2D marine controlled-source electromagnetic modeling: Part 1 — An adaptive finite-element algorithm

Abstract

In Part 1 of this work, we develop an adaptive finite-element algorithm for forward modeling of the frequency-domain, marine controlled-source electromagnetic (CSEM) response of a 2D conductivity structure that is excited by a horizontal electric dipole source. After transforming the governing equations for the secondary electromagnetic fields into the wavenumber domain, the coupled system of two partial differential equations for the strike-parallel electric and magnetic fields is approximated using the finite-element method. The model domain is discretized using an unstructured triangular element grid that readily accommodates arbitrarily complex structures. A numerical solution of the system of linear equations is obtained using the quasi-minimal residual (QMR) method, which requiresmuch less storagethan full matrix inversion methods. We implement an automatedadaptive grid refinement algorithm in which the finite-element solution is computed iteratively on successively refined grids. Grid refinement is guided by an a posteriori error estimator based on a recently developed gradient recovery operator. The error estimator uses the solution to a dual problem in order to bias refinement toward elements that affect the solution at the electromagnetic (EM) receiver locations and enables the computation of asymptotically exact solutions to the 2.5D partial differential equations. We validate the finite element formulation against the canonical 1D reservoir model and study the performance of the adaptive refinement algorithm. An example model study of a complex offshore structure of interest for petroleum exploration illustrates the utility of the adaptive finite-element method for CSEM modeling.