Solution of potential distributions excited by multi-double layers in 2-D vertically-stratified inhomogeneous media

The research background of the work is concerned with the spontaneous potential (SP) log, which has endured as an important downhole logging measurement. The fundamental problem for an SP log is about to find the potential distributions excited by multi-double layers at the interfaces in 2-D inhomogeneous media, which simulate a stack of beds penetrated by a borehole and both vertical and radial conductivity variations. For such a model, the typical means to solve the problem was usually with 2-D FD and integral equation methods, which were time consuming and always accompanied by simplification of the models. In this paper we expand the use of the NMM method in double-layer excitation situations to give a highly efficient way to solve the complex boundary-value problem with more general models by strictly matching the horizontal boundaries and exciting conditions.