刘燕东^1,2,,
纪晓琳²,
孟小红^1,,,
王万银²,
王俊¹
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

基金项目: 国家自然科学基金项目（41974161，41804099）和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


详细信息

作者简介: 刘燕东, 女, 1997年生, 博士研究生, 主要从事位场方法技术与应用研究.E-mail: YanD_Liu@163.com

通讯作者: 孟小红, 女, 1958年生, 教授, 主要从事位场方法技术与综合地球物理应用研究.E-mail: mxh@cugb.edu.cn

中图分类号: P631

收稿日期:2020-10-21
修回日期:2021-09-03
上线日期:2021-10-10

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

LIU YanDong^1,2,,
JI XiaoLin²,
MENG XiaoHong^1,,,
WANG WanYin²,
WANG Jun¹
1. School of Geophysics and Information Technology, China University of Geosciences, Beijing 100083, China
2. School of Geology Engineering and Geomatics, Chang'an University, Xi'an 710054, China


More Information

Corresponding author: MENG XiaoHong,E-mail:mxh@cugb.edu.cn

MSC: P631

--> Received Date: 21 October 2020
Revised Date: 03 September 2021
Available Online: 10 October 2021


摘要
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.
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

Abstract: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 parameter μ is 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.
Key words:Choice of optimal regularization parameters/
Density interface inversion/
Stable estimation/
Gauss-Newton method



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