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 ma gnitude determination are usually ignored in regression models of stro ng ground motion as a function of magnitude and distance from the eart hquake source. This practice has the potential to bias estimates of st rong ground motion. A method is given for taking account of tile uncer tainty of each magnitude determination in fitting such models. It exte nds previous methods in which the error variance is partitioned into b etween earthquake and within-earthquake components. It allows for furt her decomposition of the between-earthquake component into a part attr ibutable to magnitude uncertainties and a part attributable to other c auses. The method has been applied to the well-known attenuation data of Joyner and Boore (1981). The M-w determinations in this dataset fal l into two subsets with distinctly different levels of precision, name ly, those determined directly and those inferred from values of M-L. I t is shown that most of the between-earthquake component of variance c an be attributed to the relatively low precision of the magnitudes in the latter subset.