基于拟态有限体积法的频率域可控源三维正演计算

3D frequency-domain CSEM forward modeling based on the mimetic finite-volume method

大规模地球物理电磁数据的定量解释需要发展高效、稳定的三维正反演算法.本文通过求解离散化的三维电场矢量Helmholtz方程,实现了基于有限体积法的频率域可控源电磁(CSEM)三维正演算法.为模拟具有强电性差异的三维电性介质,该算法采用拟态有限体积法(MFV)对Maxwell方程组进行离散化;另外,为获得稳定、高精度的正演数值结果,采用直接矩阵分解技术来求解离散所得到的大型稀疏线性方程组.对于具有多个发射源的CSEM测量来说,一次矩阵分解结果能够用于同频率下所有场源的正演计算.为降低场源奇异性及边界条件对数值精度的影响,采用虚拟场源校正技术,避免了散射场公式中在构建场源项时所需的大量时间.对于具有多个频率的CSEM的模拟计算,采用分频并行策略来加快三维正演计算.最后,通过与一维层状模型及三维模型的数值结果的对比验证了本文所开发的正演算法对频率域CSEM模拟计算的准确性及有效性,表明该正演算法能够有效应用于三维介质的数值计算.另外,对于多频率CSEM的并行测试结果表明基于分频并行策略的并行计算能够显著地降低正演计算时间.

Quantitative interpretation of large-scale controlled-source electromagnetic（CSEM）data in the frequency domain requires efficient and stable three-dimensional（3D）forward modeling and inversion codes.In this paper,we present a 3Dforward modeling scheme for frequency-domain CSEM surveys based on the mimetic finite volume（MFV）method,which solves the Helmholtz equation for the total electric field.An important step in this 3D modeling scheme is to solve the large linear equation system resulting from MFV discretization.In order to obtain stable and accurate numerical solutions,thelinear equation system is solved by a direct-matrix solver,namely MUMPS,which is more robust than commonly used iterative solvers（e.g,Krylov subspace iterative techniques）for numerically difficult cases.The algorithm is very suitable for multi-source CSEM modeling by separating the solving process into a single expensive matrix factorization and relatively inexpensive forward backward substitutions for many right-hand sides.For total-field formulation,dense gridding in the vicinity of source points is usually required to mitigate source singularities,and extra padding cells at the boundaries are needed to meet boundary conditions.Both of them can quickly increase the size of the linear equation system to be solved,making it computationally expensive for direct solutions.To avoid substantial increase of the size of the discretized model,a source correction technique is applied to reduce source singularities and boundary effects.In addition,considering the independence of computation for different frequencies,a parallel forward modeling scheme based on frequency partition is implemented to speed up the simulation of multi-frequency CSEM problems.Numerical experiments have been carried out to evaluate the performance of our forward modeling algorithm.Numerical solutions using this algorithm show good agreement with quasianalytic solutions for 1Dlayered models,and numerical errors are significantly reduced with source correction in the vicinity of source points.In addition,comparison of simulated data generated by our algorithm to published 3D data for a typical marine 3D model validates our algorithm.Besides,statistical results demonstrate that parallel computing based on simple frequency partition approach can achieve nearly linear speedup due to the independence of computation between frequencies for multi-frequency CSEM simulation.