An Theoretical Method for Computing Near-Fault Ground Motions in Layered Half-Spaces Considering Static Offset due to Surface Faulting

考虑地表断层引起的静态偏移的层状半空间中近断层地震动计算的理论方法

基本信息

批准号：
14580508
负责人：
HISADA Yoshiaki
金额：
$ 0.96万
依托单位：
Kogakuin University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2002
资助国家：
日本
起止时间：
2002 至 2003
项目状态：
已结题

项目摘要

An efficient mathematical method is presented for computing the near-fault strong ground motions in a layered half-space, giving explicit consideration to the static offset due to surface faulting. In addition, the combined effects of "fling step" (e.g., Abrahamson, 2001) and "rupture directivity" (e.g., Somerville et al., 1997) on the near-fault ground motions are investigated. First, after checking the fault integration in the representation theorem, it is found that when an observation point is close to the fault plane, Green's functions exhibit near-singularities, which consist of extremely sharp peaks in a narrow band close to the observation point. Therefore, direct numerical integration becomes quite onerous for computing near-fault ground motions, because the dynamic Green's functions must then be distributed very densely in order to evaluate accurately the effects of the near-singularities. Instead, a new form of the representation theorem is introduced, which exploits the pro … More perty that the dynamic Green's functions can be approximated by the corresponding static Green's functions in the vicinity of the singularities. The modified theorem, which involves the device of adding and subtracting the static Green's functions from the dynamic ones, is the sum of two fault integrations. The first integration involves the difference of the dynamic and the corresponding static Green's functions, while the second contains only the static Green's functions. This formulation requires much less CPU time than the original one when near-fault ground motions are considered, because the near-singularities of the dynamic Green's functions in the first integration are completely eliminated by subtracting the static Green's functions. While the second integration does require a densely distributed set of points to capture the near-singular behavior of the static Green's function, it needs to be performed only once, as it is valid for all frequencies. Subtraction of the static Green's functions from the dynamic functions has the added benefit of making the integration over the wavenumber in the determination of the Green's functions much more efficient, especially for considering surface faulting. This is because the difference of the dynamic and static integrands converges rapidly to zero with increasing wavenumbers, whereas the original integrands diverge in the case of a source point on the free surface.The proposed methodology is used to investigate the two most important effects in near-fault ground motions, "fling step" and "rupture directivity", by paying special attention to the contribution of static and dynamic Green's functions. It is found that the fling effects are mainly contributed from the second integral in the modified representation theorem, which involves the static Green's function. These effects attenuated rapidly with distance from the fault, r, as 0 (1/r2). The fling effects are dominant in the slip direction only in the vicinity of the surface fault, and are negligible for buried faults. By contrast, the directivity effects stem mainly from the first integral, which involves the dynamic Green's function, and occur primarily in the fault normal direction. They attenuate much more slowly than the flings, on the order from 1/r to. Due to the combined effects of fling and directivity in the vicinity of the surface fault, the directions of the maximum velocities and displacements are inclined with respect to the fault plane. On the other hand, when softer surface layers are added to the medium, the directivity effects become more significant than the fling effects, because the dynamic Green's functions are more pronounced than the static ones. Less

提出了一种有效的数学方法来计算分层半空间中的近断层强地面运动，明确考虑了由于地表断层引起的静态偏移。此外，“抛步”（例如，亚伯拉罕森， 2001）和“破裂方向性”（例如，Somerville 等人，1997）对近断层地震动进行了研究。首先，在检查表示定理中的断层积分后，研究发现，当观测点靠近断层面时，格林函数表现出近奇异性，即在靠近观测点的窄带内出现极其尖锐的峰值，因此直接数值积分对于计算近奇异性变得相当繁重。断层地面运动，因为动态格林函数必须非常密集地分布，以便准确评估近奇点的影响，相反，引入了一种新形式的表示定理，该定理利用了断层地震动的优点。动态格林函数可以用奇点附近相应的静态格林函数来近似。修正的定理涉及从动态格林函数中添加和减去静态格林函数，它是两个故障积分的总和。积分涉及动态和相应的静态格林函数的差异，而第二个仅包含静态格林函数，当考虑近断层地面运动时，该公式所需的 CPU 时间比原始公式少得多，因为通过减去静态格林函数，可以完全消除第一次积分中动态格林函数的近奇异性，而第二次积分确实需要一组密集分布的点来捕获静态格林函数的近奇异行为。仅执行一次，因为它对所有频率都有效，从动态函数中减去静态格林函数还有一个额外的好处，即使确定格林函数时对波数的积分更加有效，特别是考虑到这一点。这是因为随着波数的增加，动态和静态被积函数的差异迅速收敛到零，而在源点位于自由表面的情况下原始被积函数发散。所提出的方法用于研究两个最重要的问题。通过特别关注静态和动态格林函数的贡献，研究了近断层地震动中的“甩动步”和“破裂方向性”效应，发现甩动效应主要来自于二次积分。修正的表示定理，涉及静态格林函数，这些效应随着距断层的距离 r 迅速衰减，为 0 (1/r2)，抛掷效应仅在表面断层附近的滑移方向上占主导地位。相比之下，方向性效应主要来自涉及动态格林函数的第一积分，并且主要发生在断层法线方向上，它们在断层上的衰减速度要慢得多。从 1/r 到，由于地表断层附近的冲刷和方向性的综合影响，最大速度和位移的方向相对于断层平面倾斜。添加到介质中，方向性效应变得比投掷效应更显着，因为动态格林函数比静态格林函数更明显。