Fast 3D inversion of transient electromagnetic data based on the backward-Euler direct-splitting finite-difference time-domain method

ABSTRACT The correct interpretation of time-domain electromagnetic (TEM) data acquired in complex geologic 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 in applying the 3D inversion technique to practical problems. The most time-consuming parts of 3D inversion are 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, whether by direct or iterative methods. We develop an algorithm framework designed to accelerate 3D TEM inversion. To solve the forward problem quickly, we use our previously proposed backward-Euler direct-splitting finite-difference time-domain algorithm, which can downgrade and reconstruct the large sparse matrices into a series of low-order tridiagonal matrices. 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 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; instead, low-order matrices are used, which saves computation time. To further accelerate the 3D inversion, the forward and adjoint equations are solved on graphics processing units in parallel. This inversion algorithm is first tested on two synthetic models. The experiment results demonstrate the effectiveness of the inversion algorithm, 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.