Robert Viesca in Tufts University will visit us on 2/26, and give a hybrid special seminar.
Please join if you are interested.

Title: From slow-to-fast in rate-and-state fault models: delimiting model behavior using linear and non-linear analysis
Time: 2/26 (Thu)
Place: E232D in Uji campus + zoom

Abstract: The prevalent physical model for the operation of faults throughout the seismic cycle is coupling of a rate- and -state dependent fault strength with the elastic deformation of the adjoining rocks. This model is not only capable of reproducing punctual earthquakes followed by a quiescent interseismic period, but also admits the possibility of steady fault creep, and the spontaneous emergence of aseismic transients, or slow slip. This non-linear description of fault frictional strength is widely used today to interpret observations and began almost 50 years ago; however, a keystone of our understanding of the role of friction in these models has been based on early, idealized analyses of uniform, unbounded faults that can provide no more than a rule of thumb. Consequently, model design has often relied on the variation of parameters on an informed, yet essentially trial-and-error basis to discover fundamental changes in fault behavior. Here we present an analysis incorporating more realistic fault model details that can quantitatively predict, a priori, sharp transitions in model fault behavior from slow steady creep to fast earthquake rupture. We examine two scenarios that move beyond the classical case: an asperity driven by the steady creep of its surroundings, and a finite fault experiencing a constant rate of shear loading. We identify the critical fault dimension Lc at which point linear stability is lost. Beyond this linear regime, the non-linear nature of the friction law implies the loss of memory of loading conditions as instability progresses and the existence of universal solutions describing this process. We refine prior analyses of this non-linear instability and find the minimum fault or asperity size that can support self-sustaining, unstable acceleration towards dynamic rupture. For demonstration purposes, the focus will be on relatively simple fault conditions, but we will demonstrate that the analyses can also be appleid to various state evolution laws, frictional heterogenetiy, and a variation of the geometry of the fault. Through comparisons with full elastodynamic numerical solutions, we'll show that our analyses precisely predict transitions in model behavior. Approximate but accurate algebraic expressions for the transition boundaries are presented. These results provide means for careful model design and to delimit plausible regions of parameter space when considering physical observations of stable creep, aseismic (slow slip) or seismic transients.