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

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.

Determination of Mmax from Background Seismicity and Moment Conservation

“…One common method to estimate M max is simply to use the largest earthquake in the historical record and add 0.5 (Kijko and Graham, 1998;Sokolov et al, 2001). There is no statistical foundation to that approach.…”

Statistical tools for maximum possible earthquake magnitude estimation

“…It can be shown (Kijko and Graham 1998) that the procedure provides an estimator of m max , which, in terms of mean-squared error, is substantially better than the respective T-P estimator described in Section 2.1.1. The drawback of the current procedure is that it requires integration, which for some distribution functions can be performed only numerically.…”

“…From eq. (1), Kijko and Graham (1998) derived an alternative equation, which is approximate, but which demonstrates the required value of m max in a more explicit way (Pisarenko et al 1996) max max max 1 ( )…”

“…(4) provides the estimated value of m max , max m , and in this paper is referred to as the Tate-Pisarenko estimator of m max or in short as T-P. The approximate variance of the T-P estimator, which contains both, aleatory and epistemic components, is of the form (Kijko and Graham 1998) …”

Seismic hazard assessment – a holistic microzonation approach

“…The Guwahati Figure 9 also depicts four broad seismic source zones demarcated by on the basis of spatial seismicity patterns represented by b-value, and fractal correlation dimension of the epicenters overlaid on the regional tectonic framework. predicted the maximum earthquakes in each zone by means of a maximum likelihood method (Kijko, 2004;Kijko and Graham, 1998) that employs a modified form of the standard Gutenberg-Richter relation with an exponential tail of a Gamma function at larger magnitudes taking into account the uncertainty of the b-value. Maximum earthquakes of M w 8.3 and 8.7 could be respectively associated with the Eastern Himalayas and the Shillong zone, which corresponds to the major contributing seismic source zones for Sikkim and Guwahati city (Nath et al, 2008b).…”