Earthquakes nucleate as accelerating slip over a region of finite size. Understanding what controls the length and time scales of this process is important for assessing earthquake early-warning systems and for interpreting data obtained by monitoring earthquake-generating faults within tens to hundreds of meters of the source (such as at the 2.5-km-deep San Andreas Fault Observatory at Depth, or SAFOD; see Figure 1).
Theoretical models of earthquake nucleation require coupling the equations of elasticity with a constitutive law for the evolving strength of the fault surface. For more than 2 decades the most complete constitutive laws have been various incarnations of “rate- and state dependent friction”, meaning that the frictional strength depends upon the micromechanical state of the fault surface as well as the current slip speed. Despite this lengthy history, it is most likely that no numerical simulation has ever employed the “correct” constitutive law. This is because no proposed law fits even all the available experimental data, let alone the conditions of temperature, pressure, and fluid chemistry that might be appropriate in situ. To make matters worse, the strongly nonlinear nature of friction has made it very difficult to obtain an intuitive understanding of the differences between the underlying equations that people use. This combination of poorly-constrained constitutive laws and opaque equations is a significant impediment to extrapolating from numerical simulations to fault slip in the Earth.
Over the last several years, the work I have done with post-doc Jean-Paul Ampuero (now an assistant professor at Caltech) has gone a log way toward developing this intuitive understanding. Using standard methods of fracture mechanics, we now have analytic expressions for the length and time scales of nucleation under the most commonly-used law for the evolution of state (the “aging” law; see Figure 2). Under this law, nucleation zones can grow to be so large that they might often be detectable from the Earth’s surface. However, our analytical solutions also let one see immediately that the properties of the aging law that generate these large nucleation zones are directly contradicted by lab experiments. This has led to a collaboration with Chris Marone (Penn State), where we recently showed that lab data relevant to earthquake nucleation are much more consistent with the “slip” evolution law (Figure 3).