical anisotropy of medium, the modeling algorithm has to incorporate the electrical anisotropy especially when analyzing time-lapse MT data sets, for monitoring engineered geothermal system (EGS) reservoir, because changes in different-vintage MT-data sets are small. This study developed a MT modeling algorithm for the simulation MT responses in the presence of electrical anisotropy by improving a pre-existing staggered-grid finite-difference MT modeling algorithm. After verifying the developed algorithm, we analyzed the effect of vertical transversely isotropic (VTI) anisotropy on MT responses. In addition, we are planning to extend the applicability of the developed algorithm which can simulate not only the horizontal transversely isotropic (HTI) anisotropy, but also the tiled transversely isotropic (TTI) anisotropy.

Out-of-quadrant impedance phases (POQ) have been observed in several magnetotelluric (MT) data sets around the world, hampering the modelling and interpretation of the data. These anomalous responses are usually observed in small groups of sites and have been variously interpreted as due to electrical anisotropy, galvanic distortion, 2-D structures with large resistivity contrasts, or 3-D conductive bodies, such as L-shaped conductors. We present here what is possibly a unique land-based MT data set characterized by an exceptionally large number of sites with POQ. The MT data were collected in the southeastern margin of the Capricorn Orogen (Western Australia). This is an area with a complex geological history, which is evident in the MT responses. Given the characteristics of the study area, which includes very high resistivity Archean terrains surrounded by low resistivity Palaeoproterozoic basins, strong resistivity contrasts involving complex 3-D structures are a possible cause of this unusual behaviour. This is confirmed by 3-D forward modelling using models based on the general geology of the study area, as well as by the 3-D inversion results. A comparison of the real and synthetic data, derived from 3-D forward modelling, using the same parameters suggests that the proposed scenario is a realistic explanation for most of the anomalous phases observed in this data set. Synthetic data are not affected by galvanic distortion or electrical anisotropy, so the good match observed between the real and synthetic MT responses is likely due to 3-D inductive effects. Previous explanations for POQ responses, such as blocks with electrical anisotropy and 3-D L-shaped conductors, are not required and are considered to be less likely causes of the POQ responses on geological grounds.

<div> <p>In the context of whole-lithosphere structure, the joint inversion of magnetotelluric (MT) with seismic data is particularly interesting as they provide complementary information on the thermal structure, fluid pathways and water content. Both data sets can put tight constrains on the first-order thermal structure and mineralogical structure of the lithosphere, but only MT is strongly sensitive to anomalous features such as hydrogen content, minor conductive phases and/or small volumes of fluid or melt. This makes joint inversions of MT with other observables a powerful means to detect fluid pathways in the lithosphere including the locus of partial melting, ore deposits and hydrated (or metasomatized) lithologies. This unique potential of joint inversions of MT with other datasets has given impetus to the acquisition of collocated MT and seismic data over large regions. Concrete examples are the US Array, Sinoprobe in China, and the AusLAMP/AusArray in Australia. These multi-disciplinary programs are providing high-quality seismic and MT data with unprecedented resolution and coverage, allowing the pursuit of large-scale 3D joint inversions to image the structure, dynamics and evolution of the whole lithosphere and upper mantle.</p> <p> </p> <p>Within probabilistic approaches the solution to the inverse problem is given by the so-called posterior probability density function which provides complete information about the unknown parameters and their uncertainties conditioned on the data and modelling assumptions. Joint probabilistic inversions of MT and seismic data have been successfully implemented in the context of 1D MT data only. For the cases of 2D and 3D MT data, however, the large computational cost of the MT forward problem has been the main impediment for pursuing probabilistic inversions, as the number of forward solutions required are typically on the order of 10<sup>5</sup> – 10<sup>7</sup>. To overcome this limitation, we have recently presented a novel strategy [2,3], called RB+MCMC, that computes 3D MT surrogate models and uses complementary parameterizations to couple different data sets. This strategy reduces the computational cost of the 3D MT forward solver and allow us to perform full joint probabilistic inversions of MT and other datasets for the 3D imaging of deep thermochemical anomalies.</p> <p> </p> <p>In this contribution, we first illustrate the benefits and general capabilities of our method for 3D joint probabilistic inversions of MT with other datasets using whole-lithosphere synthetic models. Last, as part of the Exploring for the Future program, we present results of the first joint probabilistic inversion of 3D MT in southeast Australia using the AusLAMP data and a seismic velocity model derived from teleseismic tomography [4]. These results demonstrate the capabilities of our conceptual and numerical framework for 3D joint probabilistic inversions of MT with other geophysical data sets and open up exciting opportunities for elucidating the Earth’s interior in other regions.</p> <p> </p> <p> </p> </div><p> </p><p><strong>References</strong></p><p>[1] Afonso, J.C. et al., (2016), Journal of Geophysical Reseach, 121, doi:10.1002/2016JB013049</p><p>[2] Manassero, M. C., et al., (2020), Geophysical Journal International, 223(3), doi: 10.1093/gji/ggaa415</p><p>[3] Manassero, M. C., et al., (2021), doi: 10.1029/2021JB021962</p><p>[4] Rawlinson, N., et al., (2016), Tectonophysics, doi: 10.1016/j.tecto.2015.11.034</p>

