A double-layer neural network combining a fully convolutional network (FCN) and U-Net is introduced to improve the accuracy of 2.5-D magnetotelluric (MT) inversion. The initial model obtained through the Bostick inversion method is randomly transformed to generate the dataset for the training of the convolutional neural network (CNN). The training input consists of the apparent resistivity obtained through the forward modeling of transformed models, while the output represents the resistivity of those same models. The proposed method has the local optimization of the neural network inversion method and narrows the range of network optimization by employing an initial solution obtained from the Bostick inversion method. The results of the inversion experiments, including an actual measurements, demonstrate a significant enhancement in the accuracy of the inversion results when employing the neural network method. This demonstrates the efficiency of neural networks in solving 2.5-D magnetotelluric (MT) inversion problems.

This article first presents machine-learning (ML) inversion of resistivity profiles from multifrequency electromagnetic measurements on undulating terrain surfaces based on synthetic data training by the mixed spectral element method (MSEM). The inversion method combines several advanced technologies with various merits. A semiregular mesh generation method is designed and developed for adaption to complex undulating terrain and multifrequency measured data, and the proposed meshing technology is also suitable for modeling different training models under the same undulating terrain. By simulating the application scenarios of measurements, the apparent resistivity data at eight frequencies from 1 to 2048 Hz are simulated with the 2.5-D MSEM to ensure the accuracy and efficiency of the simulation of undulating terrains. Fast simulation of stochastic models for training datasets is achieved by twisting and extruding the initial model obtained by Bostick inversion. Since the unknown weight matrices are solved only once in the training process, the extreme learning machine (ELM) is used for ML inversion to reduce the training cost and obtain high-precision inversion results. Then it is applied to reconstruct a metallogenic model to verify the method’s validity and accuracy and to reconstruct the resistivity profile of underground ore bodies with actual measurements. The results show that the proposed method can be effectively used to detect metal ores at a depth of less than 3000 m underground.

In this letter, a new full-wave inversion (FWI) scheme is proposed to reconstruct multiple dielectric parameters of 3-D arbitrary anisotropic objects buried in layered media. Three inverse solvers, including the isotropic one, biaxial anisotropic one, and the arbitrary anisotropic one, are cascaded sequentially. The dielectric parameters obtained by the first solver are used as the initial values of the next solver. Meanwhile, the inversion domain is synchronously downsized on the basis of discrepancies between the inverted dielectric parameters and the background ones. Numerical simulations show that, compared with the direct arbitrary anisotropic inverse solver, the cascading inversion scheme not only can produce more reliable reconstructed profiles but also significantly lowers the computational cost. In addition, the antinoise ability of the cascaded solvers is also tested.

This article presents a novel hybrid electromagnetic inversion method. The traditional 3-D variational Born iterative method (VBIM) is combined with the unsupervised machine-learning expectation maximization (EM). In each iteration, VBIM first outputs the pseudo-randomly distributed model parameters in all discretized cells in the inversion domain. Then the EM algorithm is used to classify them and estimate the mean model parameter values of each homogeneous scatterer or subscatterer supposing that the reconstructed model parameters in all cells comply with the Gaussian mixture model (GMM). At last, partial cells in the inversion domain classified as “background” will be removed and the unknowns in the next VBIM iteration are reduced. This process is implemented iteratively until no “background” cell can be removed anymore and the data misfit between the measured scattered field and reconstructed field reaches the stop criterion. Finally, the mean value of the model parameter estimated by EM is mandatorily assigned for each homogeneous scatterer or subscatterer. Numerical examples show that the proposed hybrid method works efficiently for the reconstruction of isotropic, anisotropic, homogeneous, or inhomogeneous scatterers. It also has a certain antinoise ability.

In electromagnetic (EM) well logging for petroleum exploration, off-centered tools within a noncircular borehole and invasion zones in multilayered media represent a challenging 3-D problem for traditional numerical methods. The 3-D finite-element numerical mode-matching (FNMM) method and the spectral numerical mode-matching (SNMM) method are developed to address this problem in this work. The numerical mode-matching (NMM) methods reduce the original 3-D well logging problem into a series of 2-D open waveguide eigenvalue problems plus a 1-D layered medium problem, which can be analytically solved by a recursion procedure. These waveguide eigenvalue problems with anisotropic inhomogeneous media in the horizontal directions are solved numerically by the mixed finite-element method (MFEM) with the flexibility for the complex geometry and the mixed spectral element method (MSEM) with the exponential convergence. A general operator form of Maxwell’s equations is also derived to obtain the source excitation vector independent of the$z$-axis. Therefore, the NMM solvers can effectively and accurately simulate the response of off-centered EM well logging tools in an irregular borehole in complex formations. The NMM methods are applied to simulate three formations including a five-layer isotropic homogeneous formation, an off-centered logging tool in a noncircular borehole with anisotropic invasion zones in a five-layer anisotropic formation, and the Oklahoma formation. Numerical experiments indicate that the NMM methods are highly efficient and accurate for the EM well logging models.