Dikun Yang

Summary: Magnetotellurics (MT) provides critical constraints on Earth’s electrical conductivity structure and thereby illuminates lithosphere and mantle processes. The EarthScope USArray MT program provides a unique opportunity to investigate large-scale tectonic and compositional variations across the contiguous United States (U.S.). However, uniform MT interpretation is hindered by data quality and the computational and initialization demands of 3D inversion. To provide a physically consistent and uncertainty-aware continental-scale baseline, we develop CURIE (continental U.S. 1D resistivity inference ensemble), comprising two complementary probabilistic reference model ensembles obtained by independently inverting the Zxy and Zyx components from 1773 MT stations using unsupervised, physics-driven normalizing flows. For each station and mode, CURIE provides posterior resistivity distributions, uncertainty estimates, and predicted MT responses. We assess the 1D assumption using filtered data misfit, mode differences, and phase tensor skew and ellipticity. Most stations yield filtered misfits below 4, indicating that 1D models reproduce the dominant responses. Low phase-tensor skew and ellipticity broadly coincide with low-misfit regions across the Interior Plains and the Intermontane Plateaus, whereas elevated indicators and misfits along tectonic and continental margins identify areas where 1D interpretation requires greater caution. At shallow depths, CURIE recovers resistivity patterns associated with major geological provinces; at mid- to lower-lithospheric depths, it resolves the broad contrast between the tectonically active western U.S. and the stable eastern craton. Differences between the Zxy and Zyx results along the Pacific and Gulf coasts, and in Florida further reflect orthogonal sensitivities to conductivity gradients and indicate 3D structural orientations, with some near-coast misfits influenced by the coast effect. The resulting dataset provides a continent-wide probabilistic reference that offers a first-order view of the U.S. electrical structure while supporting data quality assessment, identification of potential 3D effects, and development of initial or reference models for future 3D inversion and geodynamic interpretation.

Three-dimensional time-domain electromagnetic (TEM) simulations typically use sequential time-stepping, requiring early-time calculations before late times, reducing parallelizability compared to frequency-domain methods. To address this issue, a decomposition method was developed to parallelize forward modeling of TEM time-stepping for arbitrarily complex waveforms. Based on the theory of survey decomposition and scale matching principle, the approach computed the time-domain responses of each time channel separately in parallel. Computational efficiency came from two ideas. First, TEM fields diffused at later times, so that each time channel can be stepped at a step length adapted to its temporal scale. Second, exact simulation of the entire on-time waveform was not always necessary — early off-time channels only needed a narrow portion of the pulse width before the turn-off to be precisely described; late off-time channels needed the time integration of the on-time waveform to account for the total energy transmitted. The approach first empirically determined a characteristic step length (δt) for a particular time channel by exploiting those two properties. Then, a step-off response was obtained by stepping at a constant δt. Next, the discrete impulse response was calculated by differentiating the step-off response with an impulse width δt. Finally, the discrete impulse response was convolved with the effective portion of the transmitter waveform discretized by δt. By experimenting with a variety of TEM waveforms and many random models, the study obtained a set of empirical parameters for δt and the effective pulse width for practical use. Three-dimensional TEM examples using the VTEM and HELITEM waveforms demonstrated that multiscale and parallel time-stepping consumed a small fraction of what was required by the conventional sequential method. The decoupled computation enabled accelerated wide-band TEM time-stepping modeling in massively parallel environments by eliminating interchannel dependencies similar to the frequency-domain methods.

Full-waveform inversion (FWI) provides high-resolution velocity models by exploiting the complete information embedded in seismic waveforms. However, the advantages of FWI come with cycle skipping when sufficient information is not available to build an accurate initial model. To integrate nonseismic data into seismic FWI, this study established a direct conversion method, leveraging the correlation between multiphysical models. The diffusive nature of electromagnetic (EM) data made it an independent, low-cost information source that complemented seismic low-frequency data. Unlike joint inversion approaches, the flexible FWI framework initialized FWI using EM resistivity inversion results. This novel approach extracted low-frequency skeleton structure from electromagnetic data to construct an initial FWI model. By design, it avoided strong assumptions about petrophysical correlation and structural alignment and did not require complex multiphysics objective functions, resulting in a straightforward implementation. The three-stage implementation began by inverting EM data to generate a blurred resistivity image. Pixels in this image were then clustered into models; each was assumed to have a constant velocity. To prevent cycle skipping, a preliminary FWI was performed to roughly fit seismic data by determining velocities for these models. Finally, a full-bandwidth FWI refined the preliminary velocity model, which had already incorporated EM and low-frequency seismic information, aiming for the highest possible resolution. Applied to the Marmousi model, the approach outperformed conventional seismic-only FWI methods in terms of data fitting and computational performance. Using EM to warm up FWI was theoretically similar to initializing FWI with a smoothed version of the true model because EM surveys could be regarded as a low-pass filter of the subsurface structure, as EM surveys physically averaged subsurface structures. The findings underscore the importance of incorporating nonseismic data in seismic imaging and offer a robust workflow for joint multiphysical data acquisition and analysis.

