基于几何多重网格算法的海洋可控源电磁法三轴各向异性介质的三维正演研究

3D MCSEM modeling using GMG method in tri-axial anisotropy media

海洋可控源电磁法(MCSEM)三维正反演理论现如今已经成为地球物理学研究的热点和难点之一,准确、高效、稳定的正演计算是实现快速反演计算的基础.三维正演数值模拟技术的发展已相对成熟,一些学者已将研究如何提高正演计算效率的目光转移到研究如何提高线性方场组的计算速度.为了提高MCSEM的三维正演问题的计算效率,本文首先从频域三维海洋电磁控制方程出发,然后利用Yee氏交错网格有限体积法在三维空间离散方程组,并施以第一类Dirichlet边界条件获得大型稀疏复系数线性方程组,最后引入3种不同几何多重网格迭代算法求解该线性方程组.为了检验GMG算法的正确性,通过建立一维层状油气模型,将3种GMG算法计算结果与Kerry Key等开发的二维开源程序MARE2DEM计算结果进行对比,两种程序求解电场分布的曲线能够很好的吻合,表明GMG算法能正确求解海洋电磁正演问题,且两种程序求解的相对误差数量级在1以下,表明GMG算法具有较高的求解精度.为分析GMG算法的计算效率,我们首先想要模拟出一个更加真实的海洋地下环境,将沉积(背景)层电阻率设计为三轴各向异性,然后在此环境中建立三维海洋油气油气模型,实现MCSEM三维正演计算.通过改变网格数,实施3种GMG迭代算法与GCROT迭代算法求解,结果表明:GMG算法求解三维海洋可控源电磁正演问题算法稳定,计算效率高.GMG算法作为Krylov子空间迭代算法的预条件器求解三维海洋可控源电磁正演问题,不仅能加快求解速度,而且能提高算法的稳定性.

The 3 D forward and inverse theory of Marine Controlled Source Electromagnetic method(MCSEM) has now become one of the hotspots and difficulties in geophysical research. Accurate, efficient and stable forward calculation is the basis for fast inversion calculation. The development of 3 D forward numerical simulation technology has been relatively mature, and some scholars have turned their attention to how to improve the calculation efficiency of forward modeling to how to improve the calculation speed of linear square field groups. In order to improve the calculation efficiency of MCSEM’s 3 D forward modeling problem, this paper first starts from the frequency domain 3 D marine electromagnetic control equation, and then uses the Yee staggered grid finite volume method to discretize the equations in 3 D space, and impose the first type of the Dirichlet boundary condition to obtain a large-scale sparse complex coefficient linear equation system, and finally three kinds of different geometric multi-grid iterative algorithms are introduced to solve the linear equation system. In order to test the correctness of the GMG algorithm, by establishing a 1 D layered oil and gas model, the calculation results of the three kinds of GMG algorithms are compared with the calculation results of the 2 D open source program MARE2 DEM developed by Kerry Key and others. The two programs can solve the electric field distribution curve very well. A good agreement indicates that the GMG algorithm can correctly solve the marine electromagnetic forward problem, and the relative error of the two programs is less than 1, which indicates that the GMG algorithm has a higher solution accuracy. In order to analyze the computational efficiency of the GMG algorithm, we first want to simulate a more realistic marine underground environment, design the sedimentary(background) layer resistivity to be triaxial anisotropy, and then establish a 3 D marine oil and gas model in this environment, realize the MCSEM 3 D forward calculation. By changing the number of grids, three kinds of GMG iterative algorithms and GCROT iterative algorithms are implemented. The results show that the GMG algorithm for solving the 3 D marine controlled source electromagnetic forward problem has a stable algorithm and high computational efficiency. As the preconditioner of the Krylov subspace iterative algorithm, the GMG algorithm solves the 3 D marine controlled source electromagnetic forward problem. It not only speeds up the solution,but also improves the stability of the algorithm.