Forward modeling of 3D electromagnetic problems using vector and scalar potentials in a mixed space-wavenumber domain

Fast and accurate 3D electromagnetic (EM) forward modeling is the core problem of inversion and quantitative interpretation for field data. The computation and memory requirements of practical numerical modeling in space domain are enormous, which leads to the difficulty of deploying highly efficient and detailed inversions for large-scale models with complex geology. A new 3D EM forward modeling in a mixed space-wavenumber domain is proposed to mitigate the difficulty. By performing a two-dimensional Fourier transform along two horizontal directions, three-dimensional partial differential equations in the spatial domain are transformed into a group of independent 1D differential equations engaged with different wave numbers. Importantly, the computation and memory requirements of modeling are greatly reduced by this method, and the independent differential equations are highly parallel among different wave numbers. The method preserves the vertical component in the space domain, thus, a mesh for modeling can be fine at shallow depth and coarse at deep depth. Generally, the new method takes into account of both the calculation accuracy and efficiency. Finite element method is used to solve the transformed differential equations with different wave numbers, moreover the efficiency of solving fixed bandwidth linear equations is further improved by a chasing method. In a synthetic test, a model with prism-shaped anomaly is used to verify the accuracy and reliability of the proposed algorithm by the comparison between the proposed and classical IE solutions. Furthermore, The numerical experiments indicate that the proposed method not only has high accuracy, but also has charracteristics of high parallelism, small memory consumption and fast calculation speed. The calculation efficiency of about 1 similar to 2 orders of magnitude higher than the traditional 3D modeling by using FEM are obtained, and the larger the mesh size of the model, the more obvious the efficiency advantage of the proposed algorithm.