SCEC Award Number 15184 View PDF
Proposal Category Individual Proposal (Integration and Theory)
Proposal Title Role of heterogeneity in friction parameters in determining the location of earthquake nucleation
Investigator(s)
Name Organization
Robert Viesca Tufts University
Other Participants Sohom Ray (Ph.D. student)
SCEC Priorities 4b, 3d, 1b SCEC Groups Seismology, CS, FARM
Report Due Date 03/15/2016 Date Report Submitted 11/14/2016
Project Abstract
 A spatial variation of frictional behavior is the basis of current seismic-cycle models: some fault domains are thought to have rate-weakening behavior, and can nucleate earthquakes, while others are thought to be rate-strengthening, and, consequently, are unconditionally stable. However, beyond this dichotomy lies the question of whether any property variation within one domain or the other or plays a first-order role in earthquake cycles. Here we considered spatial variations in frictional properties within rate-weakening regions (e.g., rate-weakening magnitude) and asked whether variations may control, for example, where an earthquake may nucleate. This was done in the context of a rate- and state-dependent friction, for which recent results [Viesca, 2016a,b] show that earthquake-nucleating instabilities, resulting from coupling fault friction to elasticity, lend themselves to nonlinear analysis. For this frictional description, the strength of a logarithmic, steady-state, rate-weakening is proportional to the difference a–b, where a and b are the so-called direct- and evolution-effect coefficients. We investigated the role of variations of a, b, fault normal stress σ, and characteristic slip distances Dc for frictional evolution. We find variations in the latter two may be understood in terms of variations of a and b. Our principal result is that variations create preferential nucleation sites: given a property distribution, we can anticipate, a priori, where fault slip rate will proceed to accelerate unstably, independent of initial conditions and the manner of external forcing. We find the strongest factor in determining a preferential site is the distribution of the ratio a/b.
Intellectual Merit The results of the project provide an understanding of frictional controls on determining where an earthquake-generating dynamic rupture nucleates, the starting gate of an earthquake. We assessed the predictability of the nucleating slip-instability development considering the coupling of off-fault elastic deformation with fault friction. We find that during the very short timescales of rapid, quasi-static acceleration, the location of instability development, including lengthscales, slip rate distributions, and quasi-static moment release can be anticipated if frictional property distributions are known. We evaluated the relative importance of variations of key material (frictional) properties and fault stress condition (the normal stress). Specifically, and perhaps somewhat unexpectedly, we found that the relative rate weakening (given by the ratio of frictional parameters a/b), rather than the rate-weakening magnitude (given by the difference a – b), has the greatest control of whether an area is the most attractive location for instability to develop. The results of this work provides a rigorous explanation for the spatio-temporal patterns of seismicity (i.e., why earthquakes nucleate where they do) in current computational models coupling rate- and state-dependent friction with elastodynamic response of the host medium and incorporating heterogeneous frictional properties. The work also informs what may be missed in homogenizing an otherwise heterogeneous fault friction.
Broader Impacts This project supported one Ph.D. student (Sohom Ray) and an early career research (Robert C. Viesca). In advancing understanding of the processes that control earthquake nucleation, the results of the project help provide a framework for interpreting the earliest aseismic and seismic signals crucial for early warning systems.
Exemplary Figure Figure 2. (top) Black dashed line indicates a distribution of the relative rate weakening parameter r(x) = [b(x)-a(x)]/b(x). Each colored overlay indicates a region where a blowup solution exists. (middle) Plot of distributions W for slip-rate blow-up solutions of the form V(x,t) = W(x) Dc / tf(t). (bottom) In this example, we varied the direct- and evolution-effect coefficients, a and b, such the local magnitude of rate-weakening, m(x) = b(x) – a(x), varies out of phase with r. We find that the locations of the blow-up solutions are determined not by the local extrema of m, but rather those of the relative magnitude, r.