Mapping the frequency‐magnitude distribution in asperities: An improved technique to calculate recurrence times?

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Abstract
We hypothesize that highly stressed asperities may be defined by mapping anomalously lowbvalues. Along the San Andreas fault near Parkfield the asperity under Middle Mountain, with itsb=0.46, can be distinguished from all other parts of the fault surface. Likewise, along the Calaveras fault the northern asperity of the Morgan Hill 1984 (M6.2) rupture can be identified by its lowbof 0.5 as a high stress patch along the fault. We add further evidence to the observations that thebvalue of the frequency‐magnitude relationship of earthquakes is inversely proportional to stress by showing that it decreases with depth in the Parkfield segment of the San Andreas and along the Calaveras fault. In both of these areas,bvalues above and below 5 km depth are ∼1.2 and 0.8, respectively. We propose that probabilistic recurrence timesTr, based on the seismicity parametersaandb, should be calculated from their values within asperities only, instead of from the values of the entire rupture area of the maximum expected earthquake. The strong patches on faults control the time of rupture because they are capable of accumulating larger stresses than the rest of the fault zone, which slips along passively when an asperity breaks. Therefore no information onTris contained in the passive fault segments, only in the asperities. At Parkfield the probabilistic estimates ofTrderived from the data in the whole rupture and in the asperity only are 72 (−18/+24) and 23 (−12/+18) years, respectively, compared to the historically observed repeat time of 22 years. At Morgan Hill theTrestimates are 122 (−46/+76) and 78 (−47/+110) years, respectively, compared to the observed repeat time of 72 years.