A Comparison of Different Divergence-free Solutions for 3D Anisotropic CSEM Modeling Using Staggered Finite Difference Method

Abstract

This paper presents a staggered finite difference (FD) method for numerical modeling of 3D controlled-source electromagnetic (CSEM) data in an anisotropic conductive medium. The traditional Krylov subspace methods may not be convergence for EM modeling in strong electrical anisotropy due to the variation of the conductivity in the sea-bottom sediments over a range of frequencies (0.1-10 HZ). The algorithm is based on a modified version of the curl-curl equations with scaled grad-div operator (CCGD) in frequency domain. In this approach, we integrate the divergence correction term in the original system with its importance controlled by scaling factors (the same values as model resistivities are used in this paper) and avoid the application of the iterative divergence correction. The corresponding responses calculated by the CCGD and the traditional CC-DC approach for the VTI ocean canonical reservoir model are nearly identical. Then based on the case, we examine the numerical performance of the CCGD approach, and compare it with the CC-DC in terms of computing time and iteration number. The results indicate that the proposed CCGD approach is efficient and stable over different frequencies.