Estimation of attenuation relations for strong-motion data allowing for individual earthquake magnitude uncertainties

Standard errors of earthquake magnitudes are routinely calculated and vary appreciably between earthquakes. However, the uncertainties of magnitude determination are usually ignored in regression models of strong ground motion as a function of magnitude and distance from the earthquake source. This practice has the potential to bias estimates of strong ground motion. A method is given for taking account of the uncertainty of each magnitude determination in fitting such models. It extends previous methods in which the error variance is partitioned into between-earthquake and within-earthquake components. It allows for further decomposition of the between-earthquake component into a part attributable to magnitude uncertainties and a part attributable to other causes. The method has been applied to the well-known attenuation data of Joyner and Boore (1981). The Mw determinations in this dataset fall into two subsets with distinctly different levels of precision, namely, those determined directly and those inferred from values of ML. It is shown that most of the between-earthquake component of variance can be attributed to the relatively low precision of the magnitudes in the latter subset.