Space-time model for repeating earthquakes and analysis of recurrence intervals on the San Andreas Fault near Parkfield, California

We propose a stochastic model for characteristically repeating earthquake sequences to estimate the spatiotemporal change in static stress loading rate. These earthquakes recur by a cyclic mechanism where stress at a hypocenter is accumulated by tectonic forces until an earthquake occurs that releases the accumulated stress to a basal level. Renewal processes are frequently used to describe this repeating earthquake mechanism. Variations in the rate of tectonic loading due to large earthquakes and aseismic slip transients, however, introduce nonstationary effects into the repeating mechanism that result in nonstationary trends in interevent times, particularly for smaller-magnitude repeating events which have shorter interevent times. These trends are also similar among repeating earthquake sites having similar hypocenters. Therefore, we incorporate space-time structure represented by cubic B-spline functions into the renewal model and estimate their coefficient parameters by maximizing the integrated likelihood in a Bayesian framework. We apply our model to 31 repeating earthquake sequences including 824 events on the Parkfield segment of the San Andreas Fault and estimate the spatiotemporal transition of the loading rate on this segment. The result gives us details of the change in tectonic loading caused by an aseismic slip transient in 1993, the 2004 Parkfield M6 earthquake, and other nearby or remote seismic activities. The degree of periodicity of repeating event recurrence intervals also shows spatial trends that are preserved in time even after the 2004 Parkfield earthquake when time scales are normalized with respect to the estimated loading rate.