全空间瞬变电磁全区视电阻率优化二分搜索算法  

Optimized binary search algorithm of full space transient electromagnetic method all-time apparent resistivity

作　　者：姜国庆[1,2] 程久龙[2] 孙晓云[2] 陈丁[2] 王海彦[2] 

机构地区：[1]江苏省地质调查研究院基础地质研究所,江苏南京210018 [2]中国矿业大学(北京)煤炭资源与安全开采国家重点实验室,北京100083

出　　处：《煤炭学报》2014年第12期2482-2488,共7页Journal of China Coal Society

基　　金：国家自然科学基金资助项目(51034003;51174210);高等学校博士学科点专项科研基金资助项目(20120023110014)

摘　　要：将优化二分搜索算法应用于全区视电阻率计算,以期提高计算精度和运算效率。以均匀全空间回线源中心的瞬变响应为基础,探讨全空间磁感应强度垂向分量Bz及其时间变化率Bz/T核函数曲线特征,推导晚期视电阻率表达式。给出全空间条件下由Bz/T数值积分计算Bz的方法,并通过模拟计算对转换精度进行分析。对瞬变延时T一定时Bz和Bz/T相对于电阻率ρ的单调性进行研究,结果表明Bz为ρ的单值函数,满足对ρ二分搜索的条件,而Bz/T为ρ的双值函数,其二分搜索的前提是辅助参数Z在变量ρ的取值区间内恒满足Z≤1.225,并在此基础上对二分搜索的初始区间和具体流程进行了优化。模型算例和应用实例表明,该优化算法计算速度快、精度高,并可同时获得由Bz和Bz/T定义的全区视电阻率ρall和ρ'all。For the purpose of higher precision and efficiency,the optimized binary search algorithm was used for the calculation of all-time apparent resistivity. Based on the transient response of loop center in homogeneous full space,the kernel function curve feature of full space was discussed and the expression of late period apparent resistivity was derived. Method for calculating Bzfrom Bz/ T by numerical integration in full space was given,and the transition precision was analyzed through simulation. The function monotonicity of Bzand Bz/ T according to resistivity ρ at certain transient delay T was studied,and the results indicate that Bzis a single value function of ρ and it constantly satisfies the condition of binary search for ρ,but Bz/ T is a double value function of ρ and the precondition for binary search is instrumental variable Z constantly meeting the formula Z≤1. 225 during the value interval of variable ρ,on the basis of systematic study both the initial value interval and detailed flow chart of binary search algorithm were optimized.Model calculation and applied case indicate that the optimized binary search algorithm proposed in this paper has the characteristics of fast calculation speed,high calculation precision and can obtain all-time apparent resistivity ρallandρ＇allat the same time respectively from Bzand Bz/ T,it has a better practicability and better detection effect in fullspace transient electromagnetic method.

关 键 词：全空间瞬变电磁法 中心回线装置 全区视电阻率 二分搜索算法 优化 

分 类 号：P631.3[天文地球—地质矿产勘探]