Adaptive finite element modelling of two-dimensional magnetotelluric fields in general anisotropic media

Abstract

An adaptive unstructured mesh finite element (FE) procedure is presented for improving the quality of numerical solutions to the magnetotelluric forward problem in a general 2-D anisotropic conductivity structure. We implement a self-adaptive, goal-oriented grid refinement algorithm in which a finite element analysis is performed on a sequence of refined meshes. The mesh refinement process is guided by a dual error estimate weighting to bias refinement towards elements that affect the solution at the EM receiver locations. We validate the finite element code against a layered 1-D model with a sea water layer. Further, we compare the FE results with those obtained by a finite-difference (FD) scheme for both a block seamountain and a sea bottom hill model. Both FE and FD schemes show very good agreement for the block seamountain model. For the sea bottom hill model, however, only on the flat seafloor segments both the FE and FD solutions fit very well, but on the seafloor slope, FD results are oscillating due to a simplistic staircase approximation of the bathymetric undulations. The FD scheme for 2-D anisotropic conductors, developed primarily for the modelling of magnetotelluric data on a flat Earth surface, is thus not an adequate tool for dealing with structures with sloping bathymetry and topography, whereas the FE method with adapting mesh can easily handle such structures at almost any level of complexity.