Parallelized 3-D CSEM Inversion With Secondary Field Formulation and Hexahedral Mesh

Presently, the 3-D inversion technique has started playing a more important role in controlled-source electromagnetic (CSEM) data interpretation. With the development of hardware and computation algorithm, 3-D inversion technique has developed rapidly during the past decades. In this article, we present a newly developed 3-D parallelized inversion algorithm in the frequency domain with hexahedral discretization. Within the framework of this approach, we use the finite-element method (FEM) in the forward modeling and GaussNewton optimization technique in the inversion. We solve the forward modeling and adjoint problem efficiently with Math Kernel Library (MKL) Pardiso parallel direct solver. Considering the fact that the forward modeling and sensitivity calculation are frequency independent, we further parallelize the algorithm over frequency using Message Passing Interface (MPI) to speed up the modeling and inversion process. The sensitivity matrix is calculated explicitly, which enables us to estimate the optimized regularization parameter easily based on the spectral radius estimation. We proposed a new roughness operator for hexhedral discretization which works well for CSEM inversion problems. We applied the developed algorithm to several realistic CSEM models. The inversion results demonstrate the effectiveness and stability of our inversion scheme.