Numerical Modeling of Cascading Foreshocks and Aftershocks in Discrete Fault Network

Earthquakes often come in clusters formed of foreshock-mainshock-aftershock sequences. This clustering is generally thought to result from a cascading process which is commonly modeled using either the phenomenological ETAS model or a stress-based model assuming an earthquake nucleation process governed by Coulomb stress changes and Rate-and-State friction (CRS). In this work, we numerically investigated the foreshock and aftershock sequence in a discrete fault network with rate and state friction law and compared the result with the ETAS model. We set a fault zone consisting of dense fault segments and an off-fault area consisting of sparsely distributed smaller faults in the simulation domain. The CRS simulations are conducted 100 times with 1000 discrete faults with randomly generated fault location, initial velocity, and fault length within the weighted distribution, yielding a Gutenberg-Richter law. The simulations produce realistic foreshocks and aftershocks sequences. Aftershocks occur in the area of increased Coulomb stress and decay following Omori law as observed in nature. Individual foreshock sequences do not show a clear trend, but once stacked, they show an apparent inverse-Omori law acceleration. The prediction from our CRS model can be fitted with the ETAS model. This is not surprising since ETAS incorporates the Omori and Gutenberg-Richter laws. However, our CRS model predicts significantly more foreshocks than would be expected from the ETAS model. This results from the fact that the triggering productivity is lower in the aftershock sequence than in the foreshocks due to the depletion of critically stressed faults in our simulations. In other words, the ETAS is not compatible with the CRS model because Coulomb stress changes result in a time advance (if positive) or delay (if negative). This clustering process is fundamentally different from the additive process assumed in ETAS. As a result, the claim made that foreshocks more frequent than expected based on ETAS imply pre-seismic slip might be incorrect. It could alternatively be a manifestation of the nucleation process.