The boundary element method for 3-D dc resistivity modeling in layered earth

The integral equation for dc resistivity modeling of 3-D inhomogeneous bodies buried in a layered earth is derived by using Green's theorem. The main features of this method are (1) the layers above and below the 3-D object can be included, (2) multiple subsurface inhomogeneous bodies can be embedded in the different layers, and (3) the boundary element method (BEM) is used to solve the integral equation using triangular surface elements. Linear variation of the electrical properties is assumed within each element. The potential on the ground surface is obtained by solving the linear equation system with Gaussian elimination. Model calculations demonstrate that the results obtained by this method compare well with the analytical solution of a sphere in a uniform half-space and the asymptotic behavior for the solution of a buried body beneath a surficial layer as the layer resistivity approaches that of the half-space. A comparison of responses over elongate 3-D bodies with responses over 2-D bodies of identical cross-section also shows satisfactory agreement.