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Magnitude of the largest possible earth quake M max
In PSHA, Mmax usually refers to the magnitude of the largest earthquake a seismic source is capable of producing. Alternatively, some authors suggest a formal smoothing of the FMD truncated intherangeoflargemagnitudes(MainandBurton,1984;Kagan,1991),preservingthepossibility of larger magnitudes. However, Pisarenko et al. (2010) put forward the definition of Mmax as the maximum for a given future time interval. The following material is restricted to the definition traditionally used in PSHA. The estimation of Mmax is crucial for seismic hazard analysis because large earthquakes produce the most severe ground motions and dominate the hazard at large return periods. The available methods for estimating Mmax are classified as either deterministic or probabilistic. Deterministic methods. The most frequently used methods of this category are those based on empirical relationships between the magnitude and the physical dimensions of the ruptured area (Kanamori and Anderson, 1975). Fault rupture length has been extensively used for estimating the earthquake magnitude, and numerous studies aimed at investigating the correlation between magnitudeandfaultrupturelength(e.g. Tocher,1958;Mark,1977;Bonillaetal.,1984;Wellsand Coppersmith, 1994) have demonstrated the general nature of these relationships. As seismic moment is proportional to fault rupture area, it appears that magnitude would be more fundamentally related to fault rupture area than fault rupture length. The relationships in terms of fault rupture area(e.g. Geller,1976;Wyss,1979;Singhetal.,1980;Wells and Coppersmith,1994) demonstrate smaller variations compared with the relations of fault rupture length. However, any attempt to specify the rupture scenario for a future earthquake is associated with considerable uncertainties that inevitably propagate to Mmax estimates.
ControversiesoftheCornell-McGuiremethod
Despite significant development in the Cornell-McGuiremethod,adegree of controver syremains, that requires attention and further research. Several aspects of the Cornell-McGuire method are subject to criticism,among which are the treatment of uncertainties (e.g. Kl¨ugel,2008;2011),and the use of logic tree formalism (e.g. Krinitzsky, 1995; 2003; Casta˜nos and Lomnitz, 2002). In addition,some authors have raised question on the correctness of the mathematical foundations of the method (e.g. Wang and Zhou, 2007; Wang, 2009). The upper bound of a hazard curve has been indicated as an absent piece of PSHA (Bommer, 2002), and such absence has led to extremely inconsistent hazard assessments for very low probabilities of excee dance (Steppetal.,2001;Corradini,2003;Stamatakos,2004;Kl¨ugel,2005). The main factor contributing to seismic hazard assessments at low probabilities is ground motion variability. The log-normal distribution commonly used to model ground motion variability is unbounded, and, as a result, unrealistic high values of ground motion parameters are encountered when very low probabilities are considered in the analysis. Recently, a number of devastating earthquakes have occurred in unexpected locations (Ellsworth, 2012), in particular the 2011 Tohoku earthquake. Such events have stimulated debate on how adequate the available seismic hazard maps and the methods applied for their preparation were (e.g. Stein et al., 2011; 2012; Hanks et al., 2012; Stirling, 2012), emphasising the necessity of testing the seismic hazard assessments with observations. The results of the GSHAP (1992-1999) have been subjected to systematic tests. Kossobokov and Nekrasova (2012) compared the shaking predicted by the GSHAP map (Giardini et al., 1999) withtheshakingobservedduringstrongearthquakesthatoccurredin2002-2009. Wyssetal.(2012) have performed a similar comparison for the number of casualties. The authors of these studies concluded that both tested quantities have been severely underestimated by the GSHAP, and that the methods applied by this program therefore require reassessment and modifications.
1 Introduction
1.1 Introduction and background
1.2 Deterministic Seismic Hazard Analysis
1.3 Probabilistic Seismic Hazard Analysis
1.4 The Cornell-McGuire method
1.5 Parameters of seismic regime
1.6 Controversies of the Cornell-McGuire method
2 Effect of alternative distributions of ground motion variability on results of probabilistic seismic hazard analysis
2.1 Abstract
2.2 Introduction
2.3 Methods
2.4 Results and discussion
2.5 Implication for Probabilistic Seismic Hazard Analysis
2.6 Conclusion
3 Estimation of the upper bound of seismic hazard curve by using the generalized extreme value distribution
3.1 Abstract
3.2 Introduction
3.3 The Cornell-McGuire procedure
3.4 Generalised extreme value distribution
3.5 Applied procedure and data
3.6 Results and discussion
3.7 Conclusion
4 OnAnisotropicAttenuationLawofModifiedMercalliIntensity
4.1 Abstract
4.2 Introduction
4.3 Applied models
4.4 Case studies
4.5 Conclusion
5 Comparative study of three probabilistic methods for seismic hazard analysis: Case studies of Sochiand Kamchatka
5.1 Abstract
5.2 Introduction
5.3 Materials and Methods
5.4 Results and discussion
5.5 Conclusion
6 Concluding remarks
