中心回线瞬变电磁法全期视电阻率的二分法求解  

Bisection Algorithm of Central Loop Time Domain Transient Electromagnetism All Time Apparent Resistivity

作　　者：李文尧[1] 晏冲为[1] 

机构地区：[1]昆明理工大学国土资源与工程学院,云南昆明650093

出　　处：《昆明理工大学学报（自然科学版）》2013年第2期26-33,共8页Journal of Kunming University of Science and Technology(Natural Science)

基　　金：中国地质调查项目(1212011121273)

摘　　要：通过对均匀半空间中归一化感应电动势核函数的研究,发现在(0,+∞)存在一个最大值点max,其横坐标为1.613 63,且在(0,1.613 63)为单调递增,在(1.613 63,+∞)为单调递减,本文基于归一化感应电动势核函数在(0,+∞)上分段单调的特性,提出计算全期视电阻率的二分算法,计算速度快,计算一个测道的z值最多只需55次计算,二分法的精确度可人为设定,全期视电阻率的计算精度高,可进行精度评价,算法稳定,在无解时通过结合有解的数值进行三次厄米特(Hermite)多项式插值,可得到一条平滑的视电阻率曲线.Through the research on the transient electromagnetic field analytic expression in homogeneous half space, it is discovered that the kernel function has a maximum value at z = 1. 613 63, and is monotonously increas- ing in （0, 1. 613 63） interval and monotonously decreasing in （ 1. 613 63, ＋ w ） interval. According to the monot- onous features in （0, 1. 613 63） and （1. 613 63, ＋ ~ ） interval, a bisection method is proposed to calculate full time domain apparent resistivity. The calculating speed of this method is quick as the solution of z is got by no more than 55 times calculations in every channel. The precision of this bisection method can be set manually. It is proven that the precision of apparent resistivity is high and evaluable and that the algorithm is stable. A smooth curve of apparent resistivity can be acquired by piecewise cubic Hermite interpolation when there is no solution.

关 键 词：中心回线瞬变电磁法 全期视电阻率 二分法 HERMITE插值 

分 类 号：P631.34[天文地球—地质矿产勘探]