Magnetotelluric Inversion Research Articles

2D Magnetotelluric Inversion Using Linear Finite Element Methods and a Discretize‐Last Strategy With First and Second–Order Anisotropic Regularization

AbstractWe present a new inversion scheme for 2D magnetotelluric data. In contrast to established approaches, it is based on a mesh‐free formulation of the Quasi‐Newton Broyden–Fletcher–Goldfarb–Shanno (BFGS) iteration which uses the cost function gradient to implicitly construct approximations of the Hessian inverse to update the unknown conductivity. We introduce conventional first–order regularization as well as second–order regularization where inversions based on the latter are more appropriate for sparse data and can be read as maximum likelihood estimation of the unknown conductivity. We apply first–order finite element method (FEM) discretizations of the inversion scheme, forward and adjoint problems, where the latter is required for the construction of the cost function gradients. We allow for unstructured first–order triangular meshes supporting an enhanced ground level resolution including topographical features and coarsening at the far field leading to significant reduction in computational costs from using structured mesh. Formulating the inversion iteration in continuous form prior to discretization eliminates bias due to local refinements in the mesh and gives way for computationally efficient sparse matrix techniques in the implementation. A keystone in the new scheme is the multi‐grid approximation of the Hessian of the regularizations to construct efficient preconditioning for the inversion iteration. The method is applied to the Commeni4 benchmark and two field data sets. Tests show that for both first and second–order regularization an anisotropic approach is important to address the vast differences in horizontal and vertical spatial scale which in conventional approaches is implicitly introduced through the elongated shape of grid cells.

Inversion of 2D Magnetotelluric (MT) Data with Axial Anisotropy using Adaptive Particle Swarm Optimization (PSO)

In the presence of anisotropic resistivity structures, Magnetotelluric (MT) data inversion based on an isotropic resistivity model will be insufficient. Recent work on anisotropic MT inversions is primarily conducted using gradient-based, deterministic methods which may converge towards local minima and in general, suffer from ill-posedness of the inversion problem. Alternatively, meta-heuristical methods, such as Particle Swarm Optimization (PSO), are able to find the global minima of cost function. At the same time, they are easy to implement and do not require access to the dense Jacobian (and Hessian) matrix as needed by deterministic inversion methods. In this paper we propose PSO inversion for the anisotropic MT inversion problem using an adaptive inertia weights control strategy to balance exploration and exploitation during the PSO search. Higher order differential regularization is introduced with a Gaussian filter, where the conventional first order, Occam-like regularization term is replaced by a variance term. We investigate the performance of the proposed PSO inversion for an isotropic as well as an axial anisotropic synthetic case to demonstrate improvements over an Occam-like regularization. For the COPROD2 benchmark data set, the proposed PSO inversion can not only reproduce the extend of the North American Central Plains (NACP) conductive anomaly, but also to predict an anisotropy ratio of two orders of magnitude, which is in accordance with laboratory findings.

3D magnetotelluric inversion with arbitrary data orientation angles

The survey setup of 3D magnetotelluric inversion is typically chosen to best reflect the underlying geological structure. Typically, the individual observation azimuths are distinct from this preferred survey layout orientation; in fact, measured electric and magnetic fields are aligned with local geomagnetic North. When that happens, either data preprocessing (rotation) is required before the inversion may be performed, or the orientation of the modeling grid is aligned with the data orientations. None of these approaches is optimal, possibly resulting in a reduction of data quality, the loss of statistical accuracy of the error estimates, or in unnecessary grid cells, resulting in increased computation times. In situations when the data quality may be improved by allowing distinct individual site orientations, such as when cultural noise or faulty instrumentation cause a degradation of one of the modes, data loss due to rotation is especially detrimental. In this paper, we present a modified 3D magnetotelluric inversion algorithm, based on the ModEM software, that allows for direct interpretation of observations with arbitrary data orientation angles (ModEM ADORA). In ModEM ADORA, the modeling responses are rotated to the observation orientation angles after each forward calculation and before the data misfit is evaluated. This allows for direct interpretation of observation data with distinct orientations at each site and (as needed for some historical data) at each frequency. The derivative of the penalty functional is computed by pre-multiplying the derivatives of the data functionals (or the complete Jacobian matrix) by the relevant sparse block-diagonal rotation operators. We describe the principle and implementation of ModEM ADORA, and provide a collection of synthetic and real data tests for validation and an analysis of effectiveness of the ADORA option of ModEM. We show that by decoupling modeling grid and sensor orientations, ModEM ADORA supports both computational efficiency and ease of use, as well as allows for the maximum quality and quantity of inverted data.

