Evidence for a constant b‐value above magnitude 0 in the southern San Andreas, San Jacinto and San Miguel Fault Zones, and at the Long Valley Caldera, California

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Abstract
The cumulative b‐value (the slope of the Gutenberg — Richter relationship between earthquake occurrence rate and magnitude) is commonly found to be constant (∼1). Network catalogues, however, reveal a decrease at small magnitudes (< 3). Some recent studies have suggested that this decrease in b‐value is not just an artifact of catalogue incompleteness, but that small earthquakes are really not as numerous as a constant b‐value extrapolated from larger events would predict. Brune & Allen [1967] recorded microseismicity in both the San Andreas and San Jacinto fault zones in southern California, calculating that they were complete to magnitude 0. Reyes et al. [1975] performed a similar study of the San Miguel fault zone, Baja California, estimating completeness above magnitude −0.5. We compare the results of these studies with the occurrence rates of earthquakes on the same faults recorded by the Southern California and RESNOR seismic networks. The observed microseismicity rates are in good agreement with the rates predicted by extrapolating the b‐values of the larger earthquakes. In a new microseismicity survey at the Long Valley caldera, Mammoth Lakes, California, microearthquakes were recorded and counted within 24 km of stations CLK and CHS. This study is estimated to be complete above 0.6 M at CLK and 0.9 M at CHS, and the microseismicity rates are found to be in good agreement with the rate predicted by extrapolating the b‐value from the local network recorded seismicity. The constant b‐value in the magnitude range 0 to 5 observed in all four areas considered is consistent with a scale invariant earthquake rupture process.