Spatiotemporal Analyses of Earthquake Productivity and Size Distribution: Observations and Simulations
We use relocated catalogs of microearthquakes to investigate earthquake interaction along sections of the Sargent, Calaveras, and San Andreas faults in California. We examine the stress dependence of seismicity rate change along the three fault segments and find that the seismicity rate following a mainshock decays approximately as 1/time, the duration of the aftershock activity seems to be independent of distance from the mainshock, and the seismicity rate at lag times of up to about 100 sec is nearly constant. In the San Andreas and the Calaveras catalogs, where the return of the seismicity rate to the background level is well resolved, we find that the return to the background in the distance range of 1–2 rupture radii from a previous earthquake is preceded by a period during which the seismicity rate falls about 30% below the background rate. We also examine the effect of a stress step on earthquake size distribution along these faults and find that the exponent of the power-law distribution of earthquake magnitudes within 104 sec of a previous earthquake is significantly lower than that of the long term. While the 1/time decay of seismicity rate, the independence of aftershock duration from distance from the mainshock, and the constant seismicity rate at short lag times are predicted by Dieterich's (1994) model, the decrease of seismicity rate below the background level and the changes in earthquake size distribution are not.For comparison with our observations, we simulate earthquake activity on an inherently discrete fault model that is governed by an approximate constitutive friction law similar to the one used by Dieterich (1994). We find that the observed response of earthquake productivity and size distribution to a stress step are produced by these simulations. The effect of the mainshock is not only to raise the local seismicity rate, but also to systematically modify the earthquake size distribution. This is because fault patches that are near failure at the time of the stress step are strengthened, whereas fault patches that at the same time were far from failure are weakened. As a result, similar to what is observed for the Calaveras and the San Andreas segments, late during the aftershock sequence the seismicity rate may decrease below the background rate. We suggest that the time-dependent modification of the earthquake size distribution by a stress step can explain observations of lower b-values immediately following a stress step.