稳定正则化参数估计方法及其在盆地基底重力异常反演中的应用  

A stable regularization parameter estimation method and its application to gravity anomaly inversion of basin basements

作　　者：刘燕东 纪晓琳[2] 孟小红[1] 王万银[2] 王俊[1] LIU YanDong;JI XiaoLin;MENG XiaoHong;WANG WanYin;WANG Jun(School of Geophysics and Information Technology,China University of Geosciences,Beijing 100083,China;School of Geology Engineering and Geomatics,Chang′an University,Xi′an 710054,China)

机构地区：[1]中国地质大学(北京)地球物理与信息技术学院,北京100083 [2]长安大学地质工程与测绘学院,西安710054

出　　处：《地球物理学报》2021年第10期3756-3765,共10页Chinese Journal of Geophysics

基　　金：国家自然科学基金项目(41974161,41804099);中央高校基本科研业务费专项资金项目(2-9-2019-040)联合资助.

摘　　要：正则化方法通过带有正则化参数的约束项,将不适定问题转换为一个适定问题.如何选取最优正则化参数一直以来都是正则化研究的难点和热点.本文通过定义解的不稳定性度量来直接估算正则化参数μ的最优值,并将这种正则化参数估计方法应用到二维沉积盆地基底重力反演中.测试该方法在通过对一次野外测量的数据加不同噪声得到的多组数据与多次野外测量中得到的多组数据这两种情况中的反演效果.最后将该方法应用到非洲西海岸的北加蓬次盆进行盆地基底反演,测试该方法的实用性.模型测试的结果显示,在这两种情况下获得的反演解非常接近且能够反演得到较为准确的模型基底深度,故该方法适用于一般情况下只进行一次野外测量的实际重力勘探情况且能得到稳定的最优反演解;实际资料的最优反演结果稳定且符合当地的地质构造背景.在模型测试与实际资料测试中,都能够确定最优正则化参数并得到最优反演结果,证明了该方法在重力反演中的正确性和实用性.In the regularization method,the ill posed problem is transformed into a well posed problem by a constraint term with regularization parameters.How to select the optimal regularization parameters has always been a difficult issue in the research of regularization.In this paper,the optimal value of regularization parameterμis directly estimated by defining the instability measure of the solution,and this regularization parameter estimation method is applied to gravity data inversion of two-dimensional sedimentary basins.The inversion effect of this method is tested in two cases:one is the multiple groups of data obtained by adding different noises to the data of one field survey and the other is the multiple groups of data obtained from multiple field measurements.Finally,the method is applied to basement inversion of the North Gabon sub-basin on the west coast of Africa and the practicability of the method is tested.The results of the model test show that the inversion solutions obtained in these two cases are very close and can obtain accurate model base depth.Therefore,this method is suitable for the actual gravity exploration with only one field survey in general,and can obtain stable optimal inversion solution.The optimal inversion result of the actual data is stable and consistent with the local geological structure background.In both model and actual data tests,the optimal regularization parameters can be determined and the optimal inversion results can be obtained,which proves the correctness and practicability of this method in gravity inversion.

关 键 词：正则化参数的选取 密度界面反演 稳定估计 高斯牛顿法 

分 类 号：P631[天文地球—地质矿产勘探]