Rank-ordering statistics of extreme events: Application to the distribution of large earthquakes

Journal of Geophysical Research: Solid Earth

Volumn 101, Issue 6, 1996, Pages 13883-13893

  Sornette, D ^a,b,c,d   Knopoff, L ^b,c   Kagan, Y Y ^b,c   Vanneste, C ^a,d  

^a UNIVERSITÉ CÔTE D'AZUR   (France)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

^d CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EARTHQUAKE; POWER LAW DISTRIBUTION; RANK ORDERING; SEISMICITY; STATISTICAL ANALYSIS;

EID: 0030454979     PISSN: 21699313     EISSN: 21699356     Source Type: Journal    
DOI: 10.1029/96jb00177     Document Type: Article

References (26)

1. Aharony, A., and J. Feder (Eds.) Fractals in physics, Physica D, 38 (1-3) 1989.
2. Aki, K., Maximum likelihood estimate of b in the formula log N = a-bm and its confidence limits, Bull. Earthquake Res. Inst. Univ. Tokyo, 43, 237-239, 1965.
3. Bouchaud, J. P., D. Sornette, C. Walter, and J.-P. Aguilar, Taming large events: Optimal portfolio theory for strongly fluctuation assets, J. Math. Finan., in press, 1996.
4. Deemer, W. L., and D. F. Votaw, Estimation of parameters of truncated or censored exponential distributions, Ann. Math. Stat., 26, 498-504, 1955.
5. Dziewonski, A. M., G. Ekstrom, and M. P. Salganik, Centroid-moment tensor solutions for January-March, 1992, Phys. Earth Planet. Inter., 77, 143-150, 1993.
6. Ekstrom, G., and A. M. Dziewonski, Evidence of bias in estimation of earthquake size, Nature, 332, 319-323, 1988.
7. Epstein, B., and M. Sobel, Life testing, J. Am. Stat. Assoc., 48, 486-502, 1953.
8. Gumbel, E. J., Statistics of Extremes, Columbia Univ. Press, New York, 1960.
9. Hill, B. M., A simple general approach to inference about the tail of a distribution, Ann. Stat., 3, 1163-1174, 1975.
10. Hutton, L. K., and L. M. Jones, Local magnitudes and apparent variations in seismicity rates in southern California, Bull. Seismol. Soc. Am., 83, 313-329, 1993.
11. Kagan, Y. Y., Observational evidence for earthquakes as a nonlinear dynamic process, Physica D, 77, 160-192, 1994.
12. Kagan, Y. Y., and L. Knopoff, A stochastic model of earthquake occurrence, Proc. 8-th Int. Conf. Earthq. Eng., San Francisco, Calif., vol. 1, 295-302, 1984.
13. Kanamori, H., The energy release in great earthquakes, J. Geophys. Res., 82, 2981-2987, 1977.
14. Kanamori H. and D. L. Anderson, Theoretical basis of some empirical relations in seismology, Bull. Seismol. Soc. Am., 65, 1073-1095, 1975.
15. Knopoff, L., and Y. Y. Kagan, Analysis of the theory of extremes as applied to earthquake problems, J. Geophys. Res., 82, 5647-5657, 1977.
16. Mandelbrot, B. B., The Fractal Geometry of Nature, W.H. Freeman, New York, 1983.
17. Mantegna, R. N., S. V. Buldyrev, A. L. Goldberger, S. Havlin, C.-K. Peng, M. Simons, and H. E. Stanley, Systematic analysis of coding and noncoding DNA sequences using methods of statistical linguistics, Phys. Rev. E, 52, 2939-2950, 1995.
18. Okal, E. A., and B. A. Romanowicz, On the variation of b-values with earthquake size, Phys. Earth Planet. Inter., 87, 55-76, 1994.
19. Pacheco, J. F., C. H. Scholz, and L. R. Sykes, Changes in frequency-size relationship from small to large earthquakes, Nature, 355, 71-73, 1992.
20. Riste, T., and D. Sherrington (Eds.), Spontaneous Formation of Space-Time Structures and Criticality, NATO ASI Ser. C, Kluwer Acad., Norwell, Mass., 1991.
21. Romanowicz, B., Strike-slip earthquakes on quasi-vertical transcurrent faults: Inferences for general scaling behavior, Geophys. Res. Lett., 19, 481-484, 1992.
22. Romanowicz, B., and J. B. Rundle, On scaling relations for large earthquakes, Bull. Seismol. Soc. Am., 83, 1294-1297, 1993.
23. Rundle, J. B., Derivation of the complete Gutenberg-Richter magnitude-frequency relation using the principle of scale invariance, J. Geophys. Res., 94, 12,337-12,342, 1989.
24. Sornette, D., and A. Sornette, On scaling relations for large earthquakes from the perspective of a recent nonlinear diffusion equation linking short-time deformation to long-time tectonics-Comment, Bull. Seismol. Soc. Am., 84, 1679-1683, 1994.
25. Sornette, D., C. Vanneste, and A. Sornette, Dispersion of b-values in Gutenberg-Richter law as a consequence of a proposed fractal nature of continental faulting, Geophys. Res. Lett., 18, 897-900, 1991.
26. Zipf, G. K., Human Behavior and the Principle of Least-Effort, Addison-Wesley, Reading, Mass., 1949.