Fast 3D inversion for transient electromagnetic data based on the BEDS-FDTD method

The correct interpretation of time-domain electromagnetic (TEM) data acquired in complex geological environments relies on 3D inversion. However, the complexity of the TEM problem makes 3D inversion extremely time-consuming. This is one of the main obstacles to the application of the 3D inversion technique to practical problems. The most time-consuming parts of the 3D inversion are the forward modeling and the calculation of the sensitivity matrix. This is because both operations require dealing with large sparse matrices, which is very time-consuming either by direct or iterative methods. In this paper, we present an algorithm framework designed to accelerate 3D TEM inversion. To solve the forward problem quickly, we use our previously proposed algorithm, BEDS-FDTD, which can downgrade and reconstruct the large sparse matrices into a series of low-order tridiagonal ones. The sensitivity matrix is implicitly computed by adjoint forward modeling to reduce memory requirements. Based on the characterizations of the forward equations and the inverse time series solving of the adjoint field, we derive the control equations for the adjoint forward modeling with low-order tridiagonal coefficient matrices. In the new inversion algorithm, there is no longer a need to solve large sparse matrices, but instead low-order ones, which saves computation time. To further accelerate the 3D inversion, the forward and adjoint equations are solved on graphics processing units (GPUs) in parallel. This inversion algorithm is first tested on two synthetic models. The experiment results demonstrate the effectiveness of the inversion algorithm proposed in this paper, and the time spent on 3D inversion is reduced significantly. Finally, we use this inversion algorithm for field data, and the inversion results agree well with the known information.