Two‐dimensional magnetotelluric inversion using reflection seismic data as constraints and application in the COSC project

Magnetotelluric (MT) inversion algorithms are an essential tool in exploration geophysics because they provide us with resistivity models of the subsurface. Inverse problems are ill-posed and non-unique. Resistivity models produced by geologically unconstrained MT inversions are typically smooth, which means that the geological interpretations obtained based on the resistivity models will be ambiguous and uncertain. To solve the above problems, geophysicists have made many efforts over the years to introduce any prior information (such as geological structure information and physical property data) into models, which could help to better constrain the inverted model with the inversion algorithms. In the last few years, there has been renewed interest in machine learning techniques. Various machine learning methods have been applied to inversions. Using the fuzzy c-means (FCM) clustering method, geophysicists proposed new inversion algorithms that are capable of building petrophysical information into the inversion. Although the FCM has been used and advanced in previous work, geophysicists concluded that a priori information of the correct number and value of cluster centers is very important for a successful FCM inversion. In fact, it is difficult to obtain the appropriate clustering information in some geophysical survey areas. In this study, we present an effective way to build the petrophysical information for the MT inversion based on FCM clustering algorithm. When the actual petrophysical information is insufficient, considering the characteristics of MT data, we perform a one-dimensional blocky inversion that can clearly identify the interface with distinct electrical property contrast; then, we obtain the number and value of cluster centers from 1D blocky inversion for the further MT inversion with FCM clustering. The algorithm uses guided FCM clustering to improve the model within the iterative minimization during MT inversion. In our MT inversion method, we integrate the geophysical inversion and geological differentiation into a unified scheme, which interact and enhance each other. The resistivity models obtained from the inversion respect the geophysical and petrophysical data and are easy to geologically interpret. We tested the algorithm using two synthetic examples and a field data example.

Magnetotelluric (MT) inversion is widely used to image subsurface electrical resistivity structures, but three-dimensional (3-D) MT inversion is inherently non-unique, and the resulting models can depend strongly on the choice of the initial model. Despite this well-known sensitivity, systematic evaluation of initial-model-induced variability remains uncommon in practical 3-D MT studies due to the high computational cost of running multiple inversions. In this study, we propose a practical and computationally efficient framework to quantify inversion uncertainty arising specifically from differences in the initial model. The approach employs a low-dimensional parameterization based on representative points and uses Kriging interpolation to generate an ensemble of smooth, geologically plausible starting models. Each realization is inverted independently using identical inversion settings, allowing initial-model effects to be isolated under fixed regularization and data-error assumptions. The method is applied to a 3-D MT dataset from the Yuzawa geothermal field in northeastern Japan. A total of 100 inversions were performed, from which 55 well-converged realizations (final RMS ≤ 2.15) were selected for analysis. Ensemble statistics reveal that shallow conductive structures are reproduced consistently across realizations, whereas variability increases with depth and exhibits strong spatial dependence. Bootstrap resampling confirms that the depth-dependent variability patterns are statistically stable under the present ensemble size. Although the proposed framework does not account for all possible sources of inversion uncertainty, it provides an operationally realistic lower-bound estimate of model variability associated with initial-model choice. By identifying which parts of the resistivity structure are robust and which are weakly constrained, the method supports uncertainty-aware interpretation of 3-D MT inversion results and demonstrates its practical applicability through a geothermal case study.

How to get the rapid and stable inversion results and the clear geological interfaces is a focus problem in current Magnetotelluric (MT) inversion. Constable et al (1987,1990) provided the OCCAM as a smoothing inversion, and the focusing inversion which is based on the minimum gradient support functional provided by Portniaguine, O. and Zhdanov, M. S.(1999,2002,2004). We integrate the ideas of smoothing inversion and Focusing inversion to construct a new objective function for inversion. Meanwhile, We introduce a diagonal gradient support into the objective functional to enhance oblique geo‐electrical interface.

A radio magnetotelluric (MT) field data set, acquired in scalar mode, over a buried waste site has been successfully analyzed using a 3D MT inversion scheme using nonlinear conjugate gradients. The results of this analysis demonstrate the utility of the scheme where more than 4800 data points collected on multiple measurement profiles have been inverted simultaneously. The resulting image clearly detects the buried waste; when receiver profiles cross pit boundaries, the image maps the lateral extent of the pit. However, the base of the pit is poorly resolved, and depends upon the starting model used to launch the inversion. Hence, critical information on whether contamination is leaching into a resistive gravel bed lining the base of the pit, as well as the deeper geological horizons consisting of brown coal, clay, and tertiary sands, is inconclusive. Nevertheless, by incorporating within the inversion process a priori information of the background media that is host to the waste, sharper images of the base of the pit are obtained, which are in good agreement with borehole data. The 3D analysis applied in this paper overcomes previous limitations in the radio magnetotelluric (RMT) method using 2D data analysis and inversion. With 3D analysis, it is unnecessary to make assumptions regarding geological strike, and near‐surface statics can be accommodated in both source polarizations. Our findings also indicate that 2D MT interpretation can overestimate the pit's depth extent. This may lead to the erroneous conclusion that the geological horizons beneath the pit have been contaminated.

