Multigrid IE method for large‐scale models with inhomogeneous background

Abstract

We present a multigrid integral equation (IE) method for three‐dimensional (3D) electromagnetic (EM) field computations in large‐scale models with inhomogeneous background conductivity (IBC). This method combines the advantages of the iterative IBC IE method and the multigrid quasi‐linear (MGQL) approximation. The new EM modeling method solves the corresponding systems of linear equations within the domains of anomalous conductivity, Da and inhomogeneous background conductivity, Db; separately on coarse grids. The observed EM fields in the receivers are computed using grids with fine discretization. The developed MGQL IBC IE method can be also applied iteratively by taking into account the return effect of the anomalous field inside the domain of the background inhomogeneity Db; and vice versa. The iterative process described above is continued until we reach the required accuracy of the EM field calculations in both domains, Da and Db. The method was tested for modeling the marine CSEM field for complex geoelectrical structures with hydrocarbon petroleum reservoirs and a rough sea bottom bathymetry.