3-D numerical mode-matching (NMM) method for resistivity well-logging tools

A three-dimensional (3-D) numerical mode-matching (NMM) method is presented for Poisson's equation in general inhomogeneons media. It reduces the original 3-D problem into a series of two-dimensional (2-D) eigenvalue problems plus a one-dimensional (1-D) layered medium problem, which can be modeled efficiently by a recursion procedure. The algorithm is tested for several 3-D inhomogeneous media and an excellent agreement between the NMM and analytical solutions is obtained for all test cases. We demonstrate some typical applications of the 3-D NMM algorithm in resistivity well logging, including invasion zones of noncircular shape, vertical and horizontal fractures, and horizontal wells. The solution procedure proposed is directly applicable to wave propagation in 3-D inhomogeneous media.