A fundamental question in earthquake physics is whether aftershocks are predominantly triggered by static stress changes (permanent stress changes associated with fault displacement) or dynamic stresses (temporary stress changes associated with earthquake shaking). Both classes of models provide plausible explanations for earthquake triggering of aftershocks, but only the static stress model predicts stress shadows, or regions in which activity is decreased by a nearby earthquake. To test for whether a main shock has produced a stress shadow, we calculate time ratios, defined as the ratio of the time between the main shock and the first earthquake to follow it and the time between the last earthquake to precede the main shock and the first earthquake to follow it. A single value of the time ratio is calculated for each 10 × 10 km bin within 1.5 fault lengths of the main shock epicenter. Large values of the time ratio indicate a long wait for the first earthquake to follow the main shock and thus a potential stress shadow, whereas small values indicate the presence of aftershocks. Simulations indicate that the time ratio test should have sufficient sensitivity to detect stress shadows if they are produced in accordance with the rate and state friction model. We evaluate the 1989 M W 7.0 Loma Prieta, 1992 M W 7.3 Landers, 1994 M W 6.7 Northridge, and 1999 M W 7.1 Hector Mine main shocks. For each main shock, there is a pronounced concentration of small time ratios, indicating the presence of aftershocks, but the number of large time ratios is less than at other times in the catalog. This suggests that stress shadows are not present. By comparing our results to simulations we estimate that we can be at least 98% confident that the Loma Prieta and Landers main shocks did not produce stress shadows and 91% and 84% confident that stress shadows were not generated by the Hector Mine and Northridge main shocks, respectively. We also investigate the long hypothesized existence of a stress shadow following the 1906 San Francisco Bay area earthquake. We find that while Bay Area catalog seismicity rates are lower in the first half of the twentieth century than in the last half of the nineteenth, this seismicity contrast is also true outside of the Bay Area, in regions not expected to contain a stress shadow. This suggests that the rate change is due to a more system wide effect, such as errors in the historical catalog or the decay of aftershocks of the larger 1857 Fort Tejon earthquake.
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