Suppression of large earthquakes by stress shadows: A comparison of Coulomb and rate‐and‐state failure

Stress shadows generated by California's two most recent great earthquakes (1857 Fort Tejon and 1906 San Francisco) substantially modified 19th and 20th century earthquake history in the Los Angeles basin and in the San Francisco Bay area. Simple Coulomb failure calculations, which assume that earthquakes can be modeled as static dislocations in an elastic half‐space, have done quite well at approximating how long the stress shadows, or relaxing effects, should last and at predicting where subsequent large earthquakes will not occur. There has, however, been at least one apparent exception to the predictions of such simple models. The 1911 M >6.0 earthquake near Morgan Hill, California, occurred at a relaxed site on the Calaveras fault. We examine how the more complex rate‐and‐state friction formalism based on laboratory experiments might have allowed the 1911 earthquake. Rate‐and‐state time‐to‐failure calculations are consistent with the occurrence of the 1911 event just 5 years after 1906 if the Calaveras fault was already close to failure before the effects of 1906. We also examine the likelihood that the entire 78 years of relative quiet (only four M ≥6 earthquakes) in the bay area after 1906 is consistent with rate‐and‐state assumptions, given that the previous 7 decades produced 18 M ≥6 earthquakes. Combinations of rate‐and‐state variables can be found that are consistent with this pattern of large bay area earthquakes, assuming that the rate of earthquakes in the 7 decades before 1906 would have continued had 1906 not occurred. These results demonstrate that rate‐and‐state offers a consistent explanation for the 78‐year quiescence and the 1911 anomaly, although they do not rule out several alternate explanations.