Research on numerical simulation method for 3D marine direct current resistivity

Abstract

As one of the most important methods in marine electromagnetic exploration, the marine direct current (DC) resistivity method has been widely used in the exploration of marine minerals, oil and gas, as well as in large-scale engineered geological exploration and other fields. Efficient and high-precision forward algorithms are the foundation for an accurate quantitative interpretation of the marine DC resistivity method. We have implemented an efficient and high-precision forward modeling approach for 3D marine DC resistivity. First, the wave number domain anomalous potential control equations are obtained by performing a 2D Fourier transform along the horizontal direction based on the differential control equations satisfied by the marine DC anomalous potential. Instead of directly solving the 3D numerical simulation problem, we transform the 3D numerical simulation problem into multiple 1D numerical simulation problems in the wavenumber domain by dimensionality reduction for computational efficiency. Second, the boundary conditions of the governing equations are given to obtain the corresponding boundary value problems, and the anomalous potential is solved using the 1D finite element method in the wavenumber domain. Next, we perform a 2D inverse Fourier transform on the wave-number domain anomalous potential to obtain the spatial domain anomalous potential. Furthermore, compact operators are used to iteratively modify the potential and obtain high-precision numerical solutions. Finally, we demonstrate the correctness of the proposed algorithm’s solution strategy by using a hierarchical ocean model, and the efficiency of the proposed algorithm by using a spherical model.