Modeling Statistical and Dynamic Features of Earthquakes

Abstract:

The cellular automaton earthquake model by Sacks and Rydelek (1995) is extended to explain spatio-temporal change in seismicity with the regional tectonic stress buildup. Our approach is to apply a simple Coulomb failure law to our model space of discrete cells, which successfully reproduces empirical laws (e.g. Gutenberg-Richter law) and dynamic failure characteristics (e.g. stress drop vs. magnitude and asperities) of earthquakes. Once the stress condition supersedes the Coulomb threshold on a discrete cell, its accumulated stress is transferred to only neighboring cells, which cascades to more neighboring cells to create various size ruptures. A fundamental point here is the cellular view of the continuous earth. We suggest the cell size varies regionally with the maturity of the faults of the region.

Seismic gaps (e.g. Mogi, 1979) and changes in seismicity such as indicated by b-values have been known but poorly understood. There have been reports of magnitude dependent seismic quiescence before large event at plate boundaries and intraplate (Smith et al., 2013). Recently, decreases in b-value for large earthquakes have been reported (Nanjo et al., 2012) as anticipated from lab experiments (Mogi, 1963). Our model reproduces the b-value decrease towards eventual large earthquake (increasing tectonic stress and its heterogeneous distribution). We succeeded in reproducing the cut-off of larger events above some threshold magnitude (M3-4) by slightly increasing the Coulomb failure level for only 2 % or more of the highly stressed cells. This is equivalent to reducing the pore pressure in these distributed cells. We are working on the model to introduce the recovery of pore pressure incorporating the observed orders of magnitude higher permeability fault zones than the surrounding rock (Lockner, 2009) allowing for a large earthquake to be generated. Our interpretation requires interactions of pores and fluids. We suggest heterogeneously distributed patches hardened by dilatancy eventually break down rapidly and generate a large event. Various reports of macroscopic earthquake precursors may be indicative of this break down stage. We will however need observational means sensitive to aquifer changes to quantify the process.