Earthquake nucleation on rate and state faults: Theory (mostly) and some observations

地震并不是从空间中的一个点开始的，而是通过在一个有限大小的区域内加速滑动而开始的，这个区域被称为成核区。成核过程很重要，因为它确定是否或在什么条件下可以产生可检测到的前兆信号，以及断层对突然施加的应力步骤的反应，例如附近的大地震。尽管断层摩擦的“速率和状态”公式已经被广泛使用了20多年，但目前还没有确定天然(弹性变形)断层上成核带大小的通用理论。在最近的一项数值和分析研究中，PI和博士后Jean-Paul Ampuero在断层上绘制了两个地震成核区域，这些断层受“老化定律”(两个常用的经验定律中较流行的一个，用于“速率和状态”摩擦的“状态变量”部分的演化)的支配。在一种情况下，成核区自发地演化为在固定长度的斑块上加速滑移的状态。另一方面，对于相关本构参数“a”(与“速率”效应有关)和“b”(与“状态”效应有关)的实验值，成核区采取扩展裂纹的形式，该扩展裂纹的长度渐近接近a/b=0.95的100倍的长度。这将导致有时可以使用地面地震仪检测到的成核事件。然而，这些大尺寸是有效断裂能随着老化规律所暗示的滑动速度的增加而迅速增加的直接结果。事实上，如此迅速的增长几乎没有实验支持，这表明尽管老化定律很受欢迎，但它不能很好地描述成核作用。相反，在“滑移定律”下，形核的有效断裂能随滑移速度的增加较慢，这与相关实验结果吻合较好。初步计算表明，对于a/b的实验值，该定律下的成核以单向滑移“脉冲”的形式存在，该脉冲在小得多的区域内最活跃。PI目前正在数值和解析地研究滑移定律和其他类演化定律下的地震成核，很像对老化定律所做的那样。由于目前关于“状态变量”演化的法律完全是经验性的，所以试图从根本上理解不同类别的法律的区别是非常重要的。虽然这项研究主要是理论上的，但其结果也被用于分析由加利福尼亚州摩根山6.2级地震激活并在一年内“关闭”的几个小重复地震群。这些地震可能发生在卡拉维拉斯断层的近速度中性(a/b~1)斑块上，其大小接近成核长度。这项研究的结果已被证明有助于设计实验室实验，以区分不同的拟议演化规律，并应有助于解释预计将来自美国国家科学基金会赞助的两个主要项目--圣安德烈亚斯断层上的SAFOD钻孔和南非深井中的NELSAM实验--地震孕育深度的地震成核的观测结果。这项研究还将支持一年级研究生岳天工作

Earthquakes do not begin at a single point in space, but via accelerating slip over a region of finite size termed the nucleation zone. The nucleation process is important because it determines whether or under what conditions detectable precursory signals may be produced, as well as the response of the fault to a suddenly-applied stress step, such as from a nearby large earthquake. Despite the fact that the "rate and state" formulation for fault friction has been widely used for over two decades, there is currently no general theory for determining the size of the nucleation zone on natural (elastically deformable) faults. In a recent numerical and analytical study, the PI and post-doc Jean-Paul Ampuero mapped out two regimes of earthquake nucleation on faults governed by the "aging law" (the more popular of two commonly used empirical laws for the evolution of the "state variable" part of "rate and state" friction). In one regime, the nucleation zone spontaneously evolves to a state of accelerating slip on a patch of fixed length. For laboratory values of the relevant constitutive parameters "a" (pertaining to "rate" effects) and "b" (pertaining to "state" effects), on the other hand, the nucleation zone takes the form of an expanding crack that asymptotically approaches a length that for a/b=0.95 is 100 times larger. This would lead to nucleation events that might sometimes be detectable using surface seismometers. However, these large sizes are a direct consequence of the rapid increase in effective fracture energy with increasing slip speed that the aging law implies. In fact, such a rapid increase has little experimental support, suggesting that despite its popularity the aging law is a poor descriptor of nucleation. In contrast, and in better agreement with relevant experiments, under the "slip law" the effective fracture energy of nucleation increases more slowly with slip speed. Preliminary calculations show that for laboratory values of a/b, nucleation under this law takes the form of a unidirectional slip "pulse" that is most active over a much smaller region.The PI is currently investigating, numerically and analytically, earthquake nucleation under the slip law and other classes of evolution laws, much as was done for the aging law. Because current laws for the evolution of the "state variable" are strictly empirical, trying to obtain a fundamental understanding of what distinguishes different classes of laws is quite important. Although this study is primarily theoretical, the results are also being applied to the analysis of several clusters of small repeating earthquakes that were activated by the M6.2 Morgan Hill, California, earthquake and that "turned off" within a year. These earthquakes may have occurred on nearly velocity-neutral (a/b~1) patches of the Calaveras fault with a size close to the nucleation length. The results of this study have already proven useful for the design of laboratory experiments that can distinguish between different proposed evolution laws, and should be useful for interpreting observations expected to come from two major NSF-sponsored projects to image earthquake nucleation at seismogenic depths - the SAFOD borehole along the San Andreas fault, and the NELSAM experiment in deep South African mines. The study will also support a first-year graduate student, Yue Tian to work