Comparison of Earthquake Scaling Relations Derived from Data of the Instrumental and Preinstrumental Era

Abstract

Estimates of surface rupture displacement and magnitude for crustal earthquakes from the preinstrumental era (pre-1900) tend to be greater than the corresponding estimates derived from modern scaling relations. We investigate this tendency using an expanded and updated version of the earthquake dataset of Wells and Coppersmith (1994) to fit regression relations of moment magnitude on surface rupture length and rupture area and average surface displacement on surface rupture length. Separate relations are fitted to preinstrumental and instrumental data and the results compared to the equivalent relations of Wells and Coppersmith. We find that our relations for instrumental data remove some, but not all, of the differences between the preinstrumental data and the relations of Wells and Coppersmith. We attribute the remaining differences largely to natural censoring of surface displacements less than about 1 m and surface rupture lengths less than about 5 km from the dataset for the preinstrumental era because regressions constructed from similarly censored instrumental data are indistinguishable from the preinstrumental regressions. Since the regressions for our censored instrumental data (i.e., restricted to moderate to large earthquakes) are different from regressions for our complete dataset of instrumental earthquakes and from the regressions of Wells and Coppersmith (both with a larger proportion of small-to-moderate earthquakes), the results may indicate that large earthquakes have different scaling relationships from those of smaller earthquakes.