Parametric-historic Procedure for Probabilistic Seismic Hazard Analysis Part I: Estimation of Maximum Regional Magnitude mmax

Abstract

—A new methodology for probabilistic seismic hazard analysis (PSHA) is described. The approach combines the best features of the "deductive" (Cornell, 1968) and "historical" (Veneziano et al., 1984) procedures. It can be called a "parametric-historic" procedure.¶The maximum regional magnitude m _max is of paramount importance in this approach and Part I of our work presents some of the statistical techniques which can be used for its evaluation. The work is an analysis of parametric procedures for the evaluation of m _max, when the form of the magnitude distribution is specified. For each of the formulae given there are notes on its origin, assumptions made of its derivation, and some comparisons. The statistical concepts of bias and variance are considered for each formula, and appropriate expressions for these are also given. Also, following Knopoff and Kagan (1977), we shall demonstrate why there must be a finite upper bound to the largest seismic event if the Gutenberg-Richter frequency-magnitude relation is accepted.