Preferential earthquake-nucleating locations on faults determined by heterogeneous direct- and evolution-effect parameters of rate- and state-dependent friction

Abstract:

Rock friction experiments show that low-velocity fault friction may have a direct and subsequent evolutionary response to changes in slip velocity; the magnitude of which are respectively proportional to parameters a and b in constitutive relations of such rate- and state-dependent friction [e.g., Dieterich 1979; Ruina, 1983]. When a and b are uniform on a fault, translational invariance implies any location is a potential nucleation site, the choice determined by pre-instability conditions and external forcing. With heterogeneous parameters, symmetry is broken, which can create preferred nucleation sites. Recent work showed such heterogeneity does create favorable sites (Ray and Viesca, AGU ’14). Here we study how distributions of (i) relative (0<a/b<1) and (ii) absolute (a-b<0) rate-weakening parameters determine the location of preferred sites. We examine the influence of (i) and (ii) by varying one or varying both (similarly or disparately). The smallest wavelength of variation is comparable to or larger than the size of the developing instability. We consider that elasticity may set either nonlocal (slip between half-spaces) or local (slip below and near a free surface) interactions. We use a dynamical system approach (Viesca, AGU’14) complemented by solutions for slip rate and state evolution during instability development to determine the preferred sites. When (i) varies and (ii) is fixed or varied, an instability develops where relative rate-weakening is locally or globally strongest (a minimum of i) for both types of elastic interactions. This may or may not coincide with the strongest absolute rate-weakening (a minimum of ii). This indicates that parameter (i) is comparatively dominant in deciding the location of a slip instability. However, fixing (i) and varying (ii), we find that elasticity contributes to determining the preferred site: i.e., nucleation occurs at the local minimum and maximum of (ii) for nonlocal and local interactions, respectively. Also, the number of potential nucleation sites increases if the constituent wavelengths of parameter variation are small compared to a characteristic lengthscale for the developing instability. We find that the finite number of densely spaced preferential sites can complicate the prior determination of the location of instability.