A possible mechanism for aftershocks: time-dependent stress relaxation in a slider-block model

Abstract

SUMMARY We propose a time‐dependent slider‐block model which incorporates a time‐to‐failure function for each block dependent on the stress. We associate this new time‐to‐failure mechanism with the property of stress fatigue. We test two failure time functions including a power law and an exponential. Failure times are assigned to ‘damaged’ blocks with stress above a damage threshold, σW and below a static failure threshold, σF. If the stress of a block is below the damage threshold the failure time is infinite. During the aftershock sequence the loader‐plate remains fixed and all aftershocks are triggered by stress transfer from previous events. This differs from standard slider‐block models which initiate each event by moving the loader‐plate. We show the resulting behaviour of the model produces both the Gutenberg–Richter scaling law for event sizes and the Omori’s scaling law for the rate of aftershocks when we use the power‐law failure time function. The exponential function has limited success in producing Omori’s law for the rate of aftershocks. We conclude the shape of the failure time function is key to producing Omori’s law.

Power-law rheology controls aftershock triggering and decay

“…The observed time decaying rate of aftershocks can also be an artifact of the ways the rates were constructed and analyzed. The realistic decay rates of aftershocks were observed in a model where an ad hoc power-law stress transfer mechanism was specified58.…”

Viscoelastic Slider Blocks as a Model for a Seismogenic Fault

“…Purely elastic slider-block models often lack these aftershock patterns, reducing the applicability of these models to real-life earthquake forecasting or risk assessments. It is because of this that recent studies have introduced slider-block models with additional components or processes to better resemble seismologic observations, primarily through the introduction of physical properties such as viscoelasticity [19,[26][27][28][29][30][31]. The addition of viscoelastic components to existing slider-block models serves to recreate the physical properties of the Earth's crust along a seismogenic fault, in the hopes of recreating realistic aftershock sequences following a sufficiently large event.…”

Record-Breaking Intervals: Detecting Trends in the Incidence of Self-Similar Earthquake Sequences

“…This suggests that earthquake (mainshock)-triggering processes are dominated by sequences of numerous small earthquakes, more so than one or two large events. This further suggests a connection between PSA and elevated seismic hazard based on contemporary failureunder-stress and ''stress corrosion'' models in which micro-failures (small earthquakes) occur, weakening the material, at a rate related to the local ratio of applied shear stress to material strength (MICHALSKE and FRIEMAN, 1983;SCHOLZ, 2012;GRAN et al, 2012;DIETERICH, 1978). At the same time, dislocations along the fault surface (from past failures or earthquakes) heal under compressive stress (LI et al, 2003;MARONE et al, 1995).…”