3D magnetotelluric (MT) inversion based on the Gauss–Newton (GN) framework plays an important role in deep mineral exploration by imaging subsurface electrical conductivity structures. However, large-scale 3D MT inversion remains computationally expensive due to the high cost of sensitivity-matrix construction. To address this challenge, we develop a stochastic Gauss–Newton (SGN) framework that reduces computational cost through random data subsampling while preserving the practical convergence behavior of GN inversion. In the proposed framework, only a randomly selected subset of data is used to approximate the GN search direction. By exploiting a key property of MT forward modelling, namely that responses at all receivers are obtained simultaneously for each frequency, the line search is performed using the full dataset, ensuring stable convergence of the inversion process. The SGN framework is validated using both a synthetic multiblock model and a field dataset from the Akebasitao area in Xinjiang, China. The recovered models remain highly consistent with those obtained using conventional full-data Gauss–Newton inversion across a wide range of sampling ratios. For the synthetic example, reducing the sampling ratio from 100% to 10% decreases peak memory consumption from approximately 433 GB to 242 GB and reduces runtime from 86.8 h to 23.9 h while maintaining comparable inversion quality. Similar computational savings are achieved for the field-data inversion. The field application successfully recovers the major conductive structures along the margins of the intrusion that are associated with hydrothermal alteration and fluid activity, highlighting the capability of SGN to delineate geologically meaningful targets relevant to deep mineral exploration. These results demonstrate that SGN provides an efficient and scalable approach for large-scale 3D MT inversion.

Accurate and fast simulation in 3D is critical in quantitatively interpreting time-domain electromagnetic (TEM) data for complex geology, but this task has long been known to be computationally demanding and, hence, time-consuming because it involves multiple numerical solutions of 3D Maxwell’s equations at multiple spatial and temporal scales. Survey decomposition (SD) is a generic computational framework that speeds up the electromagnetic (EM) induction problem solutions by breaking down the original large domain, transmitter sources, and time-stepping sequences into many small problems with reduced ranges of scales for optimal computational efficiency and parallelism. However, the existing SD implementation uses a trial-and-error scheme to determine the number of decomposed sources, creating a sequential dependency that restricts the utilization of ultra-large-scale parallelization for further speedup. As a result, the promised embarrassing parallelism and linear scalability have not been fully verified and demonstrated. This work first optimized the large source decomposition strategy by establishing an empirical relationship between the decomposed source, time channels, and conductivity, so the decomposition was completed before the simulation; therefore, the decision-making on the fly could be eliminated. The numerical accuracy of the empirical decomposition is satisfactorily verified against other traditional numerical solutions on a variety of benchmark models. Then, the method was tested on a realistic 3D geologic model and a large-loop TEM survey in a parallel computing environment running more than 46,000 cores simultaneously. The linear speedup observed in the numerical experiments demonstrated the excellent scalability of our improved SD method that can fully capitalize on the emerging distributed and elastic computing. This study shows that, with the latest algorithms and hardware, 3D TEM modeling problems of any size can now be solved accurately in tens of seconds at a cost of tens of dollars.

SUMMARY: 3-D magnetotelluric (MT) inversion is a powerful tool for imaging the Earth’s electrical structure, yet its computational demands remain a major challenge, particularly when simulating responses across broad frequency bands. Conventional inversion schemes rely on a unified mesh for forward simulation at all frequencies, which inflates the number of model parameters and greatly extends runtime. To overcome these limitations, we present a finite-volume-based frequency-domain survey decomposition (FVFSD) method that adaptively constructs forward simulation meshes according to the skin depth of each frequency while maintaining a fixed horizontal discretization. This design decouples forward simulation meshes from the inversion mesh, striking a balance between accuracy and efficiency. To further improve the treatment of resistivity contrasts, an equivalent circuit scheme is employed to compute effective conductivities within control volumes, outperforming conventional volume-weighted averaging. We validate the proposed method through comprehensive numerical experiments, including synthetic benchmarks and real-world case studies from the Akebasitao region (China) and the Southern African MT experiment. Results demonstrate that FVFSD achieves accuracy comparable to standard finite-difference forward simulations, while significantly reducing computational time. In large-scale MT inversions, this acceleration directly translates into faster convergence and more efficient recovery of lithospheric-scale resistivity structures. The method is fully compatible with existing inversion algorithms and solvers, making it straightforward to integrate into standard workflows. Overall, FVFSD provides a scalable and accurate strategy for advancing 3-D MT inversion, with clear implications for lithospheric studies, resource exploration and tectonic investigations.

