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With the rapid development of the transient electromagnetic method (TEM), the numerical simulations of three-dimensional anisotropic media have garnered attention. This study used the rational Krylov method to realise the three-dimensional modelling of the ground magnetic-source airborne transient electromagnetic data for arbitrary anisotropic media. First, based on Maxwell's equations, a time-domain electromagnetic equation was derived for anisotropic media. The finite difference method was employed to discretise the equation, and the electromagnetic field was then expressed as the product of an exponential matrix and a vector related to the source. Subsequently, the rational Arnoldi algorithm was adopted to construct the rational Krylov subspace orthogonal basis vectors, and the electromagnetic fields at different times were obtained based on a model reduction strategy. The accuracy of the proposed algorithm was verified through the comparisons of its results with those of other software packages. We calculated the response for different anisotropic parameters of the typical three-dimensional anisotropic models, and analysed the influence of the anisotropic media on the ground magnetic-source airborne transient electromagnetic data. The proposed three-dimensional forward TEM algorithm provides important technical support for identifying the anisotropic geological bodies and lays the foundation for further inversion research. [ABSTRACT FROM AUTHOR]

This document discusses recent advances in forward modeling and inversion of geophysical electromagnetic data. The research community studying electromagnetic methods has grown in recent years, with applications expanding to include airborne, marine, and borehole scenarios. However, there are still challenges to accurate modeling and inversion, such as the computational requirements and noise in the data. The document presents eight articles on topics including numerical modeling, inversion, signal processing, and case studies. While 3D inversion is a widely discussed topic, this special issue does not include any articles specifically addressing it, suggesting that it may not yet be practical for real-life situations. [Extracted from the article]

3D controlled-source audio frequency magnetotelluric (CSAMT) responses can be distorted strongly by topography and should be accounted for in data inversion and interpretation. In this paper we present a scheme to incorporate topographic distortions into the inversion instead of correcting them. This approach has been verified by comparing the modelling results with 2D FEM CSAMT solutions and synthetic inversion examples. Compared with the responses generated from a half-space model with flat surface, it is found that not only the topography in the survey area but also that at the source position may strongly distort the CSAMT responses. The field example indicates that results with topography are much better than those without considering topography to map the distribution of coal seam underground, which also illustrates the effectiveness of our approach. [ABSTRACT FROM AUTHOR]

The controlled-source audio-frequency magnetotelluric (CSAMT) method has become an important method in geophysical electromagnetic exploration. However, traditional CSAMT only gathers a single set of orthogonal electric and magnetic data, which cannot describe the whole subsurface geological structure. Due to increasingly complex geological targets, the drawbacks of traditional CSAMT have gradually become more significant, promoting the need for tensor CSAMT. Tensor CSAMT can gather richer information, but the 3D forward and inversion models of this method have developed slowly since it was first proposed. The common method for inverting the data of the tensor CSAMT is still magnetotelluric (MT). This paper adopts a staggered-grid finite difference method to realise the 3D forward modelling of the tensor CSAMT. On this basis, we adopt a limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) method to implement a 3D inversion with full impedance data. Through inverting synthetic and real data, we prove that: (1) directly using an MT method to invert the data of the tensor CSAMT will obtain an incorrect result, (2) the inversion result of tensor CSAMT is more reliable than that of the traditional CSAMT, and (3) LBFGS is more efficient than the nonlinear conjugate gradient (NLCG) for tensor CSAMT.Our research shows that 3D tensorCSAMTinversion with LBFGS is very useful and practical for electromagnetic exploration. [ABSTRACT FROM AUTHOR]