改进的特征量方法及其在震源动力学模拟中的应用

基于曲线网格有限差分方法, 针对震源动力学模型中的边界条件的问题, 本文提出了一种改进的特征量方法, 即将牵引力镜像方法和特征量方法相结合, 在保守形式的方程中通过镜像操作完成单边导数的计算, 然后有约束地调整边界处的速度和应力值, 以此保证满足模型中的边界条件.改进的特征量方法可用于处理曲线网格当中一般的边界条件, 从而也可用于构建曲线网格有限差分法的分裂节点模型.我们将改进的特征量方法分别用于自由表面和断层面, 并分别与前人计算结果进行了比较.计算结果表明, 在相同的网格划分的情况下, 改进的特征量方法能够得到与其他方法相似的计算结果, 但改进方法的异常震荡更小, 从而证明了本文提出的改进的特征量方法用于曲线网格有限差分法分裂节点模型的可行性.

Modified Characteristic Variable Method and its application to seismic source dynamics

Based on the curved-grid finite-difference model, a modified Characteristic Variable Method (mCVM) is proposed to address the boundary conditions in the earthquake source dynamics. This modified method is the combination of Traction Image Method and Characteristic Variable Method. It calculates the one-sided derivatives in the conservative form of equations with an imaging technique, and then changes the boundary-values of velocity and stress with constraints to satisfy the boundary conditions. The mCVM can deal with general boundary conditions in curved grid, and therefore, can be particularly used to construct a split-node model of curved-grid finite-difference method. We applied this method to the free surface and the fault plane respectively, and compared our results with former studies. It is shown that the results of our method are similar to those of former studies when using the same grid, but the results of our method have much smaller artificial oscillations when it is applied to a fault plane. These prove the feasibility of using mCVM to construct a split-node model of curved-grid finite-difference method.