Deep resistivity geophysics of the San Juan–Silverton caldera complex, San Juan County, Colorado (USA)

Magnetotelluric (MT) and audiomagnetotelluric (AMT) data are used to better understand the subsurface geology and mineral resources in the San Juan–Silverton caldera complex located near Silverton, Colorado, western United States, as part of the extensive southern Rocky Mountains volcanic field that covers much of southwestern Colorado and northern New Mexico. Seven MT and AMT profiles of varying lengths image resistivity structure to depths of ~5 km. The AMT inversion models characterize geophysical responses of near-surface lithologies, structures, and mineralized systems and also help corroborate airborne electromagnetic data at shallow levels. The MT inversion models extend our depth of investigation from near the surface to great depths (~5 km) and help to form hypotheses about roots of the hydrothermal plumbing that fed shallower mineralized systems. Subsurface high resistivities occur beneath intermediate-composition lava flows and Proterozoic units. Subsurface moderate- to low-resistivity values may reflect hydrothermal plumbing that served as flow paths for mineralizing fluids and metallic ore formation. The model interpreta­tions presented in this study could be utilized in remediation planning or mineral resource applications. The methods used could be applied to other watersheds with similar volcanic environments containing acid-generating historical mines or hydrothermally altered and mineralized source rocks.

2-D probabilistic inversion of MT data and uncertainty quantification using the Hamiltonian Monte Carlo method

SUMMARY Bayesian methods provide a valuable framework for rigorously quantifying the model uncertainty arising from the inherent non-uniqueness in the magnetotelluric (MT) inversion. However, widely used Markov chain Monte Carlo (MCMC) sampling approaches usually require a significant number of model samples for accurate uncertainty estimates, making their applications computationally challenging for 2-D or 3-D MT problems. In this study, we explore the applicability of the Hamiltonian Monte Carlo (HMC) method for 2-D probabilistic MT inversion. The HMC provides a mechanism for efficient exploration in high-dimensional model space by making use of gradient information of the posterior probability distribution, resulting in a substantial reduction in the number of samples needed for reliable uncertainty quantification compared to the conventional MCMC methods. Numerical examples with synthetic data demonstrate that the HMC method achieves rapid convergence to the posterior probability distribution of model parameters with a limited number of model samples, indicating the computational advantages of the HMC in high-dimensional model space. Finally, we applied the developed approach to the COPROD2 field data set. The statistical models derived from the HMC approach agree well with previous results obtained by 2-D deterministic inversions. Most importantly, the probabilistic inversion provides valuable quantitative model uncertainty information associated with the resistivity structures derived from the observed data, which facilitates model interpretation.

Two-dimensional magnetotelluric inversion using unstructured triangular mesh implemented in Julia

This study presents a 2-D magnetotelluric inversion code tailored for unstructured triangular meshes, developed using Julia, a high-level, high-performance programming language designed for scientific and numerical computation. The forward modeling engine utilizes a node-based finite element method to solve electromagnetic fields throughout the modeling domain. The inversion process employs the Gauss-Newton optimization algorithm, iteratively updating the model via the minimization of a regularized least-squares objective function. We verified the accuracy of the forward modeling using two reference models and performed a synthetic inversion experiment to validate our inversion method and stress the necessity of accurately handling topography-influenced data. Through its application to constructing an electrical resistivity model beneath the northwestern end of Sumatra Island, Indonesia, we demonstrate the practicality of our code for inverting field datasets.

Analysis of two-dimensional magnetotelluric inversion for the delineation of the petroleum system in the Kutai basin, East Kalimantan, Indonesia

The Kutai Basin in East Kalimantan is known as a potential area for oil and gas exploration. Two-dimensional magnetotelluric (MT) analysis is applied to investigate the geological structure and distribution of subsurface resistivity. This study aims to delineate the petroleum system using MT data and identify zones with potential for the accumulation of hydrocarbons. MT data has been collected at several strategic locations in the Kutai Basin, and two-dimensional cross-sections have been constructed to obtain vertical resistivity imaging at several depths. In this study, there were nine measurement points located on one line. The data is then inverted to obtain a two-dimensional resistivity model, which qualitatively represents the subsurface structure. The results of this study indicate that there is a low resistivity anomaly zone that identifies the presence of source rock with a resistivity value of 1-12 Ωm. In this line, it is suspected that the petroleum system that allows trapped hydrocarbons is found in the area, below the KT36 and KT13 measurement points. In this area there are folded structures in the form of synclines and anticlines, which raises suspicions about the types of traps formed from structural traps.

