Inversion of fault dip angle based on the random sampling consistency combined with the grid search algorithm

It is of great significance to quantitatively study the geometric parameters of deep fault by using the cluster activity data of small earthquakes. If there is a high ratio of outliers, it will have a serious impact on the estimated parameters. Therefore, in order to improve the robustness of parameter estimation, this paper combined the random sampling consistency （RANSAC） algorithm with the grid search （GS） algorithm, and gave the RANSAC-GS algorithm. In the numerical simulation tests, 1%, 5%, 10% and 20% outliers were added to the simulated observations, respectively. At the same time, both GS and RANSAC-GS were used to compute the dip angle of the fault. The robustness of the RANSAC-GS was proved by the residuals of the inversion parameters, the tightness between the calculated values and the observations, the objective function, and the correlation, even if in the cases with a high ratio of outliers. And then we took the Taigu fault as an example to verify the RANSAC-GS algorithm. Basing on the fine locations of small earthquakes in the Ordos area from January of 2008 to December of 2012, we obtained the dip angle of Taigu fault to be 52.5° by RANSAC-GS algorithm with the minimum distance from the source point to the fault surface as the criterion. The dip angle result agrees well with the previous results, suggesting the effectiveness of the RANSAC-GS algorithm.