Due to the strong capability of building complex nonlinear mapping without involving linearization theory and high prediction efficiency; the deep learning (DL) technique applied to solve geophysical inverse problems has been a subject of growing interest. Currently, most DL-based inversion approaches are fully data-driven (namely standard deep learning), the performance of which largely depends on the training sample sets. However, due to the heavy burden of time and computational resources, it can be challenging to supply such a massive and exhaustive training dataset for generic realistic exploration scenarios and to perform network training. In this work, based on the recent advances in physics-based networks, the physical laws of magnetotelluric (MT) wave propagation is incorporated into a purely data-driven DL approach (PlainDNN) and thus builds a physics-driven DL MT inversion scheme (PhyDNN). In this scheme, the forward operator modeling MT wave propagation is integrated into the network training loop, in the form of minimizing a hybrid loss objective function composed of the data-driven model misfit and physics-based data misfit, to guide the network training. Consequently, the proposed PhyDNN method will take the advantage of the fully data-driven DL and conventional physics-based deterministic methods, allowing it to deal with complex realistic exploration scenarios. Quantitative and qualitative analysis results demonstrate that the PhyDNN can honor the physical laws of the MT inverse problem, and with other conditions unchanged, the PhyDNN outperforms the PlainDNN and the classical deterministic Occam inversion method. When processing field data, the PhyDNN method yields considerably impressive inversion results compared to the Occam method, and the corresponding simulated MT responses agree well with the real measurements, which confirms the effectiveness and applicability of the PhyDNN method.

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.

An extensive magnetotelluric (MT) survey comprised of 85 sites has been acquired over the Darajat geothermal field in Indonesia to map the geothermal reservoir and the overlying clay cap. The rouged topography and the geometry of the margin of the clay cap makes the resistivity structure 3D at reservoir depth. Although 3D MT inversion is now commonly used in geothermal interpretations 1D and 2D MT inversions are still effective tools for a variety of tasks such as quality assurance. Lower dimensional inversion can also play two critical roles in determining and assessing the resistivity model derived by 3D inversion: 1) by providing a good starting model to reduce the computational cost of the 3D inversion, and 2) by providing a computationally feasible path to stochastic inversion of the data that provides realistic parameter’s standard deviations for use in assessing reliability of the resistivity model. Using a spatially constrained 1D stochastic inversion of the MT data, we investigate the common claim that 1D inversion can provide a pseudo 3D model which closely matches the 3D inversion for the overburden and clay cap layers. The discrepancy between the pseudo 3D and true 3D inverse models increases with depth, however the presence of the core resistive feature of the field is still indicated at approximately the same depth as found in the true 3D model. Analysis of the 1D model parameter probability density functions shows that layer thicknesses are better determined than layer resistivities.

The geoelectrical features of the Travale geothermal field (Italy), one of the most productive geothermal fields in the world, have been investigated by means of three-dimensional (3D) magnetotelluric (MT) data inversion. This study presents the first resistivity model of the Travale geothermal field derived from derivative-based 3D MT inversion. We analyzed MT data that have been acquired in Travale over the past decades in order to determine its geoelectrical dimensionality, directionality, and phase tensor properties. We selected data from 51 MT sites for 3D inversion. We carried out a number of 3D MT inversion tests by changing the type of data to be inverted, the inclusion of static-shift correction at some sites where new time-domain electromagnetic soundings (TDEM) were acquired, the grid rotation, as well as the starting model in order to assess the connection between the inversion model and the geology. The final 3D model herein presents deep elongated resistive bodies between the depths of 1.5 and 8 km. They are transverse to the Apennine structures and suggest a correlation with the strike-slip tectonics. Comparison with a seismic velocity model and well log data suggests a highly-fractured volume of rocks with vapor-dominated circulation. The outcome of this study provides new insights into the complex geothermal system of Travale.

<title>Abstract</title> Magnetotellurics (MT) is a geophysical method used to study subsurface structures based on resistivity properties. Inversion modeling in MT is crucial to reconstructing subsurface resistivity distributions from observed data. However, traditional inversion methods often face challenges such as computational complexity, local minimum traps, and dependence on initial models. This study proposes a novel one-dimensional (1-D) MT inversion approach using a One-to-One-Based Optimizer (OOBO) algorithm. OOBO efficiently explores the solution space using information from all population members, reducing the risk of local minima and improving accuracy. The proposed method was tested on synthetic MT data with added noise 5\% using a four-layer resistivity model (Model 1) and a five-layer resistivity model (Model 2). The results showed the best resistivity reconstructions with a percentage root mean square error (RMSE) value of 5.98\% for Model 1 and 6.40\% for Model 2, demonstrating superior accuracy compared to traditional methods such as Occam’s inversion. The algorithm was also applied to field data, demonstrating its ability to efficiently explore model spaces, even when the number of layers is unknown. OOBO's stochastic nature enables the consideration of model uncertainty, providing more consistent solutions compared to probabilistic approaches such as rj-McMCMT, with smaller uncertainty ranges. This study highlights the potential of OOBO to improve the accuracy and efficiency of MT inversion, demonstrating its broad applicability to complex geophysical problems.

본 연구에서는 최소모델영역 연산자를 MT(magnetotelluric) 2차원 역산 알고리듬에 적용하여 역산 해의 대비를 향상시키고자 하였다. 이를 위하여 creeping법에 기초한 최소자승 역산에 최소모델영역 연산자를 수치적으로 유도하여 알고리듬을 구현하였으며, 공간함수로서의 평활화 상수를 도입한 ACB (Active Constraint Balancing) 법을 동시에 적용하여 최소모델영역 연산자를 이용할 때 단점으로 지적되었던 역산 해의 안정성을 향상시켰다. 고립된 단일 이상체 모델에 대한 수치실험을 통하여 MT 역산에 있어서 최소영역 연산자의 효과를 기존의 2차 미분연산자와 비교 분석하여 MT 역산에서의 특징을 고찰하였다. 또한 다중 이상체 모델에 대한 실험을 통하여 Occam 역산과 비교하여 최소모델영역 연산자를 이용한 역산 해의 특징을 비교 분석하였으며 현장 자료에의 적용을 통하여 그 적용성을 살펴보았다. Two-dimensional magnetotelluric (MT) inversion algorithm using minimum support (MS) stabilizer functional was implemented in this study to enhance the contrast of inverted images. For this implementation, this study derived a formula in discrete form for creeping model updates in the least-squares linearized inversion. A spatially varying regularization parameter determination algorithm, which is known as ACB (Active Constraint Balancing), was also adopted to stabilize the inversion process when using MS stabilizer as a model constraint. Inversion experiments for a simple isolated body model show well the feature of MS stabilizer in concentrating the anomalous body compared with the second-order derivative model constraint. This study also compared MS stabilizer and the second-order derivative model constraints for a model having multiple anomalous bodies to show the applicability of the algorithm into field data.

A prominent TE and TM mode split is observed in magnetotelluric (MT) data below 0.5 Hz collected in the Perth Basin over the Harvey Ridge, Western Australia. We investigate the causes of mode splitting and consider implications on inversion of the MT data to subsurface electrical conductivity distribution. Twenty-five broad-band MT stations were acquired and remote reference processing was completed to arrive at a data set located midway between the Darling Fault and the Indian Ocean. We used forward modelling to test our strong suspicion that the Indian Ocean, Darling fault and architecture of the Granitic Basement were indeed the major contributors to mode splitting that we observed. Forward modelling of synthetic data was completed for comparison with the Harvey MT data. We were surprised at the match between synthetic and field data given the simplicity of the forward model and the considerable lateral distance between the MT soundings and the Indian Ocean or Darling fault. We were then able to make significant improvements to the MT inversion outcome by introducing a large scale geo-electrical architecture as the seed model for inversion. Our work demonstrates that large scale geo-electrical contrasts at considerable lateral distance from an MT transect, or the target zone need to be systematically introduced to the inversion if a quality outcome is to be achieved.

Summary The large Kevitsa Ni-Cu-PGE (platinum group elements) deposit in Finland is part of a complex geoelectrical setting. The ore zone is electrically conductive compared to the high resistivity olivine pyroxenite host rock. The ore body and host are surrounded by thin sheet like high electrical conductive carbonaceous phyllites. Unconstrained 2D and 3D inversion of magnetotelluric (MT) data was performed using seven densely sampled MT transverses ranging in length from 2500m to 7000m. Two dimensional inversions included a total of 312 MT stations along the seven transverses, while 3D inversion was completed on a subset of 270 MT stations focused around the ore zone. The inversions were conducted on the Pawsey Centre, Magnus Cray XC30 supercomputer. The challenge for this site was to resolve the ore body in the presence of the carbonaceous phyllites using sparse transverses. We compare the outcome of 2D and 3D MT inversion and find that 3D inversion appears to provide superior definition of the ore zone. This research and the resulting electrical conductivity distributions will inform our future work on full 3D cooperative inversion of seismic and MT data over the Kevitsa site.

The Sumatran Fault runs from the southeast (SE) to the northwest (NW) of Sumatra Island, with the highest slip rates reaching about 3.0 cm per year in the northwestern part. There is a seismic gap along this fault, including the northern Aceh domain, which consists of the Aceh and Seulimeum fault segments. Previous studies have used various methods to investigate the Sumatran Fault system, including seismic, geoelectric, gravity anomaly, and magnetotellurics (MT). The MT method has proven advantageous as it can non-destructively image a wide range of depths. However, previous studies using the two-dimensional (2D) MT inversion did not represent realistic information of the subsurface conditions. Therefore, a three-dimensional (3D) MT data inversion was used in this study to obtain more realistic information about the resistivity structure of the Aceh and Seulimeum segments. The results confirmed that the Sumatran Fault is a strike-slip fault, with a relatively northwest (NW)–southeast (SE) direction of conductivity strike with an angle of S 71.61° E from Groom–Bailey decomposition of MT data. The 3D resistivity distribution model from 33 stations showed that the Aceh Fault Segment is 20–30 km away, while the Seulimeum Fault Segment is 55–60 km away based on the MT data. The results also indicated a creeping zone at a depth of 2 km beneath the Aceh Fault Segment. Different rock formations were identified beneath the fault system, with the western part of the Aceh Segment dominated by high-resistivity metamorphic rocks (150–1000 Ωm) from the Triassic–Cretaceous age. The zone between the Aceh and Seulimeum fault segments exhibited low resistivity, characterized by volcanic rocks (1–15 Ωm) from the Lam Teuba Volcanic Formation and the Indrapuri Formation. Beneath the eastern part of the Seulimeum Fault Segment was found to consist of low-resistivity quaternary volcanic rocks (1–15 Ωm) and high-resistivity andesite rocks (4.5 × 104–1.7 × 105 Ωm). These findings correlated well with the geological map.

SUMMARYSimulation-based probabilistic inversions of 3-D magnetotelluric (MT) data are arguably the best option to deal with the nonlinearity and non-uniqueness of the MT problem. However, the computational cost associated with the modelling of 3-D MT data has so far precluded the community from adopting and/or pursuing full probabilistic inversions of large MT data sets. In this contribution, we present a novel and general inversion framework, driven by Markov Chain Monte Carlo (MCMC) algorithms, which combines (i) an efficient parallel-in-parallel structure to solve the 3-D forward problem, (ii) a reduced order technique to create fast and accurate surrogate models of the forward problem and (iii) adaptive strategies for both the MCMC algorithm and the surrogate model. In particular, and contrary to traditional implementations, the adaptation of the surrogate is integrated into the MCMC inversion. This circumvents the need of costly offline stages to build the surrogate and further increases the overall efficiency of the method. We demonstrate the feasibility and performance of our approach to invert for large-scale conductivity structures with two numerical examples using different parametrizations and dimensionalities. In both cases, we report staggering gains in computational efficiency compared to traditional MCMC implementations. Our method finally removes the main bottleneck of probabilistic inversions of 3-D MT data and opens up new opportunities for both stand-alone MT inversions and multi-observable joint inversions for the physical state of the Earth’s interior.

Magnetotellurics (MT) investigates the subsurface resistivity from naturally oc curring electromagnetic field fluctuations. The linearity and noise of MT data cause traditional inversion methods to fail due to the nonlinearity and noise inherent in MT data, resulting in poor resistivity reconstruction. While neural networks such as convolutional and recurrent networks have been applied to in vert MT, they cannot be used to include complex, non-local relationships over depth and frequency. In this research, we propose a hybrid model that com bines graph attention networks (GATs) and multi-head attention mechanisms. The GAT module serves the double purpose of denoiser and encoder, structur ing the input frequency-phase data into a compressed representation, and the transformer-based attention selectively emphasizes the most informative spec tral elements. This allows the model to predict resistivity distributions more accurately with depth. Experiments on both synthetic and actual datasets show enhanced robustness to noise and enhanced generalization over current deep learning models, providing a more interpretable and scalable solution to MT inversion.