基于光滑模型约束的同震滑动分布正则化反演 Regularized Inversion of Coseismic Slip Distribution Based on Smoothness-Constrained Model

同震滑动的空间分布估计问题是不适定的，其反演结果存在非唯一性。为了获取稳定的同震滑动分布，本文采用了光滑模型约束的正则化反演方法。算法实施过程中，构建了断层面非均匀离散的滑动量分布光滑约束模型，并设计一种快速稳定的正则化因子求取方法；为了获得合理的滑动分布，采用了非负最小二乘求解方法。理论均匀滑动分布模型的反演试算，验证了反演算法的有效性和稳定性，且非负最小二乘方法能规避不合理的滑动分布。利用光滑约束反演方法反演了2005年Nias地震的同震滑动分布，并与前人的研究结果进行了对比分析。2005年Nias地震反演结果显示：断层面最大滑动量为12.8 m，这与Konca等反演得到的结果一致，且滑动分布所释放的地震矩为9.91 × 1012 Nm，其地震震级为Mw = 8.6，与USGS公布的结果一致。通过理论滑动分布模型和实际震例的反演结果表明，光滑约束正则化反演方法是可行的，并能合理地重建断层面的同震滑动分布。 Estimating the spatial distribution of coseismic slip is an ill-posed inverse problem, and the solution is non-unique. In order to obtain stable solution for coseismic slip inversion, regularization method with smoothness-constrained was imposed. For the implementation of inverse algorithm, we construct a smoothness-constraint model with non-uniform slip on the fault plane, and propose a fast and stable method for choosing regularization parameter. In order to get reasonable coseismic slip distribution, non-negative least squares method is adopted. Inversion for a synthetic model with uniform coseismic slip distribution shows that the inverse algorithm is effective and stable, and non-negative least squares method can reconstruct reasonable results. We conduct inversions on the 2005 Nias earthquake with smoothness-constraint regularized method, and make a comparison of other results. The results for the 2005 Nias earthquake indicate the maximum slip is about 12.8 m, which agrees well spatially with the coseismic slip distribution of Konca. The released moment based on the estimated coseismic slip distribution is 9.91 × 1012 Nm, which is equivalent to a moment magnitude (Mw) of 8.6 and almost identical to the value determined by USGS. The inversion results for synthetic coseismic slip distribution model and real earthquakes show that the smoothness-constrained regularized inversion method is effective, and can be reasonable to reconstruct coseismic slip distribution on the fault plane.