Stochastic Approaches in Earthquake Engineering pp 385-427 | Cite as

# Statistical Analysis of Earthquake Catalogs for Seismic Hazard

## Summary

In the use of historical earthquake catalogs for seismic hazard, the main objective is to estimate the rate of earthquakes of various sizes in a region around the site of interest. This is a complicated problem, in part because of deficiencies of the catalog such as missing data, nonuniformity of the scale in which earthquake sizes are measured and errors in reported epicentral locations and magnitudes, in part because earthquake activity is non-Poissonian and varies in space, when not also in time. Standard methods of analysis are simple but often inadequate: they ignore errors in the data, use regressions among size measures as if they were functional relationships, ignore the incomplete part of the catalog, and assume homogeneous Poisson occurrences inside given “seismogenic provinces”. The scope of the present paper is to challenge these assumptions and approximations. In particular, it is proposed that seismicity be represented as the Superposition of a nonhomogeneous Poisson process of main or parent events and a process of secondary and smaller events clustered around the parent earthquakes. Various models of catalog incompleteness are also proposed. Methods aie developed for the identification of secondary events and for the simultaneous estimation of spatially varying recurrence rates of main events and of catalog incompleteness, using any desired portion of the historical record. As a special case, the model includes the assumption of homogeneous Poisson sources. More in general, seismogenic provinces are considered as geographical regions inside which the variation of seismicity possesses some regularity. Other problems addressed in this study are the estimation of earthquake size on a common scale and the automatic identification of quasi-homogeneous earthquake sources. The proposed methods are exemplified through application to Northeastern Italy.

