耦合势有限体积法高效模拟各向异性地层中海洋可控源的三维电磁响应

本文基于电场矢势与标势分解的耦合势有限体积法研究建立一套各向异性地层中海洋可控源电磁法的三维响应的高效数值模拟技术.首先引入电场的矢势和标势,将电场分解为无散场和无旋场之和,Maxwell方程转换为关于矢势与标势的混合Helmholtz方程,克服低感应数问题.在此基础上,借助Yee氏交错网格和有限体积法以及非均质单元中等效电导率公式,建立混合Helmholtz方程的离散方程.并采用直接法求解器PARDISO求解离散方程,有效保证在大的求解空间中仍然能够获得电磁场稳定可靠的数值解.此外,在数值模拟中利用差异场技术,克服源的奇异性问题,尽可能提高近场的计算精度.与解析解的对比证明了该算法的有效性.数值模拟结果表明,海洋可控源电磁法沿测线方向的电场,对油气藏的纵向电阻率敏感,对横向电阻率不敏感;对油气藏上方的覆盖层的纵向电阻率和横向电阻率都敏感.

Efficient simulation of three-dimensional marine controlled-source electromagnetic response in anisotropic formation by means of coupled potential finite volume method

A coupled potential finite volume method for simulation of three-dimensional marine controlled-source electromagnetic (CSEM) response in anisotropic formation is developed. To circumvent ill-conditioning and convergence problems, Maxwell's equations are reformulated into coupled scalar-vector potentials with Coulomb gauge and its complement by applying a Helmholtz decomposition to the electric field. Yee's staggered girds, finite volume averaging and interpolation techniques are used to make the Helmholtz equations discrete. The resulting sparse and complex linear system in large-scale models is solved by a direct solver PARDISO. In order to improve the accuracy of the near field results without significantly reducing the computational efficiency, a method using difference fields is proposed to reduce the source singularity effect of anisotropic formation. The anisotropic modeling examples show that marine CSEM response is predominantly sensitive to reservoir vertical resistivity, not to reservoir horizontal resistivity, provided that the reservoir are thin and high-resistive; but the marine CSEM response is sensitive to both horizontal and vertical resistivity of the overburden on top of the reservoir.
Keywords： marine controlled-source electromagnetic method anisotropy finite volume method direct method