The Role of Heterogeneities as a Tuning Parameter of Earthquake Dynamics

Abstract

We investigate the influence of spatial heterogeneities on various aspects of brittle failure and seismicity in a model of a large strike-slip fault. The model dynamics is governed by realistic boundary conditions consisting of constant velocity motion of regions around the fault, static/kinetic friction laws, creep with depth-dependent coefficients, and 3-D elastic stress transfer. The dynamic rupture is approximated on a continuous time scale using a finite stress propagation velocity (''quasidynamic model''). The model produces a ''brittle-ductile'' transition at a depth of about 12.5 km, realistic hypocenter distributions, and other features of seismicity compatible with observations. Previous work suggested that the range of size scales in the distribution of strength-stress heterogeneities acts as a tuning parameter of the dynamics. Here we test this hypothesis by performing a systematic parameter-space study with different forms of heterogeneities. In particular, we analyze spatial heterogeneities that can be tuned by a single parameter in two distributions: (1) high stress drop barriers in near-vertical directions and (2) spatial heterogeneities with fractal properties and variable fractal dimension. The results indicate that the first form of heterogeneities provides an effective means of tuning the behavior while the second does not. In relatively homogeneous cases, the fault self-organizes to large-scale patches and big events are associated with inward failure of individual patches and sequential failures of different patches. The frequency-size event statistics in such cases are compatible with the characteristic earthquake distribution and large events are quasi-periodic in time. In strongly heterogeneous or near-critical cases, the rupture histories are highly discontinuous and consist of complex migration patterns of slip on the fault. In such cases, the frequency-size and temporal statistics follow approximately power-law relations.

Collective behavior of earthquakes and faults: Continuum‐discrete transitions, progressive evolutionary changes, and different dynamic regimes

“…The corresponding frequency‐moment statistics have the same form as , obtained by Vere‐Jones [1976] for a critical stochastic branching and Main and Burton [1984] on the basis of maximum entropy considerations. Similar differences in the character of various response functions are produced in simulations with narrow versus wide ROSS [ Zöller et al , 2005a].…”

“…On a finite fault in elastic solid a corresponding regime of ROSS does not exist, since the ROSS can increase only to a maximum value related to the system size. As the density of strong barriers increases beyond the level where they start to coalesce, the barriers and regular fault patches interchange their roles, and the dynamics moves back to the characteristic earthquake behavior with stress drops and recurrence times associated with properties of the barriers [ Zöller et al , 2005a]. The strength change parameter ɛ D has a fuller correspondence to the temperature in the context of phase diagrams, including the regime above T c .…”

Quasi‐dynamic modeling of seismicity on a fault with depth‐variable rate‐ and state‐dependent friction

“…The distribution of the constitutive parameters is uniform along strike and varies either linearly or stepwise with depth. Thus the system investigated here is far less complex than the highly disordered systems studied by some investigators [e.g., Ben‐Zion , 1996; Zöller et al , 2005a, 2005b]. …”

“…Models adopting static/kinetic friction are not capable of producing aftershock sequences that decay according to the modified Omori law. Aftershocks in models that incorporate static/kinetic friction and creep laws arise solely from the relaxation of stresses in the creeping regions [e.g., Zöller et al , 2005a, 2005b]. In such models aftershocks are concentrated near the edges of creeping segments.…”

Steady-state solutions of rupture propagation in an earthquake simulator governed by rate and state dependent friction

“…In contrast the latter class provides less realistic simulations; these models, however, allow for robust statistics, because a large number of events may be generated. Models of this type, generally labeled as "earthquake simulators" [3,8,11,13,17,18,20,21], become increasingly popular for seismic hazard calculations, since they overcome the problem of small data sets (earthquake catalogs), at least to some degree. The tightrope walk is now to find the most relevant mechanisms that govern the dynamics of the earthquake process and to keep the model as simple as possible, simultaneously.…”