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

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 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.