Appendix E—Evaluation of Magnitude-Scaling Relationships and Depth of Rupture

Continued use of magnitude-area scaling to estimate earthquake sizes is recommended. Area based on along-strike length and downdip width remains a good measure. Although questions have been raised concerning the depth extent of ruptures during large earthquakes, the seismogenic area remains a useful proxy for the purposes of estimating earthquake sizes. Four relations are examined here in terms of their potential use. A fifth relation, the Somerville (2006) relation, was rejected based on its dependence on trimmed areas from inverse modeling, which introduces an intermediate step of highly nonunique, model, and smoothingdependent processing of the data. The four magnitude-area scaling relations examined for estimating earthquake sizes are (1) Ellsworth-B, (2) Hanks and Bakun (2002), (3) Shaw (2009), and (4) a Wells and Coppersmith-type linear relation between M and log10A. (1) The Ellsworth-B relation is: