최소모델영역 연산자를 모델제한조건으로 적용한 2차원 MT 역산

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.

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.

We present a novel 2‐D magnetotelluric (MT) inversion scheme, in which the local weights of the regularizing smoothness constraints are based on the envelope attribute of a reflection seismic image. The weights resemble those of a previously published seismic modification of the minimum gradient support method. We measure the directional gradients of the seismic envelope to modify the horizontal and vertical smoothness constraints separately. Successful application of the inversion to MT field data of the Collisional Orogeny in the Scandinavian Caledonides (COSC) project using the envelope attribute of the COSC reflection seismic profile helped to reduce the uncertainty of the interpretation of the main décollement by demonstrating that the associated alum shales may be much thinner than suggested by a previous inversion model. Thus, the new model supports the proposed location of a future borehole COSC‐2 which is hoped to penetrate the main décollement and the underlying Precambrian basement.

The global demand for unconventional energy sources such as geothermal energy and white hydrogen requires new exploration techniques for precise subsurface structure characterization and potential reservoir identification. The magnetotelluric (MT) method is crucial for these tasks, providing critical information on the distribution of subsurface electrical resistivity at depths ranging from hundreds to thousands of meters. However, traditional iterative algorithm-based inversion methods require the adjustment of multiple parameters, demanding time-consuming and exhaustive tuning processes to achieve proper cost function minimization. Recent advances have incorporated deep learning algorithms for MT inversion, primarily based on supervised learning, and large labeled datasets are needed for training. This work utilizes TensorFlow operations to create a differentiable forward MT operator, leveraging its automatic differentiation capability. Moreover, instead of solving for the subsurface model directly, as classical algorithms perform, this letter presents a new deep unsupervised inversion algorithm guided by physics to estimate 1-D MT models. Instead of using datasets with the observed data and their respective model as labels during training, our method employs a differentiable modeling operator that physically guides the cost function minimization, making the proposed method solely dependent on observed data. Therefore, the optimization algorithm updates the network weights to minimize the data misfit. We test the proposed method with field and synthetic data at different acquisition frequencies, demonstrating that the resistivity models obtained are more accurate than those calculated using other techniques. Our implementation is available at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/PAULGOYES/MT_guided1DInversion.git</uri>.

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.

WSJointInv2D-MT-DCR: An efficient joint two-dimensional magnetotelluric and direct current resistivity inversion

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.

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.

The magnetotelluric (MT) method is highly advantageous in geothermal resource exploration because of its deep probing capability, low cost, and sensitivity to key geothermal system elements, such as heat sources, reservoirs, and caprocks. To address the challenge of balancing the MT inversion resolution and computational efficiency, we develop a Gauss-Newton optimization inversion algorithm based on the solution space dimensionality reduction (SSDR) technique. This algorithm uses SSDR to establish algebraic mapping relationships between the edges of grid cells, effectively reducing the degrees of freedom in the linear equation system required for forward and pseudoforward modeling, thereby saving computational costs. In addition, during the inversion process, a multiple right-hand direct-iterative hybrid solver is used to solve the dimensionally reduced linear equations, further enhancing the computational efficiency of the inversion. We then validate and analyze the accuracy and efficiency of the forward and inversion algorithms using various synthetic models. Finally, we apply this inversion strategy to field MT data from the Dabie Mountain geothermal area in eastern China. On the basis of the inversion results, we then analyze the thermal genesis model of the region, providing technical support for the exploration and development of deep geothermal resources.

Magnetotellurics (MT) images electrical conductivity, a property influenced by fluids, alteration, graphite, and partial melt. Because many different subsurface configurations can explain the MT responses observed in the field, the preferred subsurface conductivity model estimated through inversion is often ambiguous. A central challenge is that a robust stochastic model exploration in 3D, while conceptually the best way to expose such ambiguity, is too computationally demanding to be used as a standard practice. Consequently, most studies report a single deterministic model, which obscures the range of alternative geological structures that are equally consistent with the data.In this work we propose a practical approach to stochastic model exploration in 3D MT inversion. Drawing inspiration from annealing methods, we adopt a Very Fast Simulated Annealing (VFSA) framework, with sparse parameterization that makes the optimisation feasible for large-scale problems. Our inversion algorithm is built around the widely used ModEM forward solver, ensuring compatibility with existing workflows. Instead of producing one definitive model, the workflow can generate a set of plausible models that explain the data equally well. From this ensemble one can compute statistical summaries: a mean model that captures the most consistent structures and quantitative measures of variability that highlight where geometry, depth, or connectivity remain uncertain. This representation enables geologists to make interpretations while being explicitly aware of the uncertainty inherent in the inversion. We demonstrate that the approach works at regional scale using a large-area subset of USArray MT data from Cascadia. This dataset has been extensively studied and previously modelled with deterministic 3D inversion, which allows us to benchmark our results.

We have studied the feasibility of using the geostatistical approach to enhance the analysis of sparsely obtained MT (magnetotelluric) data by combining them with gravity data. The use of geostatistics to integrate MT data with gravity data was attempted. To evaluate the feasibility of this approach, the interrelationship between the geological boundary and the density distribution was studied. The conversion of the corrected density distribution to a more sensitive geological boundary by maximizing the correlation coefficient between the distributions of resistivity yielded MT inversion and density distributions under the assumption that boundary locations have a high correlation. Next, the correlation between the resistivity structure from MT data and the density structure from gravity inversion was analyzed. Afterwards, the density distribution was converted into the resistivity distribution to yield local mean values for the residual analysis of the resistivity structure. Then, using this method, models and field data from a real intrusive igneous area were tested. The results of the model test agreed well with those of the real model. Moreover, with the real field data, the geostatistical approach used herein demonstrated relatively satisfactory results.

<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.

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.

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 non-static effect of near-surface inhomogeneity on CSAMT data