基于二次场的海洋可控源电磁法三维有限元正演

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

根据库伦规范势的定义,推导出关于磁矢量势和电标量势的偏微分方程,为了克服由电流源引起的奇异性和数值模拟计算困难,将电磁总场分解为一次场和二次场,一次场由基于Schelkunoff势函数的一维正演算法得到,二次场由有限元法计算得到,实现了海洋可控源电磁法三维有限元正演算法。通过一维数值模拟实例,验证该算法的计算精度。然后,利用该算法对带海底地形的三层储层模型进行正演,分析了海底地形对海洋控源电磁场各分量产生的影响。

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 quasi-analytically in terms of the Schelkunoff potentials secondary field, where the primary field is expressed 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.