Magnetotelluric (MT) inversion models are widely used to interpret crustal conductivity structures related to fluid pathways, deformation zones, and mineralization processes; however, evaluating the reliability of inversion-derived anomalies remains challenging when datasets contain subtle station-dependent distortions or residual cultural noise. We present a jackknife-inspired, model-space diagnostic framework based on leave-one-station-out (LOSO) inversion to quantify station influence and improve interpretation reliability. The workflow consists of (1) generating a LOSO inversion ensemble using identical inversion settings, (2) computing ensemble statistics and standardized perturbation metrics to identify sensitive zones, and (3) applying distribution-based diagnostics to classify station influence and guide construction of an ensemble-refined model. Synthetic experiments demonstrate that the framework distinguishes localized station-controlled artifacts from broadly supported structural responses, allowing targeted correction without altering robust features. Application to a field MT dataset acquired in a noise-affected environment shows that a mid-crustal conductive structure remains stable across the LOSO ensemble, while some shallow anomalies exhibit strong station dependence. The resulting ensemble-refined model introduces only localized modifications, demonstrating that ensemble-based model-space diagnostics provide a practical and reproducible strategy for validating MT inversion results and improving confidence in exploration-oriented conductivity interpretations.

Steel casings in oil and gas development have the potential to enhance controlled source electromagnetic (CSEM) responses, particularly in detecting subtle changes in reservoir properties. To map the 3D distribution of injected fluid during hydraulic fracturing, a method was proposed that incorporates the effects of such casings. We introduced an edge conductivity parameter, which combines intrinsic conductivity and the cross-sectional area of the casing, into the conductivity model. By aligning these edge conductivities with mesh edges within a finite volume framework, casing effects were captured without complex mesh refinements. The algorithm was validated through cylindrical mesh simulations and forward modeling using a line current transmitter. For inversion, an objective function combining data misfit and model smoothness constraints was optimized with the Gauss-Newton method. Synthetic scenarios involving horizontally drilled wells and top-casing sources demonstrated the method's ability to recover fluid trajectories and detect asymmetric fluid distributions. Additionally, the method proved effective in assessing casing integrity by estimating edge conductivities. This work shows that integrating steel casing data into CSEM modeling enhances reservoir characterization and supports decision-making in oil and gas exploration and CO₂ sequestration.

Modern electromagnetic (EM) surveys deliver high-quality data with broad spatial coverage and high spatial density, providing an opportunity to produce higher-quality images of the earth’s subsurface than in the past. Because geologic structures are inherently 3D, the ultimate goal of an EM survey is to recover a 3D conductivity model that supports robust decision-making and interpretation. Nonetheless, practical inversion and interpretation workflows often still rely on simplifying assumptions, such as a 1D layered earth or parametric targets like plates. This paper illustrates the value of incorporating 3D forward simulation into the interpretation workflow. By running a forward simulation for the EM responses of inversion-derived models in full 3D, practitioners can assess the consistency of inversion results with the measured data and identify potential artifacts. Using two examples, namely, a dipping conductor and a porphyry-style deposit, we demonstrated how models that appear plausible under 1D assumptions fail under 3D scrutiny. Identifying areas where 1D assumptions fail can prompt additional analysis, such as iterative hypothesis testing or more focused 3D inversions. As such, 3D forward simulation should be considered an essential tool in the EM practitioner’s toolbox.

SUMMARY: Electrokinetic signals, such as surface self-potential (SP) variations, offer a unique window into coupled fluid–electrical processes in the Earth’s crust, yet their quantitative interpretation remains challenging in complex geological settings. In this study, we develop an electrokinetic modelling framework by extending the modified Luco-Apsel-Chen generalized reflection and transmission method to simulate SP responses due to a fluid-injection source in layered geological media. After simulating electric signals, we apply location-specific amplification factors—derived from prior numerical investigations—that account for the effects of steel well casings. This post-processing step enables rigorous comparison with field observations. Using the well-documented deep fluid injection experiment at the Soultz-sous-Forêts geothermal site, we calibrate simulated pore pressure against downhole measurements to derive a realistic source function for direct comparison between modelled and observed SP signals. The model reproduces key spatiotemporal features of the mV-scale SP anomalies and, importantly, captures the observed slower decay of surface SP signals after shut-in despite the rapid decrease in deep pore pressure. Previous field-scale studies have qualitatively attributed this phenomenon to sustained ionic transport; here, our simulation results provide a quantitative demonstration that this process—driven by continued pore-fluid movement—is responsible for the slower SP decay, a mechanism not captured in earlier electrokinetic simulations. These findings provide new mechanistic insight into SP generation in stratified media, demonstrate the essential role of casing effects in field-scale interpretation, and establish a transferable framework for monitoring subsurface fluid flow in geothermal, hydrocarbon and groundwater systems.