Interaction of small repeating earthquakes in a rate and state fault model

Small repeating earthquake sequences can be located very close, for example, the San Andreas Fault Observatory at Depth (SAFOD) target cluster repeaters "San Francisco" and "Los Angeles" are separated by only about 50 m. These two repeating sequences also show closeness in occurrence time, indicating substantial interaction. Modeling of the interaction of repeating sequences and comparing the modeling results with observations would help us understand the physics of fault slip. Here we conduct numerical simulations of two asperities in a rate and state fault model (Chen and Lapusta, JGR, 2009), with asperities being rate weakening and the rest of the fault being rate-strengthening. One of our goals is to create a model for the observed interaction between "San Francisco" and "Los Angeles" clusters. The study of Chen and Lapusta (JGR, 2009) and Chen et al (accepted by EPSL, 2010) showed that this approach can reproduce behavior of isolated repeating earthquake sequences, in particular, the scaling of their moment versus recurrence time and the response to accelerated postseismic creep. In this work, we investigate the effect of distance between asperities and asperity size on the interaction, in terms of occurrence time, seismic moment and rupture pattern. The fault is governed by the aging version of rate-and-state friction. To account for relatively high stress drops inferred seismically for Parkfield SAFOD target earthquakes (Dreger et al, 2007), we also conduct simulations that include enhanced dynamic weakening during seismic events. As expected based on prior studies (e.g., Kato, JGR, 2004; Kaneko et al., Nature Geoscience, 2010), the two asperities act like one asperity if they are close enough, and they behave like isolated asperities when they are sufficiently separated. Motivated by the SAFOD target repeaters that rupture separately but show evidence of interaction, we concentrate on the intermediate distance between asperities. In that regime, the interaction can be quite complex and varying with time. One of the interesting behaviors is the overlapping rupture areas of events that nucleate on separate asperities. Another interesting behavior is alternating between events that rupture a single asperity and events that rupture both asperities at the same time. These and other features lead to variability of moment and recurrence time for individual repeaters consistent with Parkfield target repeaters.