大地测量地震断层同震滑动分布反演的两步解法

针对同震滑动分布反演中系数矩阵出现病态的问题，提出两步解法，并在两步解法反演过程中引入拉普拉斯二阶平滑矩阵进行平滑约束。该方法不仅改善了系数矩阵的病态问题，同时也很好地抑制了相邻断层面间出现大的梯度变化。在两步解法反演过程中，用L曲线法确定正则化参数。系统模拟实验表明，对于最大滑动量，该方法的反演结果较一步最小二乘法的反演结果精度提高了3.34%~19%；对于均方根误差，该方法的反演结果较一步最小二乘法减小了3.3%~13.3%。芦山地震反演结果表明，利用两步解法进行滑动分布反演是可行的。

A Two-Step Solution Method for the Co-seismic Slip Distribution Inversion of Earthquake Faults in Geodesy

As for the ill-posed coefficient matrix in the process of co-seismic slip distribution inversion, a two-step solution method is proposed, and the Laplace second-order smoothing matrix is used for smoothing constraint in this paper. This method not only solves the ill-posed problem of the coefficient matrix, but also suppresses the large gradient variation between adjacent fault patches. During the inversion process of two-step solution method, the L curve method is used to determine the regularization parameters. In this paper, systematic simulation experiments are carried out and the Lushan earthquake is used as an actual earthquake case. The maximum slip inversion results of simulation experiments show that the inversion result of two-step solution method has been improved between 3.34% and 19% than that of one-step solution method in accuracy. The root mean square error inversion result of two-step method is less between 3.3% and 13.3% than that of one-step solution method. The inversion results of the Lushan earthquake show that it is feasible to use the two-step solution for slip distribution inversion.