An integral formulation for three‐dimensional terrain modeling for resistivity surveys

A new method is presented in this paper for modeling the 3-D terrain effect that, in turn, can be approximately removed by applying a terrain correction to resistivity surveys. First, the 3-D electrical boundary value problem is transformed into an integral equation problem by use of Green’s theorem. Then the boundary element method is used to solve the integral equation. The ground surface and the boundary of the anomalous body are divided into triangular elements. Linear variation of quantities is assumed within each element and a Gaussian quadrature formula is used to calculate the integral. In this way, the integral equation is converted into a set of linear equations. The potential field value on the ground surface is obtained by solving the linear equation system with Gaussian elimination. This method uses a special triangular element mesh for division of the ground surface which is moved simultaneously with the movement of the source. Therefore, the number of computational nodes is greatly reduced....