In controlled-source electromagnetic (CSEM) inversion with conventional regularization, the reconstructed conductivity image is usually blurry and only has limited resolution. To effectively obtain more compact conductivity models, we apply the concept of multinary transformation to CSEM inversion based on the finite-element method with an unstructured tetrahedral mesh. Within the framework of multinary inversion, the model conductivities are allowed to be clustered only within the designed values, which are usually obtained from other a priori information or from conventional inversion. Synthetic studies show that multinary inversion produces conductivity images with clearer model boundaries compared to the maximum smoothness inversion and the focusing inversion for realistic geoelectric models. We further apply the developed method to a land CSEM survey for mineral exploration. The multinary inversion results are closer to the ground truth compared to the conventional maximum smoothness inversion and the focusing inversion. The developed method and the numerical algorithm provide a new approach and workflow for CSEM inversion when the models need to have clear boundaries and clustering model values. Such geoelectric models could be very useful for geologic interpretation in oil and mineral exploration when a priori information (such as the estimated conductivity values) of the exploration targets is known.

Gravity surveys in regional geophysical research can be used to estimate the depth of the sediment‐basement interface. In this study, we investigate a novel method using the convolutional neural network (CNN) for depth‐to‐basement inversion directly from gravity data. Based on the Random‐Midpoint‐Displacement method (RMD) and the features of the observed gravity data, we can generate a large set of realistic sediment‐basement interface models. This new method for model generation can significantly reduce the size of the training data sets which is usually considerably large to train a pervasive network. The application on synthetic models shows that the developed CNN inversion is able to capture the detailed features of the sediment‐basement interface for the complex geological model. However, so far, the training set obtained from the proposed method is still continuous and the CNN inversion still cannot effectively recover the models such as abrupt faults. We also successfully applied the developed method and workflow to a field study. The proposed approach opens a new window for estimating the physical contrast interfaces using potential field.

When the controlled-source electromagnetic (CSEM) data are contaminated by intense cultural noise and the signal-to-noise ratio (S/N) is lower than 0 dB, the existing denoising methods can hardly achieve good results. To overcome the problem, a new strong-noise elimination method called inception-temporal convolutional network-shift-invariant sparse coding (IncepTCN-SISC) is developed based on deep learning and dictionary learning. First, a novel deep neural network model called IncepTCN is created based on the inception block and temporal convolutional network (TCN). Then, IncepTCN is used to recognize strong-noise segments in the observed signal, which are then discarded. Finally, a dictionary-learning method based on shift-invariant convolutional coding is used to denoise the remaining weak-noise segments. A series of simulated and field data experiments indicate that the new proposed IncepTCN network has obvious advantages in accuracy and efficiency compared with alternative methods. The average recognition accuracy of IncepTCN is 96.5%, which is 25.5%, 3.2%, 1.1%, and 2.0% higher than that of the fuzzy C-means clustering, convolutional neural network (CNN), residual network (ResNet), and the nonimproved TCN, respectively. In addition, the test results of unfamiliar data indicate that the generalization ability of IncepTCN is significantly better than the CNN, ResNet, and nonimproved TCN. This IncepTCN-SISC method can improve the S/N of CSEM data from −5.0 dB to 3.1 dB or from 5.0 dB to 31.9 dB and solve the denoising problem of noisy data below 0 dB to a certain extent. After IncepTCN-SISC processing, the initially distorted apparent resistivity curves become smooth, and the result is better than dictionary learning. This method is intelligent without any manual intervention and is suitable for batch processing of CSEM data.

The correct interpretation of time-domain or transient electromagnetic (TEM) data relies on effective inversion techniques. Herein, we have developed an effective 3D-TEM inversion method based on the vector finite-element method. The domain was discretized with unstructured tetrahedra to simulate complex geologic structures. We develop a second-order backward-Euler scheme, rigorously with nonuniform time-step sizes, to approximate the time derivative of the electric field. The waveform was directly simulated and considered in the forward modeling and inversion. In a 3D inversion, the most time-consuming element of the workflow is solving a large system of linear equations. To alleviate this problem, we adopt a parallel direct solver for solving a large system of equations involved in forward modeling and sensitivity calculations. We use the Gauss-Newton approach to solve the inverse problem and formulate the least-squares problem to obtain model updates. We avoided the explicit sensitivity calculation by solving the matrix-vector multiplication between the sensitivity matrix (or its transpose) and vector. The developed inversion algorithm is validated using several realistic synthetic models. Finally, we apply the method to practical TEM data with complex topography for coal mine goaf detection. We thus obtain a detailed 3D resistivity model that revealed the layering structure and some localized anomalies related to the coal mine goaf.

One of the major problems in the modeling and inversion of marine controlled-source electromagnetic (CSEM) data is related to the need for accurate representation of very complex geoelectrical models typical for marine environment. At the same time, the corresponding forward-modeling algorithms should be powerful and fast enough to be suitable for repeated use in hundreds of iterations of the inversion and for multiple transmitter/receiver positions. To this end, we have developed a novel 3D modeling and inversion approach, which combines the advantages of the finite-difference (FD) and integral-equation (IE) methods. In the framework of this approach, we have solved Maxwell’s equations for anomalous electric fields using the FD approximation on a staggered grid. Once the unknown electric fields in the computation domain of the FD method are computed, the electric and magnetic fields at the receivers are calculated using the IE method with the corresponding Green’s tensor for the background conductivity model. This approach makes it possible to compute the fields at the receivers accurately without the need of very fine FD discretization in the vicinity of the receivers and sources and without the need for numerical differentiation and interpolation. We have also developed an algorithm for 3D inversion based on the hybrid FD-IE method. In the case of the marine CSEM problem with multiple transmitters and receivers, the forward modeling and the Fréchet derivative calculations are very time consuming and require using large memory to store the intermediate results. To overcome those problems, we have applied the moving sensitivity domain approach to our inversion. A case study for the 3D inversion of towed streamer EM data collected by PGS over the Troll field in the North Sea demonstrated the effectiveness of the developed hybrid method.

Presently, the 3-D inversion technique has started playing a more important role in controlled-source electromagnetic (CSEM) data interpretation. With the development of hardware and computation algorithm, 3-D inversion technique has developed rapidly during the past decades. In this article, we present a newly developed 3-D parallelized inversion algorithm in the frequency domain with hexahedral discretization. Within the framework of this approach, we use the finite-element method (FEM) in the forward modeling and Gauss-Newton optimization technique in the inversion. We solve the forward modeling and adjoint problem efficiently with Math Kernel Library (MKL) Pardiso parallel direct solver. Considering the fact that the forward modeling and sensitivity calculation are frequency independent, we further parallelize the algorithm over frequency using Message Passing Interface (MPI) to speed up the modeling and inversion process. The sensitivity matrix is calculated explicitly, which enables us to estimate the optimized regularization parameter easily based on the spectral radius estimation. We proposed a new roughness operator for hexhedral discretization which works well for CSEM inversion problems. We applied the developed algorithm to several realistic CSEM models. The inversion results demonstrate the effectiveness and stability of our inversion scheme.