基于电导率各向异性的海洋可控源电磁法三维正反演研究

The formation anisotropy has a significant impact on the interpretation of EM data. It is now well recognized that sedimentary formations in the marine environment are usually characterized by strong electrical anisotropy due to sedimentation. Therefore, the interpretation of MCSEM data based on the assumption of isotropic media may produce misleading geological interpretation, which will undermine the power of MCSEM technique. In this proposal, we are aiming to develop efficient and robust 3D forward modeling and inversion algorithms for MCSEM data in the presence of electrical anisotropy. The forward modeling scheme will utilize a staggered-grid finite volume method to numerically solve the Helmholtz equation for the secondary electric field. In order to account for arbitrarily electrical anisotropy, a node-based averaging approach will be used to collocate different components of the electric field. The resulting linear equation system arising from discretization will be solved by a direct-matrix solver, which can not only provide accurate and reliable solutions, but also is very suitable for multi-source MCSEM problems by separating the solving process into a single expensive matrix factorization and relatively inexpensive substitution steps for many right-hand sides. As for the inverse problem, the Gauss-Newton (GN) algorithm will be applied considering its quasi-quadratic convergence rate to limit the number of expensive matrix factorization. In addition, a multi-level parallelization will be considered to speed up the computation by efficiently exploring the computational resources with multiple cores. In summary, the goal of this project is to implement a robust MCSEM 3D modelling algorithm in arbitrarily anisotropic media and an efficient 3D anisotropic inversion code for MCSEM data assuming vertical transverse isotropy, thus improving the interpretation capacity of MCSEM data for complex geological structures in the marine environment and making MCSEM more reliable and powerful for offshore hydrocarbon exploration and geological investigations.

地层宏观电各向异性会对电磁资料的解释产生重要影响。由于海底电性结构常表现为电导率各向异性，若仅对海洋可控源电磁（MCSEM）资料进行各向同性反演，有可能无法获得准确的反演解释结果，从而削弱MCSEM技术的可靠性。本课题拟研究电导率各向异性介质中MCSEM三维正演与反演方法。正演基于二次场控制方程，使用交错网格有限体积法，通过基于网格节点的电场平均方式来满足任意各向异性模拟中电场不同分量需在同一点定义的要求；采用直接矩阵分解技术来求解离散所得的大型线性方程组，不仅准确、稳定，而且特别有利于快速计算多场源的响应。反演中对目标函数的最优化采用高斯牛顿法，具有近似二次的收敛性；使用多层次并行策略来提高并行效率，缩短反演计算时间。最终实现实用化的MCSEM任意各向异性三维正演和垂直各向异性三维反演算法，提高对海底复杂电性结构的反演解释能力，促进MCSEM在海洋油气勘探和地质调查中发挥更重要作用。

地层宏观电各向异性会对可控源电磁数据的处理与解释产生重要影响。忽略电各向异性特征可能会导致数据反演出现偏差，难以获得准确的解释结果。本项目采用多种数值方法对电各向异性介质中的频率域可控源三维正演与反演算法进行了研究。在本项目的支持下，完成了多项研究工作，具体包括：（1）实现了基于有限体积法的频率域CSEM三维任意各向异性正演算法。该算法采用散射场方法及利用直接矩阵分解技术来求解大型线性方程组，获得了任意电各向异性介质中高精度的CSEM三维正演响应；（2）实现了基于磁矢势和电标势的频率域CSEM三维任意各向异性正演算法。通过将麦克斯韦方程组转化为库伦规范下的磁矢势和电标势耦合方程，有效改善了离散所得的大型线性方程组的性质，实现了快速求解大规模CSEM三维正演问题；（3）实现了任意各向异性介质中多频率CSEM三维正演混合求解算法。该求解算法结合了迭代解法和直接解法的各自优点，有效提高了多频率CSEM三维正演的计算效率；（4）实现了基于矢量有限元的频率域CSEM三维任意各向异性正演算法。采用非结构四面体网格，实现了对复杂几何结构和起伏地形条件下的CSEM响应的高精度模拟；（5）实现了电导率垂直各向异性条件下的频率域CSEM三维反演算法，有效提高了大规模CSEM数据反演解释能力。这些工作有效提高了复杂环境下大规模海洋及陆地频率域CSEM数据反演解释能力，为高精度可控源电磁勘探奠定了基础。