Abstract

The Wells and Coppersmith (1994) M-log A data set for continental earthquakes (where M is moment magnitude and A is fault area) and the regression lines derived from it are widely used in seismic hazard analysis for estimating M, given A. Their relations are well determined, whether for the full data set of all mechanism types or for the subset of strike-slip earthquakes. Because the coefficient of the log A term is essentially 1 in both their relations, they are equivalent to constant stress-drop scaling, at least for M ≤ 7, where most of the data lie. For M > 7, however, both relations increasingly underestimate the observations with increasing M. This feature, at least for strike-slip earthquakes, is strongly suggestive of L-model scaling at large M. Using constant stress-drop scaling (Δσ = 26.7 bars) for M ≤ 6.63 and L-model scaling (average fault slip = αL, where L is fault length and α = 2.19 &times 10-5) at larger M, we obtain the relations  
\[\mathbf{M}=\mathrm{log}{\ }A+3.98{\pm}0.03,{\ }A{\leq}537{\ }\mathrm{km}^{2}\]
and  
\[\mathbf{M}=4{/}3{\ }\mathrm{log}{\ }A+3.07{\pm}0.04,{\ }A{>}537{\ }\mathrm{km}^{2}.\]

These prediction equations of our bilinear model fit the Wells and Coppersmith (1994) data set well in their respective ranges of validity, the transition magnitude corresponding to A = 537 km2 being M = 6.71.

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