Electromagnetic Fields Computation of Planar-Distribution Sources in Anisotropic Planar-Stratified Media With an Equivalent Boundary Approach

In this study, the equivalent boundary approach is applied to quickly compute the electromagnetic (EM) fields of planar-distribution sources in fully anisotropic planar-stratified media. In the derivation process, the spectral-domain EM field vector is represented as the product of the field coefficient matrix, the adjacency matrix of the source-field, and the source coefficient matrix. The adjacency matrix of the source-field is found to be independent of the source coefficient matrix and is related only to the stratigraphic structure and anisotropy parameters. Thus, the EM fields of multiple planar-distribution sources can be calculated simultaneously by extending the source coefficient matrix approach, thereby achieving fast calculation. The 2-D Fourier integral is calculated in a cylindrical coordinate system to reduce the double infinite zones to a single infinite zone. To avoid a singularity when the field locations are close to the source along the vertical direction, a double parabolic Sommerfeld integration path is constructed in the spectral complex plane to optimize the use of the properties of evanescent waves in the integration calculations and for fast decay of the integrand, thereby allowing for the robust calculation of EM fields. Numerical results using the finite element method validate the proposed method. Hence, the proposed approach significantly improves the computational efficiency of solving for the EM field of a planar-distribution source in fully anisotropic media, thus facilitating geophysical exploration.