3D marine controlled-source electromagnetic modeling using an edge-based finite element method with a block Krylov iterative solver

Abstract

Abstract An edge-based finite element method for the numerical modeling of electromagnetic fields in complex media is presented. We used the analytical solution on an electric field in a homogeneous half space to develop a source correct factor to reduce the influence of source singularity and boundary conditions on the numerical accuracy, so that we can minimize the time required to construct the field source term in the scattered field formula. The modeling domain was discretized using an unstructured tetrahedral mesh. We transformed the complex equations of the electrical field into two real-valued equations by decomposing the field into real and imaginary components. Thereafter, we adopted a block conjugate orthogonal conjugate gradient (BL_COCR) iterative solver with an incomplete LU decomposition preconditioner, which was robust for ill-conditioned systems and efficient for multiple source electromagnetic modeling to solve the real-valued equation systems. Using the analytical solution on an electric field in a homogeneous layer model, we evaluated the accuracy of our numerical forward solution and the results showed that the source correct factor can reduce forward modeling errors associated with boundary effects and source singularities. We also applied the developed algorithm to compute the CSEM responses for typical 3D marine geo-electric models with different number of sources and compared with different iterative solvers, and the results showed that the BL_COCR solver has high computational efficiency when solving multiple right-hand term problems.