Title :
3-D numerical mode-matching (NMM) method for resistivity well-logging tools
Author :
Fan, Guo-Xin ; Liu, Qing Huo ; Blanchard, Sean P.
Author_Institution :
New Mexico State Univ., Las Cruces, NM, USA
fDate :
10/1/2000 12:00:00 AM
Abstract :
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
Keywords :
Poisson equation; eigenvalues and eigenfunctions; electric potential; electrical resistivity; electromagnetic wave propagation; geophysical prospecting; inhomogeneous media; mode matching; 1D layered medium problem; 2D eigenvalue problems; 3D inhomogeneous media; 3D numerical mode-matching method; EM wave propagation; Poisson´s equation; electric potentials distribution; horizontal fractures; horizontal wells; inhomogeneous media; invasion zones; noncircular shape; recursion procedure; resistivity well logging; vertical fractures; Algorithm design and analysis; Conductivity; Eigenvalues and eigenfunctions; Electric potential; Frequency; Nonhomogeneous media; Poisson equations; Testing; Two dimensional displays; Well logging;
Journal_Title :
Antennas and Propagation, IEEE Transactions on
