To determine the electromagnetic (EM) fields of different three-dimensional (3D) controlled-source electromagnetic methods (CSEMs) using the same parameters of the forward solution, by explicitly considering the commonalities, we present a general 3D forward modeling solver for CSEMs with multitype sources and operating environments. The commonality of the solver is reflected in two aspects. First, the solver is based on a frequency-domain (FD) vector Helmholtz equation for determining the scattered electric field. The different types of sources are imposed on the right-hand term of the equation, expressed as background Green’s function. Second, sources of any CSEM can be composed of electric dipole (ED) or magnetic dipole (MD) superposition. Thus, the focus of the 3D forward modeling of CSEMs is reduced to determining the EM fields of ED or MD sources for the background medium. The quasi-minimal residual (QMR) method is used to solve the large sparse complex linear system. Once the FD EM fields have been calculated, the time-domain (TD) response can be obtained using the cosine/sine transformation. The numerical results show that the relative error is less than 5% between the 3D numerical and analytical solutions, which verifies the accuracy of the solver. We further study the difference between the real (bent) and theoretical (straight) wires. We suggest that the shape of the source must be considered for TD and FD CSEMs with a wire source during data processing and inversion. The last example investigated the characteristics of FD EM fields from a finite-length wire and TD EM fields from a rectangular fixed loop on the same conductive tilted disk model buried in resistive sediments. According to the numerical results, we recommend FD CSEMs with a wire source for detecting deep anomalies.

To further improve the efficiency and accuracy of time-to-frequency domain conversion (TFC) for transient electromagnetic (TEM) data, a UNet++ framework was established to learn and model the complex nonlinear functional relationship between time-domain (t-d) and frequency-domain (FD) electromagnetic (EM) fields. The input and output of UNet++ were defined as the t-d and FD vertical magnetic field data derived from a one-dimensional (1-D) geoelectric model, respectively. The dataset consisted of 500,000 samples, encompassing 1-D models with 2 to 6 layers. Through this process, the hyperparameters characterizing the mapping relationship between t-d and FD magnetic fields were determined. To verify the validity of the proposed algorithm, 20 models were randomly selected from the test dataset. The experimental results demonstrate that the theoretical FD responses agree well with the recovered FD responses transformed from the t-d signals via TFC, with a relative error of less than 5% for all frequencies. In addition, the algorithm was tested on an H-type model to demonstrate its superiority over the regularization inversion method in achieving precise TFC. To further validate the effectiveness of TFC for TEM data using UNet++, the algorithm was applied to measured data collected from a mining area in western Qinghai Province, China. The results indicate that reliable FD EM responses can be obtained from t-d signals using UNet++ across all frequencies. The proposed algorithm offers robust technical support for TFC of TEM data and contributes to the advancement of geophysical exploration technology.

The 3D inversion of transient electromagnetic (TEM) data remains a highly challenging optimization problem that needs to be resolved in the field of geophysical electromagnetic (EM) exploration. In this study, we present an effective 3D TEM interpretation framework based on time–frequency conversion (TFC) using UNet++ and demonstrate its capability in recovering complex 3D structures as well as its applicability in practical explorations. First, a generalized ellipsoid and Euler rotation are employed to construct 3D geoelectrical models, ensuring that the generated geological bodies possess sufficient geometric complexity while remaining geologically plausible. Second, frequency-domain (FD) data are recovered from time-domain (t-d) data using UNet++, which then serve as pseudo-observation data to be input into a 3D FD inversion code. Finally, the staggered-grid finite difference method is adopted for modeling the TEM responses, and the nonlinear conjugate gradient (NLCG) method is utilized to perform 3D inversion. Taking TEM data from a ground-wire source as an example, a synthetic test on models with complex 3D anomalies confirms that the proposed framework can accurately recover the geometry and position of subsurface bodies. Furthermore, the inversion code is tested on the field data acquired in Qinghai Province, China, and the inversion results are in good agreement with known geological and other geophysical information. Results demonstrate that performing TFC using UNet++ provides a reliable data foundation for 3D FD inversion of TEM data. This framework offers an effective approach for the practical 3D interpretation of TEM data and expands the research path for addressing complex 3D problems in geophysical EM explorations.

Gradient-based inversion methods are widely used for time-domain airborne electromagnetic (AEM) data, but their results are commonly affected by the initial model and regularization-induced smoothing. These limitations are particularly evident when thin layers or alternating high- and low-resistivity structures need to be resolved. To address this problem, we propose a gradient-guided iterative enhancement (GGIE) inversion that combines a limited-iteration Gauss–Newton (GN) inversion with a lightweight U-Net. In each GGIE inversion iteration, the GN module first produces a coarse inverted model (IM) that preserves the main data-driven geoelectric trend but is still affected by regularization-induced smoothing. The trained U-Net then predicts a structurally enhanced model (PM) from the observed data and the IM. A data-misfit-guided adaptive approach is proposed to calculate the weight coefficients of the IM and PM and to construct an update model (UM). These coefficients are further smoothed by a momentum term so that the relative contributions of the IM and the PM are adjusted adaptively during the iterations. This design reduces error propagation from either component alone and dynamically balances learned structural enhancement with physics-based data consistency. The UM then serves as the initial model for the subsequent GN inversion. GGIE inversion is tested on synthetic data, and the results show that it is most beneficial for complex multilayer structures, for which it reduces the mean relative error and root mean squared error (RMSE) by 49.0% and 28.6%, respectively. Compared with the physics-informed neural network (PINN) baseline, GGIE inversion reduces the model relative error, log-domain RMSE, and data misfit by 19.4%, 7.0%, and 71.7%, respectively. Moreover, compared with U-Net alone, GGIE inversion reduces the data misfit by 85.4%. The proposed method is further applied to field data acquired from the Fox River area in Wisconsin, USA. The main advantage of GGIE inversion is its ability to resolve complex multilayered structures, thin layers, and sharp resistivity contrasts with improved accuracy and stability.

Volcanic magma plumbing systems is essential for understanding crustal–mantle material exchange and the dynamics of volcanic activity. The magnetotelluric method (MT) offers an effective tool for imaging conductive features from the crust to the lithospheric mantle. However, current survey strategies face a tradeoff between imaging resolution and acquisition cost. Here, we construct a lithosphere-scale synthetic model of a magma plumbing system and use 3D MT inversion, sensitivity analysis, and point spread function evaluation to assess the resolving capability of sparse versus dense arrays. Our results show that large-scale conductive anomalies in the mid–lower crust and lithospheric mantle can be reliably imaged using a sparse regional array with targeted densification in the crustal anomaly zone. This approach reduces field costs and computational demand. Guided by these findings, we conducted MT observations across the Longgang volcanic field and identified low-resistivity anomalies extending from the lithospheric mantle into the mid–lower crust. These features are consistent with the dense array MT inversion results. Our study demonstrates that an array strategy combining wide-area sparse coverage with targeted densification offers a cost-effective approach to image deep conductive structures, which may provide practical guidance for optimizing MT survey design in volcanic regions.