Three-dimensional Marine Controlled-source Electromagnetic Modeling by Finite Element Method Based on Secondary Field

We deduce the double curl equations of secondary magnetic vector potential and electric scalar potential of frequency domain MCSEM method, then we derive the finite element linear equations of MCSEM three-dimensional forward modeling. In order to eliminate the singularity of the source, the total electromagnetic fields are decomposed into the primary field and the secondary field, where the primary field is expressed quasi-analytically in terms of the Schelkunoff potentials. We realize the three-dimensional finite element forward modeling algorithm of MCSEM method based on structured meshes. In the method, the hexahedral mesh is employed to the model subdivision, the Dirichlet boundary condition is considered, and the symmetric successive over-relaxation preconditioned conjugate gradient (SSOR-PCG) algorithm is used to solve large linear system derived from three-dimensional finite element MCSEM forward modeling. The high accuracy and reliance of our algorithm are validated by the one-dimensional numerical example. Finally, the applicability of the algorithm is illustrated on a resistivity model incorporating a step topography. The effect of submarine topography on MCSEM response is analyzed.