A goal-oriented adaptive finite-element approach for 3-D marine controlled-source electromagnetic problems with general electrical anisotropy

SUMMARY We present a goal-oriented adaptive finite-element algorithm for accurately modelling marine controlled-source electromagnetic responses in 3-D media with general electrical anisotropy. We formulate the primal boundary value problem in terms of the total electric field for general applications. Following the goal-oriented adaptivity concept, the dual problem is derived from a functional designed to measure the data errors of interest in light of the data quality. We approximate the solutions to the primal and dual formulations using the edge finite-element method on tetrahedral grids for a flexible treatment of complex geological settings and survey geometries. To control the mesh adaptation, we develop a reliable residual-type a posteriori error estimation that takes account of the volumetric residual and the numerical discontinuity of the normal component of the electrical current density and that of the tangential component of the magnetic field with respect to non-smooth and anisotropic coefficients. We demonstrate the proposed modelling solver on 1-D MCSEM scenarios with varying degrees of electrical anisotropy. The comparison with goal-oriented adaptivity results obtained from other three commonly used error indicators shows that our approach is robust in dealing with both moderate and strong electrical anisotropy. After that, we constructed a 3-D hydrocarbon-bearing reservoir model with slope seafloor topography and tilted transverse isotropy in the background to examine our algorithm for the case of multiple sources. Finally, we implement a sensitivity analysis procedure to evaluate the resolution of the electrical anisotropy. The quantitative results indicate limitations and preferences of conventional MCSEM data in resolving anisotropic models, providing fundamental insights for inversion based data interpretation.