MT2DInv-Unet: A 2D magnetotelluric inversion method based on deep-learning technology

Traditional gradient-based inversion methods usually suffer from the problems of falling into local minima and relying heavily on initial guesses. Deep-learning methods have received increasing attention due to their excellent nonlinear fitting ability. However, given the recent application of deep-learning methods in the field of magnetotelluric (MT) inversion, there are currently challenges associated with achieving high inversion resolution and extracting sufficient features. We develop a neural network model (called MT2DInv-Unet) based on the deformable convolution for 2D MT inversion to approximate the nonlinear mapping from the MT response data to the resistivity model. The deformable convolution is achieved by adding an offset to each sample point of the conventional convolution operation, which extracts hidden relationships and allows the flexible adjustment of the size and shape of the feature region. Meanwhile, we design the network structure with multiscale residual blocks, which effectively extract the multiscale features of the MT response data. This design not only enhances the network performance but also alleviates issues such as vanishing gradients and network degradation. The results of synthetic models indicate that our network inversion method has stable convergence, good robustness, and generalization performance, and it performs better than the fully convolutional neural network and U-Net network. Finally, the inversion results of field data show that MT2DInv-Unet can effectively obtain a reliable underground resistivity structure and has a good application prospect in MT inversion.

Deep learning-based 1-D magnetotelluric inversion: performance comparison of architectures

Deep learning-based 1-D magnetotelluric inversion: performance comparison of architectures

Three-dimensional magnetotelluric and gravimetric imaging of Mount Lawu geothermal prospect area, Indonesia

Mount Lawu is a stratovolcano located on the border of Central Java and East Java Provinces in Indonesia. At least eleven manifestations indicate its geothermal potential in the form of hot water and fumaroles. This study aims to describe a geothermal system based on an integrated analysis of magnetotelluric (MT) and satellite gravity data. Some additional geochemical and petrological data analyses were also used to explain the existing hydrothermal system in this area. It is inferred from the gravity derivative analysis that fault structures exist in a location with high permeability, which acts as a controlling structure for geothermal manifestations. The 3-D resistivity inversion was carried out using MT full-impedance tensor data, while the 3-D density model was reconstructed based on the residual anomaly computed from the topography-free gravity disturbance. The 3-D resistivity model, from magnetotelluric inversion, shows a clay cap distribution, corresponds to a low resistivity anomaly, centered at the southern part of the mountain peak with a thickness of about 1 kilometer, which narrows to the western region where the hot spring shows an outflow manifestation. The gravity inversion shows several low-density bodies in the same location as the low-resistivity anomaly attributed to a clay cap. Coincident resistivity and density anomalies constrain the horizontal location of the geothermal reservoir. Despite the incapability of the model to resolve the body of the geothermal heat source, it can be inferred from the inversion results that the heat possibly emanates through the thermal conduction passage below the reservoir zone from the source located deeper down than the reconstructed models.

Gauss–Newton With Preconditioned Conjugate Gradient Magnetotelluric Inversion for 3-D Axial Anisotropic Conductivities

Gauss–Newton With Preconditioned Conjugate Gradient Magnetotelluric Inversion for 3-D Axial Anisotropic Conductivities

A 3-D Magnetotelluric Inversion Method Based on the Joint Data-Driven and Physics-Driven Deep Learning Technology

A 3-D Magnetotelluric Inversion Method Based on the Joint Data-Driven and Physics-Driven Deep Learning Technology

Three-dimensional Magnetotelluric Inversion and Magnetic for The Characterization of The Geothermal Field Reservoir Zone “X”

Geothermal as an alternative energy source that is renewable and environmentally friendly has an important role in providing domestic energy needs. Exploration is one of the most important stages in the development of geothermal energy because it can minimize the risk at the stage of exploitation and development. Geophysical methods such as geomagnet and magnetotelluric are one of the methods used in exploration. Magnetic method can provide information on the description of rock demagnetization due to the presence of heat source. However, the magnetotelluric method will provide information about rock type resistance on geothermal fields. The existence of heat source using the geomagnetic method is represented by a low anomaly value as an indication of demagnetized rocks. The results of 3D inversion processing show a low value of type resistance in the area and form an updome. The correlation of the two results of processing the data can be seen in the southern part of the "X" geothermal field research area. Based on 3D Inversion modeling it can be seen the depth of the "X" Base of Conductor (BOC) geothermal system ranges from 1000 m to -800 m with resistivity ≤ 10 Ωm which is suspected as volcanic rocks. Geothermal reservoir is at a depth of 1000 m to -2000 m with a moderate resistivity of 40 - 60 Ωm which is suspected as an andesite volcanic rock, with temperature estimates ranging from 218o C to 255o C.

MTAINV3D: A Three-dimensional Adaptive Magnetotelluric Inversion Tool Using Unstructured Grids

Currently, 3D magnetotelluric inversion often uses a fixed inversion grid. Too sparse inversion grids cannot approximate the complex subsurface conductivity distribution, and may also lead to inversion results failing to converge. Too dense inversion grids will increase not only the computational cost, but also the non-uniqueness of the inversion. Aiming at the above problems, we have developed a three-dimensional magnetotelluric adaptive inversion strategy with unstructured finite element and limited memory BFGS (L-BFGS) algorithms. Firstly, based on the unstructured finite element method, the high accuracy forward responses of the 3D geo-electric model with arbitrary complex terrain and conductivity distributions can be obtained. Then, the forward and inversion meshes are decoupled by using the nested forward and inversion tetrahedral meshes. The Thikhonov regularization objective function with smooth constraints is established and minimized by L-BFGS optimization algorithm with inexact line search procedure, where the gradient of the objective function is solved by using the adjoint principle. Most importantly, an inversion grid adjustment strategy based on the dual constraints of sensitivity matrix and model gradient is proposed, which are used to guide the automatic refinement of inversion grid in the optimization process. Finally, a topographic model is used to validate and test the performance of the proposed adaptive inversion algorithm.

The Magnetotellurics Inversion with a Tree Based Bayesian Framework

Bayesian inversion offers a valuable means of estimating uncertainty, allowing us to evaluate the impact of inversion. However, tackling Bayesian inversion in high-dimensional spaces remains a crucial area of research. Building upon Hawkins’ work, we have developed a tree-based Bayesian inversion scheme specifically designed to address the challenges posed by the magnetotellurics inversion problem. By employing the cdf9/7 wavelet as our basis function, we conducted a numerical simulation of a low-resistance abnormal body, yielding highly accurate inversion results.

Estimation of Groundwater in Tarim Basin from Three-dimensional Resistivity Model Constructed by Magnetotelluric Data

Groundwater is an important resource of irrigation and domestic water in Tarim Basin (TB), the largest arid inland basin in China. Hydrogeologic models and hydrogeochemical analysis have provided information of groundwater flow, salinity and hydrochemical type in TB. However, there is lacking in quantitative estimation of groundwater volume due to that the underground aquifer structure is unclear. To address the problem, magnetotelluric (MT) data were collected in TB and subsurface electrical resistivity were produced by MT inversion. To estimate the porosity of aquifers by resistivity, we should determine the resistivity of groundwater which is controlled by the Total Dissolved Solids (TDS) in water. From the previously published data, TDS increases from piedmont plain to alluvial plain along groundwater flow direction in TB and other similar settings. In terms of spatial distribution of TDS and 3-D resistivity model, the effective porosity of aquifers in the study area was calculated. Finally, by taking account of the water table and thickness of Quaternary sediments collected by BGP Inc., the total groundwater volume was estimated in northern parts of TB.

Magnetotelluric insights into the formation and reactivation of trans-crustal shear zones in Precambrian basement of the eastern U.S. Midcontinent

Three-dimensional inversion of regional long-period magnetotelluric (MT) data reveals the presence of two distinct sets of high-conductivity belts in the Precambrian basement of the eastern U.S. Midcontinent. One set, beneath Missouri, Illinois, Indiana, and western Ohio, is defined by northwest−southeast-oriented conductivity structures; the other set, beneath Kentucky, West Virginia, western Virginia, and eastern Ohio, includes structures that are generally oriented northeast−southwest. The northwest-trending belts occur mainly in Paleoproterozoic crust, and we suggest that their high conductivity values are due to graphite precipitated within trans-crustal shear zones from intrusion-related CO2-rich fluids. Our MT inversion results indicate that some of these structures dip steeply through the crust and intersect the Moho, which supports an interpretation that the shear zones originated as “leaky” transcurrent faults or transforms during the late Paleoproterozoic or the early Mesoproterozoic. The northeast-trending belts are associated with Grenvillian orogenesis and also potentially with Iapetan rifting, although further work is needed to verify the latter possibility. We interpret the different geographic positions of these two sets of conductivity belts as reflecting differences in origin and/or crustal rheology, with the northwest-trending belts largely confined to older, stable, pre-Grenville cratonic Laurentia, and the northeast-trending belts largely having formed in younger, weaker marginal crust. Notably, these high-conductivity zones spatially correlate with Midcontinent fault-and-fold zones that affect Phanerozoic strata. Stratigraphic evidence indicates that Midcontinent fault-and-fold zones were particularly active during Phanerozoic orogenic events, and some remain seismically active today, so the associated high-conductivity belts likely represent long-lived weaknesses that transect the crust.

