Finite-Element Scheme With Total-Field for 3-D Marine Controlled-Source Electromagnetic Modeling With Bathymetry and Multisources

Herein, a finite element scheme with total-field formulation for 3-D frequency-domain marine controlled-source electromagnetic (CSEM) modeling with bathymetry is presented. We employ a finite-element method based on an unstructured tetrahedral mesh to directly solve the total electromagnetic field equation in terms of vector-scalar potentials. In addition, an mesh refinement approach is proposed to accurately simulate marine CSEM responses in cases involving different frequencies, transmitters, and receivers. First, the mesh is locally refined according to the volume constraints as well as the transmitter and receiver positions. Next, the mesh is adaptively refined according to a posteriori error estimation of the finite-element solution. The a posteriori error is calculated based on the gradient recovery technology and weighted using the dual-error weighting (DEW) approach. The scheme is parallelized to improve its computational efficiency for accommodating multiple field sources, receivers, and frequencies. Various numerical experiments demonstrate that the proposed scheme can effectively provide highly accurate solutions for marine CSEM responses, and the scheme is applied to the modeling of hydrocarbon reservoirs with bathymetry and multisources. The effects of bathymetry on marine CSEM responses for both inline and broadside geometries are discussed lastly.