Forecast experiment: Do temporal and spatial b value variations along the Calaveras fault portend M 4.0 earthquakes?

[1] The power law distribution of earthquake magnitudes and frequencies is a fundamental scaling relationship used for forecasting. However, can its slope (b value) be used on individual faults as a stress indicator? Some have concluded that b values drop just before large shocks. Others suggested that temporally stable low b value zones identify future large-earthquake locations. This study assesses the frequency of b value anomalies portending M 4.0 shocks versus how often they do not. I investigated M 4.0 Calaveras fault earthquakes because there have been 25 over the 37-year duration of the instrumental catalog on the most active southern half of the fault. With that relatively large sample, I conducted retrospective time and space earthquake forecasts. I calculated temporal b value changes in 5-km-radius cylindrical volumes of crust that were significant at 90% confidence, but these changes were poor forecasters of M 4.0 earthquakes. M 4.0 events were as likely to happen at times of high b values as they were at low ones. However, I could not rule out a hypothesis that spatial b value anomalies portend M 4.0 events; of 20 M 4 shocks that could be studied, 6 to 8 (depending on calculation method) occurred where b values were significantly less than the spatial mean, 1 to 2 happened above the mean, and 10 to 13 occurred within 90% confidence intervals of the mean and were thus inconclusive. Thus spatial b value variation might be a useful forecast tool, but resolution is poor, even on seismically active faults.