基于时间域半空间Green函数建立的边界积分方程及其在动态破裂模拟中的应用

Boundary integral equation based on half-space Green's function in time domain and its application to dynamic ruptures simulation

研究地震断层的自发破裂传播可以为通过震源过程了解地球介质应力状态提供理论基础,有助于理解震源破裂的机理和规律,在震源动力学研究中具有重要的地位.边界积分方程方法是研究地震断层破裂传播问题的常用方法之一,在处理复杂断层系统方面具有优势.本文从半无限空间Green函数的时间域积分形式解出发,推导出离散化的边界积分方程积分核,并将其分别应用到平面断层和弯折断层两种断层模型的动力学破裂过程的模拟中.模拟结果表明,当破裂传播到自由表面处时,会产生反射震相,反射震相与直达震相的耦合效应会导致自由表面处的破裂传播速率明显加快,同时这种耦合效应也可以促进破裂在断层弯折部位的传播.对于断层有一定埋深的情况,自由表面对破裂过程的影响较小,因而自由表面的效应仅在断层直接与地表相交或者断层上沿距离地表很近时需要纳入考虑范围.本文将自由表面的影响加入到断层的自发破裂传播研究中,有助于更真实地了解复杂断层系统中的动力学破裂过程.

The study of spontaneous rupture propagation of earthquake faults can provide a theoretical basis for understanding the stress state of the Earth medium through the source process,and is helpful to explore the mechanism and law of source rupture,which plays an important role in the study of source dynamics.The boundary integral equation method is one of the common methods to study seismic fault rupture propagation and has advantages in dealing with complex fault systems.In this paper,the integral kernel of discretized boundary integral equation is derived from the integral form solution of half-space Green's function in time domain,and is applied to the simulation of dynamic rupture process of plane fault model and bending fault model,respectively.The simulation results show that when the rupture propagates to the free surface,a reflection phase will be generated,and the coupling effect between the reflection phase and the original one will accelerate the rupture propagation along the free surface,and the coupling effect can also promote the propagation of the rupture at the fault bend.For a buried fault,however,the influence of free surface on the rupture process is limited,so the effect of free surface should be considered only when the fault directly intersects the surface or the fault is very close to the surface.In this paper,the influence of free surface is exactly included in the study of spontaneous rupture propagation of faults,which is helpful to understand the dynamic rupture process in complex fault systems more realistically.