基于区域分解法的海洋可控源电磁三维正演模拟研究

Three-dimensional MCSEM forward modeling based on domain decomposition

为准确刻画复杂海底地质结构中电磁场变化特征,有效处理大规模海洋可控源电磁三维正演模拟问题,本文将基于矢量有限元的FETI-DP(Dual-Primal Finite-Element Tearing and Interconnecting)区域分解法引入到海洋电磁三维正演模拟中.该方法首先利用非结构四面体网格对海洋地电模型进行离散,而后使用METIS剖分软件将网格分区得到一定数量的子区域并建立相应的边界条件,然后基于矢量有限元法建立各子区域的正演问题,进而将各子区域耦合得到降阶的子系统,求解该子系统后即可求得任意子区域内的电磁响应.我们利用海底均匀半空间模型验证算法的精度和有效性,并在此基础上对典型的复杂海底介质模型的电磁响应进行正演模拟.数值结果表明,本文算法是进行海洋可控源电磁正演模拟研究的有效方法,可以解决大规模海洋电磁正演问题.

In order to accurately characterize the Electromagnetic(EM) field under the complex topographic ocean and to effectively handle the forward modeling of large-scale Marine Controlled-Source Electromagnetic(MCSEM) problems, we introduce in this paper the Dual-Primal Finite-Element Tearing and Interconnecting(FETI-DP) domain decomposition method based on vector Finite Element(FE) into the forward modeling of MCSEM method. We use the unstructured tetrahedral grids to discretize the model and partition the mesh by METIS to obtain a certain number of subdomains and establish the corresponding boundary conditions, then we discretize the governing equation for each subdomain using the FE method and couple the subdomains for a subsystem with reduced order. After solving the subsystem, we get the EM responses in all subdomains. We validate the accuracy of our modeling algorithm by checking against the semi-analytical solution for a homogeneous half-space under the ocean. Based on this, we simulate MCSEM responses for typical complex seabed models. The numerical experiments show that our algorithm is very effective for MCSEM forward modeling for large-scale problems.