Finite Element Based Anisotropic 3D Inversion of Marine CSEM Data

Abstract:

In order to interpret three-dimensional (3D) marine controlled-source electromagnetic (MCSEM) data, it is critical to accurately determine electrical anisotropy because ignoring anisotropy can produce misleading artifacts. In this study, we present an inversion method for 3D subsurface imaging in media with an inhomogeneous and anisotropic conductivity distribution. Direct solvers are incorporated both in the forward and inverse problems, For the forward problem, the vector Helmholtz equation for the secondary electric field is discretized on a hexahedral mesh using edge finite elements, then a direct sparse-matrix solver is chosen to effectively reuse its factorization both in the survey simulation and Jacobian computation. The inversion method is formulated as a functional optimization with an objective functional containing terms measuring data misfit and model structure by means of smoothness and anisotropy. These measures are efficiently incorporated through the use of an iteratively reweighted least-squares scheme. The objective functional is minimized by a Gauss-Newton approach using a direct dense-matrix solver. We demonstrate the accuracy and applicability of the algorithm by testing it on synthetic data sets.