Anisotropy in the electrical conductivity of the subsurface has been recognized as one of the major difficulties in interpreting Magnetotelluric (MT) data; as it can lead to inaccurate inversion results under simple isotropic assumption. A robust modelling code producing accurate simulation results for anisotropic cases is much needed for the MT community, in order to extract more information from MT data in the inversion process. We present open-source Python package esys-Escript. It is designed to solve mathematical modelling problems using the finite element method (FEM). Its key idea is to formulate the problem in terms of general partial differential equations (PDEs) with proper boundary conditions. Its object-oriented programming style creates a flexible and easy-to-use interface for users to tackle their tasks. esys-Escript has been used to simulate 2D isotopic MT responses with a good agreement with published analytical solutions. Extending from this work, we present an implementation of the MT forward model for anisotropic media using Escript. In order to validate our code, we show anisotropic MT modelling results with the comparison of analytical solutions under an axially anisotropic setting. Then we add a general anisotropic case displaying Escript MT modelling results, validating against published anisotropic MT modelling code.

Ground Magnetotelluric (MT) data acquired today are typically broadband, covering 0.001 to >1000 Hz with inter-site spacing typically at 500 to 1000 m. Airborne Z-axis tipper data (ZTEM) are sampled at higher spatial density but usually band-limited to frequencies >30Hz. We analyze a pair of overlapping 3D surveys to examine lateral and vertical spatial sensitivity.The MT data include a 2D line and a 3D survey. The line data also has magnetic tipper data that allows for a direct comparison with ZTEM; in the overlapping frequency range the agreement between the two magnetic data sets is good, with ZTEM showing higher lateral smoothness.CGG’s RLM-3D non-linear conjugate gradient MT-CSEM inversion engine was extended to accurately model the ZTEM data, using measured sensor altimetry data and detailed 3D topography. Both single domain and joint inversions of the ZTEM and MT data were carried out. A suite of inversions were run to test the influence of starting resistivity and regularization parameters on output models, equally for MT, ZTEM, and joint MT+ZTEM inversions to allow for direct comparison.ZTEM single domain inversion results depend strongly on the starting resistivity value, confirming that the method maps relative variations rather than absolute resistivity values, as expected for magnetics-only measurements. Shallower lateral structure shows qualitative agreement with the MT, but at depth resistivity from ZTEM inversion is driven by model regularization only. Joint inversion improved the relatively shallow section, calibrating the ZTEM resistivities and adding continuity between the MT sites. Below around 1000m depth, the 3D resistivity model is controlled by the MT data alone. Our overall conclusion is that today’s 3D broadband MT only benefits from joint MT-ZTEM acquisition and inversion workflows in the case of sparse MT station spacing.

A three-dimensional (3-D) interpretation has been performed to magnetotelluric (MT) data obtained at the Atadei geothermal field, Lembata Island, Indonesia, for a detailed investigation of geothermal reservoirs. A preliminary interpretation has been made through inversion of MT data. The 3-D inversion scheme, which is based on the linearized iterative least-squares method with smoothness regularization and MT modeling algorithm using a 3D finite difference method, considers static shifts as unknown parameters in the inversion. The resulting resistivity model contains a low-resistivity in a shallow layer and a highly-resistive basement. However, for more precise interpretation of MT data at the Atadei field, we need to consider effects of surrounding sea and islands on the MT data, since the island is relatively small in a sense of MT survey. In this study, we first analyze effects of surrounding sea and islands on MT data in Lembata Island. In the analysis, we made MT simulation for several models; e.g., a model describing a large area including the Lembata Island and nearby islands and sea, a model of small area only describing part of Lembata Island and sea close to the Atadei field, and models with different areas with proper simplifications. Through the analysis, we selected a proper base model for inversion, which is as small as possible while explaining not only MT data in Lembata Island but also effects of surrounding sea and islands. Using the base model, we made 3D inversion of MT data in Lembata Island including sea effects.

