A Bilinear Source-Scaling Model for M-log A Observations of Continental Earthquakes

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 ū = α L , where L is fault length and α = 2.19 &times 10-5) at larger M , we obtain the relations \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \[\mathbf{M}=\mathrm{log}{ }A+3.98{\pm}0.03,{ }A{\leq}537{ }\mathrm{km}^{2}\] \end{document} and \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \[\mathbf{M}=4{/}3{ }\mathrm{log}{ }A+3.07{\pm}0.04,{ }A{>}537{ }\mathrm{km}^{2}.\] \end{document} 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. Manuscript received 15 April 2001.