地震同震滑动分布反演平滑因子的确定

针对大地测量地震同震滑动分布反演中平滑因子（又称正则化参数）的确定问题，一般采用模型粗糙度与数据拟合残差之间的折中曲线来确定（为便于区分，本文将该方法称为"L曲线"）。本文在L曲线的基础上提出一种确定平滑因子的新方法——折中相交曲线法。模拟试验反演结果表明，利用折中相交曲线法确定的平滑因子反演地震滑动分布各参数精度要优于L曲线法。利用折中相交曲线法确定平滑因子反演拉奎拉与台湾美浓实际地震，并与L曲线法反演结果进行对比分析。分析结果表明，利用折中相交曲线法确定的平滑因子反演拉奎拉与台湾美浓实际同震滑动分布各参数结果均在国内外其他学者研究的范围内，并且利用折中相交曲线法确定平滑因子较L曲线法具有计算效率高、无需依赖数据拟合度、确定平滑因子大小更为合适等优点。

Determination of Smoothing Factor for the Co-seismic Slip Distribution Inversion

For the determination of the smoothing factor (also known as the regularization parameter) in the co-seismic slip distribution inversion, the compromise curve between the model roughness and the data fitting residual is generally used to determine (in order to distinguish the method proposed in this paper, the method is called "L curve" according to its shape). Based on the L-curve, the eclectic intersection curve as a new method are proposed to determine the smoothing factor in this paper. The results of the simulated experiment show that the inversion accuracy of the parameters of the seismic slip distribution with the smoothing factor determined by the eclectic intersection curve method is better than that of the L curve method. Moreover, the eclectic intersection curve method and the L curve method are used to determine the smoothing factor of L'Aquila and Taiwan Meinong earthquake slip distribution inversion respectively, and the inversion results are compared and analyzed. The analysis results show that the L'Aquila and Meinong of Taiwan actual earthquake slip distribution results are in the range of other scholars at home and abroad, and compared with the L curve method, the eclectic intersection curve method has advantages of high computation efficiency, no need to depend on data fitting degree and more appropriate of smoothing factor and so on.