Earthquake statistics at Parkfield: 2. Probabilistic forecasting and testing

In paper 1 (Schorlemmer et al., 2004) we showed that the spatial b value (of the Gutenberg-Richter relation) distribution at the Parkfield segment of the San Andreas fault remained stationary for the past 35 years. In this paper (paper 2) we extend those results, construct two probabilistic forecasts (H-1 with a spatially varying b value and H-2 with a uniform b value), and test these hypotheses against each other. Both hypotheses use a spatially varying seismicity level ( a value) determined from past seismicity. We used a range of sampling parameters ( magnitude threshold, cell size, etc.) to assure robust results. We found that in most of the tests, hypothesis H-1 showed a higher likelihood than H-2, although both are a poor approximation to the seismicity data. The most positive results for H-1 are obtained for testing magnitude ranges down to M = 1.5 and with sampling radii as defined in paper 1 as appropriate for Parkfield. The superior performance of H-1 suggests that spatially varying b values should be considered in earthquake forecasts.