### Keywords

Migration Depression Geophysics Kelly Tudy## Preview

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### References

- Aki, K. (1965), “Maximum Likelihood Estimate of b in the Formula LogN=a-bM and Its Confidence Limits,” Bull. Earthquake Res. Inst., vol. 43, pp. 237–239.Google Scholar
- Aki, K. (1984), “Asperities, Barriers, Characteristic Earthquakes and Strong Motion Prediction,” J. Geophys. Res. Vol. 89, pp. 5867–5872.Google Scholar
- Bender, B. (1983), “Maximum Likelihood Estimation of nitude Grouped Data,” Bull. Seism. Soc. Am. Vol.73, No. 3, pp 831–851Google Scholar
- Benvegnu, F., Carrara, C., Iaccarino, E., Magri, G., Mittempergher, M.,Molin, D., Sennis, C. and Zaffiro, C. (1978), “Considerations on the Safety of Possible Nuclear Installations in Northeastern Italy in Relation to Local Seismotectonics,” Proceedings Specialty Meeting on the 1976 Friuli Earthquake and the Antiseismic Design of Nuclear Installations, CNEN, Rome, Italy.Google Scholar
- Bernardis, G., Giorgetti, F., Nieto, P., Russi, M. and Suhadolc, P. (1976), “Seismicity of the Friuli Venezia Giulia Region,” Boll. Geof. Teor. Appl. Vol. 19, No. 72, pp. 365–375.Google Scholar
- Cattaneo, M., Eva, C., and Merlanti, F. (1981), “Seismicity of Northern Italy: A Statistical Approach,” Boll. Geof. Teor. Appl. Vol. 23, No. 89, pp. 31–42.Google Scholar
- Chiburis, E.F. (1981), “Seismicity, Recurrence Rates, and Regionaliation of the Northeastern United States and Adjacent Southeastern Canada,” NUREG/CR-2309, USNRC, Washington, D.C.Google Scholar
- Efron, B. (1979), “Bootstrap Methods: Another Look at the Jackknife,” The Annals of Statistics Vol.
*7*, No. 1, pp. 1–26.CrossRefMATHMathSciNetGoogle Scholar - Efron, B. (1982), The Jackknife, the Bootstrap and Other Resampling Plans CBMS-NSF Regional Conference Series in Applied Mathematics, Philadelphia.Google Scholar
- Faccioli, E. (1979), “Engineering Seismic Risk Analysis of the Friuli Region,” Boll. Geof. Teor. Appl. Vol.21, No. 83, pp. 173–190.Google Scholar
- Ganse, R.A., Amemiya, Y., and Fuller, W.A. (1983), “Prediction When Both Variables are Subject to Error, with Application to Earthquake Magnitudes,” J. Amer. Statist. Assoc. Vol. 78, No. 384, pp. 761–765.Google Scholar
- Gardner, J.K. and Knopoff, L. (1974), “Is the Sequence of Earthquakes in Southern California, with Aftershocks Removed, Poissonian?,” Bulletin of the Seismological Society of America Vol. 64, No. 5, pp. 1363–1367.Google Scholar
- Howell, B.F. (1979), “The Largest Possible Earthquakes,” Earthquake Notes Vol. 50, No. 3, pp. 23–25.Google Scholar
- Kagan, Y.Y. and Knopoff, L. (1976), “Statistical Search for Non-random Features of the Seismicity of Strong Earthquakes,” Physics of the Earth and Planetary Interiors Vol. 12, pp. 291–318.Google Scholar
- Kagan, Y.Y. and Knopoff, L. (1978), “Statistical Study of the Occurrence
**of**Shallow Earthquakes,” Geophys. J.R. Astr. Soc. Vol. 55, pp. 67–86.Google Scholar - Kanamori, H. (1981), “The Nature of Seismicity Patterns Before Large Earthquakes,” in Earthquake Prediction, an International Review Edited by D.W. Simpson and P.G. Richards, American Geophysical Union, Washington, D.C.Google Scholar
- Kelly, E.J. and Lacoss, R.T. (1969), “Statistical Estimation of Seismicity and Detection Probability,” Semiannual Technical Summary, Seismic Discrimination, Lincoln Laboratory, M. I. T., Lexington, Massachusetts.Google Scholar
- Kijko, A. (1985), “Extreme Value Distribution of Earthquake Magnitude,” Comment, Physics of the Earth and Planetary Interiors Vol. 37, pp. 285–287.CrossRefGoogle Scholar
- Kijko, A. and Sellevoll, M.A. (1981), “Triple Exponential Distribution, a Modified Model for the Occurrence of Large Earthquakes,” Bull. Seism. Soc.Am. Vol. 71, No.
**6**, pp. 2097–2101.Google Scholar - Kulldorff, G. (1961), Estimation from Grouped and Partially Grouped Samples John Wiley and Sons, New York.Google Scholar
- Lee, W.H.K. and Brillinger, D.R. (1979), “On Chinese Earthquake History -An Attempt to Model an Incomplete Data Set by Point Process Analysis,” Pageoph. Vol. 117, pp. 1229–1257.Google Scholar
- Lomnitz-Adler, J. and Lomnitz, C. (1979), “A Modified Form of the Gutenberg-Richter Magnitude-Frequency Relation,” Bull. Seism. Soc. Am., Vol. 69, pp. 1209–1214.Google Scholar
- Merz, H.A. and Cornell, C.A. (1973a), “Aftershocks in Engineering Seismic Risk Analysis,” Research Report R73–25, Dept. of Civil Engineering, M. I. T., Cambridge, Massachusetts.Google Scholar
- Merz, H.A. and Cornell, Ç.A. (1973b), “Seismic Risk Analysis Based on a Quadratic Magnitude-Frequency Law,” Bull. Seism. Soc. Am. Vol. 63, No. 6, pp. 1999–2006.Google Scholar
- Montgomery, D.C. and Peck, E.A. (1982), Introduction to Linear Regression Models John Wiley and Sons, New York.Google Scholar
- Prozorov, A.G. and Dziewonski, A.M. (1982), “a Method of Studying Varitions in the Clustering Property of Earthquakes: Application to the Analysis of Global Seismicity,” Journal of Geophysical Research Vol. 87, No. B4, pp. 2829–2839.Google Scholar
