3-D inversion of transient EM data with topography using unstructured tetrahedral grids

Abstract

The transient electromagnetic (TEM) data acquired in mountainous area are seriously affected by topography, implying that consideration of topographic effect in the interpretation is in urgent need. To deal with this problem, we propose a new method to invert TEM data by simulating the topography. The unstructured tetrahedral grid with flexibility to delineate the rugged topography is adopted to discretize the inverse model. The transmitting source, including magnetic-loop and finite-length electric dipole source, is divided into short electric dipoles to simulate its practical shape, size and attitude. In the numerical simulation, we adopt the edge-based finite-element method (FEM) to discretize the governing equation in space, and the unconditional stable second-order of backward Euler (BE) scheme to discretize in time. The final forward modelling equation is solved iteratively from an initial field for all time channels. The direct solver MUMPS is used to solve the forward problem for efficiency. The calculation of Jacobian matrix of sensitivities is well addressed, especially for the electric source whose initial electric field for a step-off wave is related to the model parameters. Since the full-channel forward modelling matrix is asymmetric, we use a backward recursive method to solve the adjoint forward problem. Considering the limited power of our computational devices, we apply the limited-memory BFGS optimization method to accomplish our 3-D inversion. The inversion algorithm is firstly tested on two synthetic examples, one with a large fixed-loop transmitting source and the other with a long grounded line source as in semi-airborne TEM survey. The inversion results show that the proposed inversion scheme can invert TEM data with sharp topography. The inversion code is further tested on a ground TEM survey data acquired in Shanxi province, China and the results agree well with the geology and other geophysical information.