Interactions and triggering in a 3‐D rate‐and‐state asperity model

We present a 3‐D continuous quasi‐dynamic rate‐and‐state model of multiple seismic asperities forced by surrounding aseismic creep and motivated by observations of coplanar multiplets. Our model allows to study the physics of interactions among a set of asperities. First, we show that the amount of interactions and clustering, characterized by the Omori law and interevent time distribution, depends on how far the system is from a critical density of asperities, which is related to the friction properties of the barriers separating the sources. This threshold controls the ability of a population of asperities to destabilize the creeping barriers between them and therefore determines whether dynamic sequences including several asperities in the same event might occur, in agreement with what is expected from observed magnitude‐frequency distributions. Therefore, the concept of critical density of asperity provides a mechanical interpretation of statistical properties of seismicity. As an illustration, we used our numerical results in the specific case of Parkfield in the period preceding the M w 6, 2004 earthquake, in order to infer the steady state friction parameter ( a − b ) characterizing the creep of this part of the San Andreas Fault. We estimate a value of ( a − b ) that locally exceeds 0.001, which is in the upper range of what has already been proposed for the postseimic period of the M w 6, 2004 Parkfield earthquake.