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，用于在分层半空间中计算近错强的地面运动，从而明确考虑了由于表面断层而导致的静态偏移。此外，研究了“ Fling Step”（例如Abrahamson，2001）和“破裂方向性”（例如Somerville等，1997）对近磨损地面运动的综合作用。首先，在检查表示定理中的故障积分之后，发现当观测点接近断层平面时，绿色的功能暴露了近距离的功能，该功能由靠近观察点的狭窄带中的极尖峰组成。因此，直接数值集成在计算近门接地运动方面变得非常繁重，因为然后必须将动态绿色的功能分布得非常垂直，以便准确评估近距离的效果。取而代之的是，引入了一种新形式的表示定理，这利用了Pro…更加明显的是，动态绿色的功能可以通过相应的静态绿色功能近似于奇异性的相应静态绿色的功能。修改后的定理涉及从动态功能中添加和减去静态绿色功能的设备，是两个故障积分的总和。第一个集成涉及动态和相应的静态绿色功能的差异，而第二个仅包含静态绿色的功能。当考虑近乎失误的接地运动时，此公式所需的CPU时间比原始的时间少得多，因为通过减去静态绿色的功能，完全消除了动态绿色功能的近距离函数。虽然第二个集成确实需要一组不足的分布点才能捕获静态绿色功能的近乎单位行为，但仅需要一次执行一次，因为它对所有频率都是有效的。静态绿色功能从动态函数中的减法具有更大的好处，即在确定绿色功能的情况下对波数的积分更加有效，尤其是考虑到表面断层。 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.发现FLING效应主要源于修改的表示定理中的第二个积分，涉及静态绿色的函数。这些效果随着与断层r的距离迅速减弱，为0（1/r2）。仅在表面断层附近的滑动方向上，fling效应在滑移方向上有主导地位，并且被埋葬的断层可忽略不计。相比之下，方向性效应主要源于第一个积分，该积分涉及动态绿色的功能，主要发生在正常方向上。他们的衰减比FLINGS的速度较慢，从1/R到1/R。由于表面断层附近的fling和方向性的综合作用，最大速度和位移的方向相对于断层平面而言。另一方面，当将表面层添加到介质中时，方向性效应比Fling效应更为重要，因为动态绿色的功能比静态效果更为明显。较少的