SUMMARYBecause the magnetotelluric (MT) method uses natural sources, the electric and magnetic fields recorded in the field acquisition are not directly used but usually converted into other MT response functions for interpretation such as inversion. Considering that inversion results are dependent on types of input data, it can be helpful to analyse different characteristics of MT response functions for inversion. In this study, we examine sensitivity patterns of MT response functions used commonly in MT inversion, which are the impedance tensor, apparent resistivity, phase, tipper, effective impedance and phase tensor; and investigate how their sensitivity patterns affect inversion results. We first describe overall tendencies of 3-D sensitivity patterns of the MT response functions, and then classify the MT response functions into six groups based on 2-D sensitivity patterns computed at the surface, which are briefly called ‘surface-sensitivity patterns’ in this study. The ’diagonal components of the impedance’ and ‘off-diagonal components of the phase tensor’, which have four petals-shaped surface-sensitivity patterns along the diagonal directions, belong to Group 1, and contribute to imaging 3-D subsurface structures from receivers installed evenly at the surface. Group 2 contains the ‘xy-components of the impedance, apparent resistivity and phase’ and ‘yy-component of the phase tensor’ whose surface-sensitivity patterns are linear in the y-axis. The ‘yx-components of the impedance, apparent resistivity and phase’ and ‘xx-component of the phase tensor’ that have strong linear surface-sensitivity patterns along the x-axis are classified into Group 3. The MT response functions of Groups 2 and 3 are useful for inversion of structures close to 2-D, whose strike extends along the y- and x-axes, respectively. Groups 4 and 5 include the ‘x- and y-components of tipper’ that possess linearly aligned two petals-shaped surface-sensitivity patterns in the x- and y-axes, respectively. The tipper can be helpful in imaging both 2-D and 3-D structures. The ‘effective impedance’ belongs to Group 6, whose surface-sensitivity patterns appear as a small circle. The surface-sensitivity patterns allow the effective impedance to have an advantage in interpretation of 1-D structures. By using several MT response functions for specific cases of 1-D, 2-D and 3-D interpretation of MT data, we investigate whether characteristics of the sensitivity patterns are reflected in modelling (simulating field data) and inversion results, and then suggest optimal MT response functions for those cases. In doing so, we show how to utilize the characteristics of the sensitivity patterns in inversion, and recommend the input MT response functions for inversion according to MT exploration situations. Our study provides basic information on similarities and differences of major MT response functions for inversion and insights on which MT response functions are suitable to increase the feasibility of MT inversion for different field situations based on the sensitivity patterns.

SUMMARY Magnetotelluric (MT) data, in the form of MT tensors, are used to estimate directly the size and spatial distribution of the electric field in northern England and southern Scotland with the aim of predicting the flow of geomagnetically induced currents (GIC) in power networks in the region. MT and Geomagnetic Deep Sounding data from a number of different field campaigns, at a period of 750 s, are employed. The MT data are cast in the form of telluric vectors, which allow a joint hypothetical event analysis (HEA) of both Geomagnetic Deep Sounding and MT data. This analysis reveals qualitatively the pervasive effects of electric field distortion in the region. Two approaches are taken to understand how the spatial structure of the regional electromagnetic field is affected by local distortions, and what the origin of these distortions might be. The dimensionality, and form of electric field distortion, of the MT tensors is investigated using the Weaver et al. and Bahr classification schemes, and by examining the misfit of a galvanic distortion model as a function of rotation angle. At sites where the galvanic distortion model is found to be appropriate the regional MT tensors are recovered using tensor decomposition techniques. It is found that recovering the regional MT response reconciles the geometry of induced currents implied by the MT data with that of the Magnetic Variation anomalies. Lilley’s central impedances are used to calculate rotationally invariant effective telluric responses. In the Southern Uplands the magnitude of the effective telluric response is approximately 0.25-0.5 mV km −1 nT −1 , but as the Southern Uplands Fault is approached it rises steadily to 3 mV km −1 nT −1 . In the Midland Valley, the effective telluric response is approximately 0.5 mV km −1 nT −1 which rises steadily to 2.5 mV km −1 nT −1 as the Southern Uplands and Highland Boundary Faults are approached to the southeast and northwest, respectively. Therefore, the increase in the magnitude of the effective telluric response correlates with the approach of a major tectonic boundary such as the Southern Uplands Fault. These results show that the induced electric field strength varies considerably throughout the central Scotland region. In addition, the HEA indicates that due to lateral changes in conductivity structure the direction of the electric field deviates significantly from the regional direction implied by the polarization azimuth of the primary geomagnetic induction. Therefore, any attempts to model the flow of GIC in the region need to account for the spatial variation of both the magnitude and azimuth of the electric field.

