重力场欧拉反褶积最优化滑动窗口选择  

Optimal moving window for Euler deconvolution of gravity data

作　　者：杨博 曹书锦[1,2,3] 毛雅静 周勇 朱自强[3] 陈新跃[1,2] YANG Bo;CAO Shu-jin;MAO Ya-jing;ZHOU Yong;ZHU Zi-qiang;CHEN Xin-yue(Hunan Provincial Key Laboratory of Shale Gas Resource Utilization,Hunan University of Science and Technology,Xiangtan 411201,Hunan,China;School of Resource Environment and Safety Engineering,Hunan University of Science and Technology,Xiangtan 411201,Hunan,China;School of Geosciences and Info-physics,Central South University,Changsha 410083,China;School of Resource Environment and Tourism,Hunan University of Arts and Science,Changde 415000,Hunan,China)

机构地区：[1]湖南科技大学页岩气资源利用湖南重点实验室,湖南湘潭411201 [2]湖南科技大学资源环境与安全工程学院,湖南湘潭411201 [3]中南大学地球科学与信息物理学院,长沙410083 [4]湖南文理学院资源环境与旅游学院,湖南常德415000

出　　处：《世界地质》2021年第3期689-696,共8页World Geology

基　　金：国家自然科学基金项目(41704138,41974148);湖南省自然科学基金项目(2017JJ3069);湖南科技大学博士科研启动基金项目(E51651);页岩气资源与利用开发湖南重点实验室开放基金项目(E21722);湖南省研究生科研创新项目(CX20190796)资助。

摘　　要：针对欧拉反褶积法中使用单一构造指数难于表征多个异常源,而使用不同尺寸的滑动窗口或通过枚举构造指数易于导致欧拉解集庞大,增加不必要的后续处理解释工作。为此,利用聚类分析划分欧拉反褶积解集,采用截断奇异值分解法解欧拉齐次方程,以评价因欧拉反褶积所构成的大型线性方程组条件数过大而造成欧拉解的非唯一性和不稳定性问题。在此基础上,进一步对比分析相同尺寸异常源在不同尺寸滑动窗口下所产生的欧拉解集中优解的比例,借此分析滑动窗口尺寸和异常源尺寸间的比例关系,并以此为依据选择最优化窗口。模型试验结果表明:当测量点距为异常源尺寸的1/10时,最优化窗口应为异常源尺寸的3倍且小于勘探区尺寸的1/2。In the Euler deconvolution method,it is difficult to characterize multiple anomalous sources using a single structural index.However,looping over survey grid with different sized square moving window,Euler solution set often with huge size,which increases unnecessary subsequent processing and interpretation work.Therefore,the authors use clustering method to analyze the Euler solution set,which is obtained by solving the Euler homogeneous equations with truncated singular value decomposition.Each large linear equations formed by Euler deconvolution on a square moving window have the excessive conditions number.This phenomenon easily leads to the non-uniqueness and instability of Euler solutions and is estimated by truncated singular value decomposition.Furthermore,the proportion of the optimal solution in Euler solution set with different sized moving windows for same sized anomalous sources is compared and analyzed,so as to analyze the proportional relationship between the size of moving window and the size of anomalous source,and the size of optimal moving window was determined.The model experiment results show that when the distance between the survey grids is one tenth of the size of the abnormal source,the size of optimal moving window should be 3 times the size of the anomalous source and less than 0.5 times the size of the exploration area.

关 键 词：最优滑动窗口 欧拉反褶积 估计函数 截断误差 

分 类 号：P631.1[天文地球—地质矿产勘探]