- Richter, C.F. (1958), Elementary Seismology W.H. Freeman and Co., San Francisco.Google Scholar
- Reasenberg, P. (1984), “Second-Order Moment of Central California Seismicity, 1969–1982,” U.S. Geological Survey, Menlo Park.Google Scholar
- Schenk, V. (1983), “On the Problem of Time-Normalization of Earthquake Magnitude-Frequency Relations,” Annales Geophysicae Vol. 1, No. 6, pp. 439–442.Google Scholar
- Schwartz, D.P. and Coppersmith, K.J. (1984), “Fault Behavior and Characteristic Earthquakes: Examples from the Wasatch and San Andreas Faults,” J. Geophys. Res. Vol. 89, No. B7, pp. 5681–5698.Google Scholar
- Shlien, S. and Toksoz, M.N. (1970), “A Clustering Model for Earthquake Occurrences,” Bulletin of the Seismological Society of America Vol. 60, No. 6, pp. 1765–1787.Google Scholar
- Shlien, S. and Toksoz, M.N. (1975), “A Branching Poisson-Markov Model of Earthquake Occurrences,” Geophys. J.R. Astr. Soc.,Vol. 42, pp. 49–59.Google Scholar
- Simpson, D.W. and Richards, P.G. (Eds.) (1981), Earthquake Prediction:.
**An**International Review American Geophysical Union, Washington, D.C.Google Scholar - Slejko, D. and Viezzoli, D. (1984), “Confronto di techniche diverse nel calcolo della scuotibilitâ,” Proceedings Meeting on Objectives and Results of the Seismometric Network in Friuli-Venezia Giulia, Trieste, Italy.Google Scholar
- Stepp, J.C. (1972), “Analysis of Completeness of the Earthquake Sample in the Puget Sound Area and Its Effect ‘cm Statistical Estimates of Earthquake Hazard,”.Proceedings Int. Conf. on Microzonation, Vol. 2, pp. 897–910.Google Scholar
- Stepp, J.C., Rinehart, W.A. and Algermissen, S.T. (1965), “Earthquakes in the United States 1963–64 and an Evaluation of the DetectionGoogle Scholar
- Capability of the United States Seismograph Stations,“ Report Nó 620, Advanced Research Projects Agency, U.S. Dept. of Commerce, Coast and Geodetic Survey, Washington, D.C.Google Scholar
- Tinti, S. and Mulatgia, F. (1985), “Effects of Magnitude Uncertainty on Estimating the Parameters in the Gutenberg-Richter Frequency-Magnitude Law,” Bull. Seism. Soc. Am. Vol. 75, No. 6, pp. 1681–1697.Google Scholar
- Utsu, T. (1961), “A Statistical Study of the Occurrence of Aftershocks,” Geophysical Magazine Tokyo, Vol. 30, pp. 521–605.Google Scholar
- Utsu, T. (1969,1970,1971), “Aftershocks and Earthquake Statistics, Parts Journal of the Faculty of Science, Hokkaido University, Ser. VII, Vol. III, No. 3 (1969), No. 4 (1970), and No. 5 (1971).Google Scholar
- Van Dyck, J. (1986), “Statistical Analysis of Earthquake Catalogs,” Ph.D. Thesis, Dept. of Civil Engineering, MIT, Cambridge, Massachusetts.Google Scholar
- Veneziano, D. and Van Dyck, J. (1985a), Volume 2 (Appendix A) of “Seismic Hazard Methdology for Nuclear Facilities in the Eastern United States,” EPRI, Nuclear Power Division, Palo Alto, California. (Referred to in text as EPRI, 1985 ).Google Scholar
- Veneziano, D. and Van Dyck, J. (1985b), “Seismic Hazard Analysis for the Friuli Region, Part I: Magnitude Conversion and EarthquakeGoogle Scholar
- Clustering,“ Consulting Report, ENEA, Rome, Italy. (Referred to in text as ENEA, 1985).Google Scholar
- Veneziano D. and Van Dyck, J. (1986a), “Estimation of Catalog Incompleteness and Seismicity Parameters for Phase II of the EPRI EasternUnited-States Project,” Consulting Report to Risk Engineering, Inc., Golden, Colorado. (Referred to in text
EPRI, 1986 ).Google Scholar**as** - Veneziano, D. and Van Dyck, J. (1986b), “Seismic Hazard Analysis for the Friuli Region, Part II: Catalog Incompleteness, Seismic Sources, and Recurrence Rates,” Consulting Report, ENEA, Rome, Italy, January 10. (Referred to in text as ENEA, 1986).Google Scholar
- Veneziano, D. and Van Dyck, J. (1986c), “Models of Seismicity and Use of Historical Data in’Earthquake Hazard Analysis,” Proceedings Workshop on Probabilistic Earthquake Hazards Assessment, U.S. Geological Survey, San Francisco, California.Google Scholar
- Veneziano, D. and Pais, A.L. (1986), “Automatic Source Identification Based on Historical Seismicity,” Proceedings 8th European Conference on Earthquake Engineering, Lisbon, Portugal.Google Scholar
- Vere-Jones, D. (1970), “Stochastic Models of Earthquake Occurrence,” Journal of the Royal Statistical Society Vol. 32, No. 1, pp. 1–62.Google Scholar
- Vere-Jones, D., Turnovsky, S., Eiby, G.A., and Davis, R.S. (1964,1965),
**“**Statistical Survey of Earthquakes in the Main Seismic Regions of**New**England, Parts I and II, ” New Zealand Journal of Geology and Geophysics Vol. 7 (1964), pp. 722–744, Vol. 9 (1965), pp. 251–284.Google Scholar - Weichert, D.H. (1980), “Estimation of thé Earthquake Recurrence Para- meters for Unequal Observation Periods for Different Magnitudes,” Bull. Seism. Soc. Am. Vol. 70, pp. 1337–1346.Google Scholar
- Weichert, D.H. and Milne, W.G. (1979), “On Canadian Methodologies of Probabilistic Seismic Hazard Estimation,” Bull. Seism. Soc. Am. Vol. 69, pp. 1549–1566.Google Scholar