基于随机抽样一致性-网格搜索方法反演断层面倾角

采用小地震的丛集性活动资料定量地研究地下断层的三维几何信息对地震危险性评估具有至关重要的意义。若所使用的资料存在高比率的离群值，将会使断层几何参数的估值产生较大偏差。为了提高断层几何参数估值的稳健性，本文将随机抽样一致性（RANSAC）与网格搜索（GS）相结合，给出了随机抽样一致性-网格搜索（RANSAC-GS）估算方法。在数值模拟试验中，对模拟观测值加入1%，5%，10%和20%的离群值，分别采用GS和RANSAC-GS两种方法估算了断层面倾角，并从反演参数的残差、反演模型计算值与观测值的密合度、目标函数及相关度等方面证明了RANSAC-GS方法即使在高比率离群值的情况下，依然能够给出稳健的参数估值。最后，利用2008年1月至2012年12月鄂尔多斯地区小震重定位结果，以震源点到断层面距离最小为准则，采用RANSAC-GS方法反演获得太谷断裂的断层面倾角为52.5°，与前人的结果有较好的一致性，在此基础上对大地测量形变观测给出合理的阐释，从而证明了本文方法的有效性。 

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.