A rapid and accurate algorithm for numerical simulation of direct current fields with arbitrary conductivity distribution

Three-dimensional (3D) numerical simulation of direct current (DC) fields is a key task in DC resistivity method, and it is usually time-consuming and memory-consuming using traditional numerical methods, such as finite element method and finite difference method. In this work, we develop a rapid and accurate algorithm to calculate the DC fields and the potential based on integral equation method. The main contribution of this work is that we propose a novel spatial domain algorithm for computation of 3D discrete convolution, and we call it BCE3D. BCE3D contributes most for the efficiency and accuracy of numerical simulation of DC resistivity. With BCE3D, DC field integral equation is solved iteratively. During implementation of our method, the subsurface is divided into many regular prisms. Each prism has constant conductivity and different prisms may have different conductivities. In this way we can simulate the fields and potential for complex 3D geological structure and arbitrary conductivity distribution. Model test shows that the new algorithm for DC resistivity method is high efficient, and it has no source effect and cut-off boundary effect appearing in finite element simulation.