同一地震多个震源机制中心解的确定

一个地震发生后，根据不同方法和资料可以求出地震的震源机制解.由于采用的方法和选择资料不同，得到的震源机制会有一定差别.为解决在多个震源机制解中确定一个合适的震源机制解进行后续分析的需求，首先推导了表示两个震源机制差别的最小空间旋转角，采用示例验证了最小空间旋转角表达了两个震源机制的差别.为找到一个与多个震源机制差别的平方和最小的震源机制，将待定震源机制与所有震源机制的最小空间旋转角的平方和作为目标函数，并且将非线性的最小空间旋转角的平方和线性化，采用Levenberg-Marquardt方法给出了求解方法.根据这种方法，给出了2008年汶川地震和2018年新疆精河地震的中心震源机制解.该方法为在多个已经求出的震源机制中确定中心解，从而进行其他诸如应力触发、地球动力学分析等提供了工具.

Determination of center of several focal mechanisms of the same earthquake

After an earthquake occurrence, the focal mechanism solutions are derived from different data and methods. The differences of focal mechanism solutions are exist for derivation from various data set and methodology. In order to determine an appropriate focal mechanism solution from several focal mechanisms of the same earthquake for later geodynamic analysis, I firstly derive the minimum 3-D rotation angle which presents the difference of the two focal mechanism solutions, and validate it through a simple example. Secondly, I use the sum of the square of the minimum 3-D rotation angles between the pending focal mechanism solution and all the focal mechanism solution as an objective function, linearize it, and realize by using Levenberg-Marquardt approach. The center of focal mechanism solutions of the 2008 Wenchuan earthquake and 2018 Jinghe, Xinjiang, earthquake are given by using this method. The method provides a tool to determine the center of focal mechanism solution from the several determined focal mechanism solutions, and can be used for other studies such as seismic stress triggering, geodynamic analysis, etc.