基于边界积分方程方法的弯折断层破裂传播过程控制因素分析

本文利用边界积分方程方法,以基于三角形网格的全空间格林函数及离散积分核计算为基础,进行了最常见的弯折断层的破裂传播过程模拟.为了去除边界积分方程方法中格林函数计算存在的高度奇异性,研究采用分部积分等方法对动力学方程进行了重整化和离散化处理.地震力学过程可以被视为断层由静摩擦转为动摩擦的过程,对于震源破裂过程的动力学模拟,摩擦准则起着重要作用,本研究采用常用的滑动弱化摩擦准则.计算引入Courant-Friedrich-Lewy比值来表达场点的影响,并控制计算的收敛性和稳定性.通过与典型算例的比对,检验了方法的正确性和有效性.地震破裂能否穿越断层弯折部位继续传播是震源动力学研究的重要内容,基于此,本文建立了多种理论弯折断层模型,模拟了断层弯折对地震破裂传播的控制作用,并通过改变断层周边初始应力场、断层弯折角度大小以及滑动弱化距离大小等来分析各个因素对破裂传播的影响.模拟结果表明:断层面上初始破裂区域内外的应力越高,破裂越容易越过断层弯折部位继续传播;初始破裂区域半径越大,或滑动弱化距离越小,破裂也越容易发生,并越过弯折部位继续传播.同样的初始条件,断层弯折角度越大,断层弯折作为障碍体,对破裂传播的阻碍作用越显著.小的弯折角,其破裂传播过程与平面断层差别不明显,基本仍以椭圆方式对称向两侧传播.

Controlling factors analysis of dynamic rupture propagation simulation of curved fault based on Boundary integral equation method

Earthquakes seldom rupture along single planar faults. Instead, there exist geometric complexities, including fault bends, branches and step overs, which affect the rupture process, nucleation and arrest. In order to understand the influences of nonplanar fault geometry on the earthquake rupture, dynamic numerical simulation provides a new insight. Boundary integral equation method(BIEM) is an appropriate method to model the dynamic rupture process of complex fault geometries, which simplifies the problem and requires small resources in computation by only discretizing the fault surfaces. In addition, it is easy to consider the singularity at the tip of crack using BIEM. When spatially discretizing the fault models, the rectangle meshes are commonly used, however, it is more detailed to describe the nonplanar fault geometries with triangle meshes. It has been recognized that an exponentially growing numerical oscillation resulting from spatiotemporal discretization is well known in the BIEM community. Therefore, an appropriate and optimum combination of space grid and time intervals is very important, which can suppress the oscillation and unstability to some extent. Here, the Courant-Fridrichs-Lewy condition is utilized to achieve the target. In this study, the relationship determined by CFL condition is Δt≤√2Δx/6 V_p.In this paper, the stress Green's functions for a constant slip rate on a triangular fault are calculated. Theorectially, the mechanics of earthquake rupture process can be regarded as a transformation from static friction to dynamic one. For the dynamic rupture modeling, friction criterion plays a very important role. Because we only focus on the rupture propagation and neglect the nucleation and cessation, slip weakening friction law is applied in our study. Nonplanar fault geometries include many types as mentioned above, and here we just take the curved faults with different bending angles as examples to study the influences of fault geometries on the rupture propagation. After modeling, it is found whether rupture can continue to propagate after curventure part is controlled by many factors, such as bending angles, initial stress in and out of the asperity, the radius of the asperity, slip weakening distance and so forth. Simulation results show that the higher the initial stress in and out of the asperity is, the easier the rupture propagates. And the larger the radius of the asperity or the smaller the slip weakening distance is, the easier the rupture propagates beyond the bend part. Given the same initial conditions, when the inclination angle is bigger, it has more obvious inhibition effect and can be taken as a barrier. However, the curved fault with small inclination angle has similar rupture propagation characteristics, and does not show obvious inhibition effect.