Parallelized 3-D Inversion of Controlled-Source Electromagnetic Data Based on Spectral Element Method With Infinite Element Boundary

This study developed an efficient 3-D inversion algorithm for the controlled-source electromagnetic method (CSEM). The spectral element method based on high-order Gauss-Lobatto-Legendre (GLL) basis functions with infinite element boundary conditions is used to quickly solve forward problems and adjoint forward problems for inversion, which can significantly reduce the computational cost while guarantee the accuracy. Due to the use of forward modeling with the high-order basis functions, we can give priority to the demand of inversion when designing the grid, and then choose the appropriate order for forward modeling based on the size of the grid, which can make the grid more scientific both for forward and inversion. The limited-memory BFGS (L-BFGS) optimization algorithm without explicit computation and storage of the Hessen matrix is used to solve the objective function minimization problem. Furthermore, a new preconditioner is introduced to update the initial approximate Hessian matrix in L-BFGS, which improves the convergence of the algorithm. To further improve the efficiency of the algorithm, we implemented parallelization based on message passing interface (MPI). The synthetic examples show the efficiency of our algorithm compared with the conventional inversion method, and the field example demonstrated the adaptability and utility of the algorithm.