Eigen-value analysis of numerical mode-matching method in resistivity logging

Numerical mode-matching method is a fast numerical and analytical method for inhomogeneous medium model with any number of horizontal layer and vertical layered. In each horizontal layer, the eigen-equation can be formed and solved by finite element method. Based on the formation process of eigen-equation, the affecting factors of eigen-value has been discussed from three aspects, that is, different resistivity, different invasion radius, and different number of radial grids. The calculation results indicate that the fluctuations of eigen-value respectively concentrate nearby small, medium and big eigen-value under the three different conditions, which has a certain guiding role to better solve the eigen-equation.