电测深法视电阻率对介质电阻率偏导数的计算

A calculation method of the partial derivatives of the apparent resistivity with respect to the various media resistivity parameter in resistivity sounding

在前人工作基础上,对电测深法一维正演解析解递推电阻率转换函数求偏导,给出了电测深法视电阻率对介质电阻率偏导数的解析计算方法;根据Seigel体激发极化理论,采用视电阻率对介质电阻率偏导数矩阵的线性组合,计算出了电测深法的视极化率,其结果与“等效电阻率法”计算视极化率最大相对误差小于1.1%。在一次正演计算过程中就可以同时得到视电阻率、视极化率以及视电阻率对介质电阻率的偏导数矩阵,提高了计算效率,也为后续的多层地电模型电测深法数据优化反演计算提供了关键性技术。

Based on the work of Ruan Baiyao and Steven C.Constable,in this paper we present an analytical method for calculating the partial derivative of the apparent resistivity with respect to the media resistivity parameter by using one-dimensional forward analytical solution of recursive resistivity transform function in the resistivity sounding method.According to the theory of Seigel's the volume induced polarization,the linear combination of the partial derivatives matrix of the apparent resistivity with respect to various media resistivity parameter,and calculating the apparent polarizability.The maximum relative error between the apparent polarizability of resistivity sounding method and that of'the equivalent resistivity method'is less than 1.1%.In a forward calculation process,the apparent resistivity,the apparent polarizability and the partial derivatives matrix of the apparent resistivity with respect to various media resistivity parameter can be obtained at the same time.This improves the calculation efficiency and provides the key technology for the follow-up resistivity sounding datum of multi-layer ground model optimal inversion calculation as well.