Abstract
The finite difference forward modeling solves the point source arbitrary 2D geoelectrical section resistivity model herein. A system of linear equations is finally formed. Two reconstruction algorithms, i.e. conjugate gradient method and Cholesky algorithm, are introduced into the numerical analysis to derive the theoretical formula. With uniform media and layered media chosen as the physical model for forward modeling, the numerical simulation results that low and high resistance objects correspond to different reconstruction algorithms in two media models are analyzed. The findings show that the Cholesky reconstruction algorithm works well in the numerical simulation of sounding low resistance object, while there is a little difference between the two reconstruction algorithms for high resistance object. But also, in the even semi-infinite medium, when the point source lies at the center of the surface mesh, the relative error Rms to the potential value and the theoretical value of the unit point source geoelectric field is obtained by the Cholesky algorithm, and the maximum error occurred when it converges for 33 iterations is more than 3.0%. As polar distance increases, relative error also has no tendency to amplify. Compared to the conjugate gradient method, the Cholesky algorithm not only greatly requires less in memory but also greatly increases the computing speed. The study provides the clues to future finite difference numerical simulation and interpretation of resistivity tomography.
