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

作　　者：彭仲秋 刘云[2] 段新力[1] 宋滔 PENG Zhongqiu;LIU Yun;DUAN Xinli;SONG Tao(Geophysical and geochemical exploration group of the Geology and Mineral Development Bureau of Xinjiang Uygur Autonomous Region, Urumqi 830091, China;State Key Laboratory of Ore Deposit Geochemistry,Institute of Geochemistry Chinese Academy of Sciences,Guiyang 550081,China;College of Mathematics and Information Science, Guiyang University, Guiyang 550005, China)

机构地区：[1]新疆维吾尔自治区地质矿产勘查开发局,地球物理化学探矿大队,乌鲁木齐830091 [2]中国科学院地球化学研究所,矿床地球化学国家重点实验室,贵阳550081 [3]贵阳学院数学与信息科学学院,贵阳550005

出　　处：《物探化探计算技术》2020年第4期503-509,共7页Computing Techniques For Geophysical and Geochemical Exploration

基　　金：国家重点研发计划(2016YFC0600505);贵阳学院科研启动金(2019)。

摘　　要：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.

关 键 词：电测深法 视电阻率 视极化率 电阻率转换函数 偏导数 

分 类 号：P631.4[天文地球—地质矿产勘探]