Classification of seismic patterns in a hierarchical model of rupture: a new phase diagram for seismicity

Abstract

SUMMARY I present a detailed description of the temporal properties of seismicity in a hierarchical model of rupture incorporating healing and faulting. At the microscopic scale, a stochastic process controls transitions between a solid and a broken state with respect to the local stress. From the distribution of broken elements, geometric rules of interaction determine the state of fracturing of domains of larger dimensions and the shape of the stress redistribution. Then, any point in space evolves with respect to its state of stress and its state of fracturing measured at different length scales. Applied to a single fault zone under a constant loading rate, this model of seismicity reproduces the main characteristics of the seismic catalogues: Gutenberg‐ Richter law for the magnitude‐frequency relationship, Omori law for the aftershock decay rate, clustering of major events, swarms of earthquakes, seismicity of creeping segment and seismic noise. I infer that the control parameter is the dimensionless parameter A, the ratio between a characteristic time of healing and a characteristic time of loading. Following the magnitude of A, different seismic scenarios emerge: if A ≈ 1, the system is in a critical state and largest events can occur over a wide range of timescales (e.g. clustering of major events); if A 1, the system is in subcritical states controlled by healing and the fault zone may be creeping. One particular feature is that the amplitude of the stress stored in the fault zone decreases and the frequency of large events increases as the critical state is approached. This can be interpreted as a weakening process. I propose a new phase diagram of seismicity to illustrate an alternative to the classical seismic cycle picture.