Feature-based magnetotelluric inversion by variational autoencoder using a subdomain encoding scheme

Magnetotelluric (MT) data inversion aims to reconstruct a subsurface resistivity model that minimizes the discrepancy between inverted and measured electromagnetic data. Conventional pixel-based minimum-structure inversion often yields a smoothed-out reconstruction with a relatively low resolution. A priori geophysical knowledge can be embedded into inversion and improve the reconstruction resolution through proper reparameterization. However, existing reparameterization approaches, such as model-based and parametric transform-based inversion, have limited ability to incorporate various a priori information. The effectiveness of existing deep generative model-based inversion algorithms is still debatable when applied to scenarios with complex backgrounds. We develop a feature-based MT data inversion method based on a variational autoencoder (VAE) with a subdomain encoding scheme. Instead of encoding the entire domain of an investigation, we adopt a 1D subdomain encoding scheme to encode the 1D resistivity-depth models using a single VAE. The latent variables for the 2D model are a combination of the latent variables for 1D models, and the encoded region of interest (ROI) can be flexibly determined. The latent variables of ROI and the pixels outside the ROI are simultaneously inverted using the gradient-descent method. Our 1D subdomain encoding scheme reduces the complexity and diversity of the data set, and it can flexibly embed a priori knowledge with various uncertainties. Synthetic data inversion and inversion of the Southern African Magnetotelluric Experiment field data validate our method’s ability to effectively improve inversion accuracy and resolution.

Geothermal Resource Mapping in Northern Botswana Inferred from Three-Dimensional Magnetotelluric Inversion

A set of magnetotelluric (MT) data collected from 28 stations at the Kasane Hot Spring in northern Botswana was used to derive a 3-D model of the electrical resistivity distribution around deep geologic structures that we associated with geothermal resources. The dimensionality analysis results revealed that 3-D modeling should be used to determine the electrical structure. The resistivity models revealed a conductive layer with an average thickness of 200 m, representing the overlying sediments of the Proterozoic volcanic rocks. The thick high-resistivity zone (>100 Ωm) below the conductive layer can be associated with Mesoproterozoic bedrock. The MT measurements in this area show a tube-shaped conductive anomaly that could serve as a fluid pathway feeding the hot spring. A fracture-controlled meteoric fluid circulation presumably determines the existence of the Kasane Hot Spring system.

Electrical Response of a Reactivated Ancient Suture Revealed by Three‐Dimensional Magnetotelluric Inversion Across the Jinsha River Suture, Northern Tibetan Plateau

AbstractThe northern Tibetan Plateau offers an excellent opportunity to investigate continental collision involving the Indian and Asian plates in this remote, high‐altitude region. However, the deep structure of the region remains incomplete and controversial, which limits our understanding of the processes of continental convergence. This study presents a new 350‐km‐long magnetotelluric (MT) profile across the Northern Qiangtang and Hoh Xil terranes in the western part of the northern Tibetan Plateau to elucidate the lithospheric structure of the reactivated Jinsha River suture. We carry out a three‐dimensional inversion to acquire the electrical structure beneath the Jinsha River suture, and reveal the presence of large‐scale conductive anomalies in the middle‐lower crust of the Northern Qiangtang and Hoh Xil terranes. The high‐conductivity anomaly beneath the Jinsha River suture extends to >80 km depth and is coincident with a zone of high melt fraction (>5%) in the middle‐lower crust beneath the Jinsha River suture, thereby indicating that this suture has become a rheological channel. The convergence of Indian and Asian lithosphere beneath the northern Tibetan Plateau may be the driving mechanism for the reactivation of this ancient suture. Continental subduction leads to enhanced convection in the mantle. This reactivated suture, which is a tectonically weak zone, provides a conduit for the upwelling of hot mantle material to result in the subsequent melting of the middle‐lower crust. Moreover, our findings provide valuable insights into the geodynamic evolution of the northern Tibetan Plateau, as well as contribute to our understanding of continental convergence processes.