瞬变电磁波场转换算法的改进  

An improvement to the transformation algorithm for the transient electromagnetic field

作　　者：薛俊杰[1] 钟华森 李海[2,3,4] 李貅 底青云[3,4] 王贺元[6] 佟昭成 XUE JunJie;ZHONG HuaSen;LI Hai;LI Xiu;DI QingYun;WANG HeYuan;TONG ZhaoCheng(College of Sciences,Liaoning University of Technology,Jinzhou 121001,China;The Key Laboratory of Mineral Resources,Institute of Geology and Geophysics.Chinese Academy of Sciences, Beijing 100029,China;Chinese Academy of Sciences University,Beijing 100049,China;Chinese Academy of Sciences University,Beijing 100049,China;School of Geology Engineering and Geomatics,Chang′an University,Xi′an 710054,China;Shenyang Normal University,Shenyang 110034,China)

机构地区：[1]辽宁工业大学理学院,锦州121001 [2]中国科学院矿产资源研究院重点实验室,中国科学院地质与地球物理研究所,北京100029 [3]中国科学院地球科学研究院,北京100049 [4]中国科学院大学,北京100049 [5]长安大学地测学院,西安710054 [6]沈阳师范大学数学与系统科学学院,沈阳110034

出　　处：《地球物理学报》2018年第12期5077-5083,共7页Chinese Journal of Geophysics

基　　金：国家自然科学基金(11572146,41474095);北京市自然科学基金青年项目(8184089);中国博士后基金面上项目(2017M610981)联合资助

摘　　要：地球物理电磁场数据与虚拟地震波场数据之间存在数学上的等效转换关系,通过这种等效转换,可有效提高地球物理电磁法对地下目标体分界面的辨识度.但是这种转换在数学上属于不适定问题,可采用奇异值分解法处理.由于大奇异值控制计算矩阵的主要信息,小的奇异值控制计算矩阵的次要信息,传统的截断奇异值分解法只保留大奇异值,而忽略小的奇异值,导致数值解不够精确.本文提出一种新的修正方案——改进截断奇异值法,采用岭估计方法计算由小的奇异值引起的虚拟波场.模型计算结果表明:改进截断奇异值法比传统的奇异值分解法得到的波场转换结果更好,对某煤矿采空区探测数据进行了处理,成功分辨出采空区分界面.Mathematically,there exist an effective transformation relationship between the electromagnetic(EM)and virtual seismic data fields,by which one can effectively to identify the underground target′s interfaces using the EM method.Such transformation is a uncertain problem,which can be treated by the singular value decomposition(SVD)method.Because large singular values control main information of inversion matrix,small singular values are usually less important.So one usually ignores small singular values during singular value decomposition caluculation,leading to low precision results.To solve this problem,a new algorithm named the modified truncated singular value decomposition method was proposed,in which the ridge estimation method is used to calculate the virtual wave field caused by small singular values.The results of model calculation show that the improved truncated singular value method is better than the traditional singular value decomposition method.Using this new method,the survey data from a gob area of a coal mine was processed,and the interface of this area was successfully identified.

关 键 词：波场变换 奇异值分解法 截断奇异值分解法 改进截断奇异值法 数值计算 

分 类 号：P631[天文地球—地质矿产勘探]