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

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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