Earthquake Nucleation on Faults With Heterogeneous Frictional Properties, Normal Stress

Abstract

We examine the development of an instability of fault slip rate. We consider a slip rate and state dependence of fault frictional strength, in which frictional properties and normal stress are functions of position. We pose the problem for a slip rate distribution that diverges quasi‐statically within finite time in a self‐similar fashion. Scenarios of property variations are considered and the corresponding self‐similar solutions found. We focus on variations of coefficients, a and b, respectively, controlling the magnitude of a direct effect on strength due to instantaneous changes in slip rate and of strength evolution due to changes in a state variable. These results readily extend to variations in fault‐normal stress, σ, or the characteristic slip distance for state evolution, Dc. We find that heterogeneous properties lead to a finite number of self‐similar solutions, located about critical points of the distributions: maxima, minima, and between them. We examine the stability of these solutions and find that only a subset is asymptotically stable, occurring at just one of the critical point types. Such stability implies that during instability development, slip rate and state evolution can be attracted to develop in the manner of the self‐similar solution, which is also confirmed by solutions to initial value problems for slip rate and state. A quasi‐static slip rate divergence is ultimately limited by inertia, leading to the nucleation of an outward expanding dynamic rupture: asymptotic stability of self‐similar solutions then implies preferential sites for earthquake nucleation, which are determined by distribution of frictional properties.

Numerical and experimental simulation of fault reactivation and earthquake rupture applied to induced seismicity in the Groningen gas field

“…the sedimentary layering), the length-scale of the induced stress perturbation, and the typical nucleation length-scales of the faulting process. If these length-scales are of the same order, frictional variability may have a large effect on the earthquake dynamics, (Ray & Viesca, 2017), as was also observed in our study. Incorporation of frictional heterogeneity along fault subjected to anthropogenic loading will lead to improved understanding of the slip behavior as well as potential rupture sizes, and the potential for rupture to propagate outside its nucleation area into other fault lithologies.…”

“…Roughness is expected to lead to a more heterogeneous stress state on the fault. I suggest further modeling to investigate the minimum length scale (with respect to the critical nucleation length and process zone size) at which variations in lithology and stress may become important (Ray & Viesca, 2017;Ray & Viesca, 2019), using the nucleation length-scales obtained in Chapter 6 and applying stress field variability on much larger or smaller length-scales.…”

“…the critical nucleation length. A modeling study by Ray & Viesca (2017) showed how sliding on a fault with frictional variability at length-scales much smaller becomes comparable to the behavior for a frictionally homogeneous fault. In the large-scale experiments, multiple patches with different lengths and lithologies may be included under different normal stresses to study the macroscopic fault response as a function of e.g.…”

Earthquake Nucleation Size: Evidence of Loading Rate Dependence in Laboratory Faults

“…By using a finite element model to match the observed fringes, we show that they seem to correspond to zones of high coulomb stresses, where the nucleation is thus likely to initiate (see Figure ). Previous studies already showed that the initial stress distribution (N. Kato & Hirasawa, ) and frictional parameters a and b (Kawamura & Chen, ; Ray & Viesca, ) would influence the rupture nucleation, but the role of the loading rate was not clear. In more recent studies, Xu et al () who observed a similar negative dependence of Lc with showed that the spatial distribution of the nucleation zones of stick‐slip events were also influenced by .…”

Earthquake Initiation From Laboratory Observations and Implications for Foreshocks

“…Heterogeneity is a key part of an increasing number of numerical models relevant to earthquake initiation (e.g., Hillers et al, 2006;Luo & Ampuero, 2018;Ray & Viesca, 2017;Skarbek et al, 2012;Tal et al, 2018). Studies that include creeping sections show nucleation that preferentially occurs at the transition between creeping and locked fault sections (Kaneko & Lapusta, 2008;Tse & Rice, 1986) or due to the coalescence of creeping fronts on a 2-D fault (Chen & Lapusta, 2009;Kaneko & Ampuero, 2011;Schaal & Lapusta, 2019).…”