As exploration is forced into more difficult areas with complex three-dimensional (3-D) structural environments, the importance of 3-D magnetotelluric (MT) modeling is essential for the correct interpretation of MT data. To reduce the complexity of the calculations introduced by 3-D models, iterative forward calculation of MT response functions is used as basis for inversion of 3-D MT data. This paper proposes an alternative procedure for making reliable 3-D MT modeling codes for forward calculation that is not only effective but also accurate. This is accomplished by using a direct method to solve the linear systems arising from the discretization process in the vector finite element approach. The vector finite element method is known for its capability of overcoming difficulties in modeling caused by possible jumps of normal components across discontinuities of material properties. Meanwhile, by using a direct method rather than an iterative method, the process of solving the linear equations does not suffer from slow convergence. Here, we present a comparison between our modeling codes and codes based on a different approach. In the resulting 3-D MT responses it was found that the proposed method has high accuracy.

At present, the most reliable information for inferring storm‐time ground electric fields along electrical transmission lines comes from coarsely sampled, national‐scale magnetotelluric (MT) data sets, such as that provided by the EarthScope USArray program. An underlying assumption in the use of such data is that they adequately sample the spatial heterogeneity of the surface relationship between geomagnetic and geoelectric fields. Here, we assess the degree to which the density of MT data sampling affects geoelectric hazard assessments. For electrical transmission networks in each of four focus regions across the contiguous United States, we perform two parallel band‐limited (101–103 s) hazard analyses: one using only USArray‐style (∼70‐km station spacing) MT data, and one incorporating denser (≪70‐km station spacing) MT data. We find that the use of USArray‐style MT sampling alone provides a useful first‐order estimate of integrated geoelectric fields along electrical transmission lines. However, we also find that the use of higher density MT data can in some areas lead to order‐of‐magnitude differences in line‐averaged electric field estimates at the level of individual transmission lines and can also yield significant differences in subregional hazard patterns. As we demonstrate using variogram plots, these differences reflect short‐spatial‐scale variability in Earth conductivity, which in turn reflects regional lithotectonic structure and history. We also provide a cautionary example in the use of electrical conductivity models to predict dense MT data; although valuable for hazard applications, models may only be able to reproduce surface geoelectric fields as captured by the MT data from which they were derived.

Vehicle noise characteristics in magnetotelluric data and vehicle noise removal using waveform fitting

A three-dimensional (3D) inversion algorithm for magnetotelluric (MT) data has been developed based on the Gauss-Newton method. The algorithm employs a 3D MT modeling algorithm based on an edge finite element method (FEM) with hexahedral elements being able to delineate surface topography. The modeling algorithm solves the resulting system of equations using a bi-conjugate gradient (BICG) method with a symmetric Jacobian preconditioner. To verify the inversion algorithm, we make inversion of MT data for a flat-earth surface model with a 3D conductive body in a homogeneous host. Further numerical tests are made for MT data over a surface topography. The model under consideration has a conductive or resistive dike under a 3D trapezoidal hill. For inversion of distorted MT data by surface topography, we first remove the topography effects using an impedance correction method. Numerical results indicate that inversion of MT data over the flat-surface model located the conductive target. Inversion of topography-effects-corrected MT data explains the presence of the conductive or resistive target while inversion of distorted MT data gives no clue.