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 mmax 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 mmax, 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.

[1]  Giuliano F. Panza,et al.  Multi-scale seismicity model for seismic risk , 1997, Bulletin of the Seismological Society of America.

[2]  Max Wyss,et al.  Estimating maximum expectable magnitude of earthquakes from fault dimensions , 1979 .

[3]  A. Kijko,et al.  An introduction to mining seismology , 1994 .

[4]  S. K. Singh,et al.  Expected earthquake magnitude from a fault , 1980 .

[5]  J. Xanthakis.  Possible periodicities of the annually released global seismic energy ( M ≧ 7.9) during the period 1898-1971—reply , 1982 .

[6]  John M. Nordquist,et al.  Theory of largest values applied to earthquake magnitudes , 1945 .

[7]  Thomas V. McEvilly,et al.  Recurrence models and Parkfield, California, earthquakes , 1984 .

[8]  G. Dargahi‐Noubary.  A procedure for estimation of the upper bound for earthquake magnitudes , 1983 .

[9]  D. P. Schwartz,et al.  Fault behavior and characteristic earthquakes: Examples from the Wasatch and San Andreas Fault Zones , 1984 .

[10]  V. Pisarenko,et al.  Statistical estimation of seismic hazard parameters: Maximum possible magnitude and related parameters , 1996, Bulletin of the Seismological Society of America.

[11]  K. Aki,et al.  Spatial and temporal correlation between coda Q and seismicity in China , 1988 .

[12]  David M. Perkins,et al.  Treatment of Parameter Uncertainty and Variability for a Single Seismic Hazard Map , 1993 .

[13]  J. Enrique Luco,et al.  Consequences of slip rate constraints on earthquake occurrence relations , 1983 .

[14]  R. Tate,et al.  Unbiased Estimation: Functions of Location and Scale Parameters , 1959 .

[15]  Haresh C. Shah,et al.  Utilization of geophysical information in Bayesian seismic hazard model , 1984 .

[16]  C. Cornell.  Engineering seismic risk analysis , 1968 .

[17]  G. Papadopoulos,et al.  Evidence for periodic seismicity in the inner Aegean seismic zone , 1987 .

[18]  G. R. Toro,et al.  Model of Strong Ground Motions from Earthquakes in Central and Eastern North America: Best Estimates and Uncertainties , 1997 .

[19]  K. Kaila,et al.  Model of earthquake-energy periodicity in the Alpide-Himalayan seismotectonic belt , 1986 .

[20]  Stewart w. Smith,et al.  Determination of maximum earthquake magnitude , 1976 .

[21]  P. Burton.  Seismic risk in southern Europe through to India examined using Gumbel's third distribution of extreme values , 1979 .

[22]  O. Nuttli,et al.  Earthquake magnitude scales , 1974 .

[23]  C. Lomnitz,et al.  A Model for the Occurrence of Large Earthquakes , 1966, Nature.

[24]  David A. Rhoades,et al.  On the handling of uncertainties in estimating the hazard of rupture on a fault segment , 1994 .

[25]  Kenneth W. Campbell,et al.  BAYESIAN ANALYSIS OF EXTREME EARTHQUAKE OCCURRENCES. PART I. PROBABILISTIC HAZARD MODEL , 1982 .

[26]  D. Wells,et al.  New empirical relationships among magnitude, rupture length, rupture width, rupture area, and surface displacement , 1994, Bulletin of the Seismological Society of America.

[27]  Maximum likelihood estimation of Gutenberg-Richterb parameter for uncertain magnitude values , 1988 .

[28]  Application of the extreme magnitude distributions to incomplete earthquake files , 1987 .

[29]  D. Rhoades.  Estimation of the Gutenberg-Richter relation allowing for individual earthquake magnitude uncertainties , 1996 .

[30]  R. Muir-Wood,et al.  From global seismotectonics to global seismic hazard , 1993 .

[31]  K. Shimazaki,et al.  Earthquake frequency distribution and the mechanics of faulting , 1983 .

[32]  P. Burton,et al.  Physical links between crustal deformation, seismic moment and seismic hazard for regions of varying seismicity , 1984 .

[33]  Luis Esteva,et al.  Statistics of small earthquakes and frequency of occurrence of large earthquakes along the Mexican subduction zone , 1983 .

[34]  Andrzej Kijko,et al.  A Modified Form of the First Gumbel Distribution Model for the Occurrence of Large Earthquakes , 1983 .

[35]  K. Oike,et al.  ON FEATURES OF SPATIAL AND TEMPORAL VARIATION OF SEISMICITY BEFORE AND AFTER MODERATE EARTHQUAKES , 1989 .

[36]  S. Turnovsky,et al.  A Statistical Survey of Earthquakes in the Main Seismic Region of New Zealand , 1964 .

[37]  H. Kanamori,et al.  Temporal variation of large intraplate earthquakes in coupled subduction zones , 1989 .

[38]  Robin K. McGuire,et al.  Effects of temporal variations in seismicity on seismic hazard , 1981 .

[39]  Andrzej Kijko,et al.  Estimation of earthquake hazard parameters from incomplete data files. Part II. Incorporation of magnitude heterogeneity , 1992 .

[40]  D. Papastamatiou,et al.  Incorporation of crustal deformation to seismic hazard analysis , 1980 .

[41]  Douglas S. Robson,et al.  Estimation of a truncation point , 1964 .

[42]  A. Frankel.  Mapping Seismic Hazard in the Central and Eastern United States , 1995 .

[43]  Application of the extreme value approaches to the apparent magnitude distribution of the earthquakes , 1985 .

[44]  L. Mcginnis,et al.  Periodic energy release in the New Madrid seismic zone , 1986 .