An Empirical Model for Earthquake Probabilities in the San

The moment magnitude M 7.8 earthquake in 1906 profoundly changed the rate of seismic activity over much of northern California. The low rate of seismic activity in the San Francisco Bay region (SFBR) since 1906, relative to that of the preceding 55 yr, is often explained as a stress-shadow effect of the 1906 earthquake. However, existing elastic and visco-elastic models of stress change fail to fully account for the duration of the lowered rate of earthquake activity. We use variations in the rate of earthquakes as a basis for a simple empirical model for estimating the probability of M 6.7 earthquakes in the SFBR. The model preserves the relative magnitude distribution of sources predicted by the Working Group on California Earthquake Probabilities’ (WGCEP, 1999; WGCEP, 2002) model of characterized ruptures on SFBR faults and is consistent with the occurrence of the four M 6.7 earthquakes in the region since 1838. When the empirical model is extrapolated 30 yr forward from 2002, it gives a probability of 0.42 for one or more M 6.7 in the SFBR. This result is lower than the probability of 0.5 estimated by WGCEP (1988), lower than the 30-yr Poisson probability of 0.60 obtained by WGCEP (1999) and WGCEP (2002), and lower than the 30-yr time-dependent probabilities of 0.67, 0.70, and 0.63 obtained by WGCEP (1990), WGCEP (1999), and WGCEP (2002), respectively, for the occurrence of one or more large earthquakes. This lower probability is consistent with the lack of adequate accounting for the 1906 stress-shadow in these earlier reports. The empirical model represents one possible approach toward accounting for the stress-shadow effect of the 1906 earthquake. However, the discrepancy between our result and those obtained with other modeling methods underscores the fact that the physics controlling the timing of earthquakes is not well understood. Hence, we advise against using the empirical model alone (or any other single probability model) for estimating the earthquake hazard and endorse the use of all credible earthquake probability models for the region, including the empirical model, with appropriate weighting, as was done in WGCEP (2002).