This paper presents a new algorithm for the three-dimensional marine controlled source electromagnetic method modeling in arbitrarily anisotropic medium based on unstructured grids and coulomb gauge. In order to avoid the effect of source singularity, we apply the secondary potential formulation for the quasi-static of Maxwell's equation. Next, solving the finite element equations with IDR(s) iterative algorithm method combined with the incomplete LU decomposition technology. Once the secondary vector and scalar potential is solved, we can use the moving least square method to calculate their spatial derivative and compute the secondary electric and magnetic field. In order to test the finite element method for numerical modeling of 3D controlled source electromagnetic data in an arbitrarily anisotropic conductive medium of this paper, we applied the developed algorithm to compute the typical CSEM response of two 3D models. The modeling results show that the proposed algorithm is feasible and effective; the IDR(s) is competitive with or superior to ILU-QMR, ILU-BICGSTAB methods; the proposed algorithm is general and can be applied to EM modeling in borehole and environment geophysics in arbitrarily anisotropic medium.

SUMMARY This paper presents a new algorithm for solving 3-D MCSEM modelling problems in an anisotropic medium using a Wavelet–Galerkin method (WGM) based on compactly supported Daubechies wavelets which are differentiable according to the requirement. In order to avoid the source singularity, we adopted a secondary potential formulation for the quasi-static Maxwell's equation. The primary field on the modelling domain is calculated using fast Hankel transform. The domain can be discretized by locally intensive nodes to deal with the model's complexity, which is observed to improve the accuracy of the solution. The sparse system of the WGM equations is solved using the direct solver MUMPS. This study's algorithm is then applied to calculate the response of the MCSEM in isotropic and anisotropic mediums. The results generated are verified against with solution obtained by FE method and confirmed the performance of the algorithm presented in this study.