M–logA Models and Other Curiosities

Abstract Magnitude ( M )–log area ( A ) relations have been the focus of considerable research in the past two decades because of their importance in estimating moment magnitude M for earthquake probability calculations and seismic‐hazard analysis. For M W , there is a strong consensus for constant stress‐drop scaling. For the larger earthquakes ( M >7) that dominate the moment balancing in continental crust, the L ‐model scaling employed by Hanks and Bakun (2002, 2008) involves fault slip growing with fault length L when L > W ∼15  km or so, requiring that static stress drops increase with increasing fault slip. Constant stress‐drop representations of the same larger‐earthquake data, such as Shaw (2009, 2013), require slip at depths significantly greater than W ∼15  km. Available evidence supports neither of these requirements leaving us perplexed as to how large‐earthquake ruptures initiate and propagate in continental crust. Deep slip M –log A models that involve an unknown amount of seismic moment/earthquake slip at unknown depths> W are not appropriate for use in earthquake probability studies governed by shallow‐slip (depths≤ W ) seismic moment/earthquake slip balancing, such as those in California during the twenty‐first century.