Multifractal Omori law for earthquake triggering: New tests on the California, Japan and worldwide catalogues

Geophysical Journal International

Volumn 178, Issue 1, 2009, Pages 215-243

  Ouillon, G ^a   Sornette, D ^b,c   Ribeiro, E ^d  

^a Lithophyse   (France)

^b ETH ZURICH   (Switzerland)

^c UNIVERSITY OF CALIFORNIA   (United States)

^d UNIVERSITÉ CÔTE D'AZUR   (France)

Author keywords

Clustering; Correlations; Earthquake interaction; Forecasting and prediction; Memory; Persistence; Self organization; Statistical seismology; Time series analysis; Wavelet transform

Indexed keywords

AFTERSHOCK; CLUSTER ANALYSIS; CORRELATION; EARTHQUAKE CATALOGUE; EARTHQUAKE MAGNITUDE; EARTHQUAKE PRECURSOR; EARTHQUAKE TRIGGER; EMPIRICAL ANALYSIS; FRACTAL ANALYSIS; MOMENT TENSOR; SEISMICITY; THERMODYNAMICS; TIME SERIES ANALYSIS; TRANSFORM; TRIGGER MECHANISM; WAVELET ANALYSIS;

ASIA; CALIFORNIA; EURASIA; FAR EAST; JAPAN; NORTH AMERICA; UNITED STATES;

EID: 67650132867     PISSN: 0956540X     EISSN: 1365246X     Source Type: Journal    
DOI: 10.1111/j.1365-246X.2009.04079.x     Document Type: Article

References (65)

1. Bacry, E., Muzy, J. & Arneodo, A., 1993. Singularity spectrum of fractal signals from wavelet analysis: Exact results, J. Stat. Phys., 70 (3/4), 635-674.
2. Baumberger, T., Berthoud, P. & Caroli, C., 1999. Physical analysis of the stae-and-rate-dependent friction law. II. Dynamic friction, Phys. Rev. B, 60, 3928-3939.
3. Ben-Zion, Y., 1996. Stress slip and earthquakes in models of complex single-fault systems incorporating brittle and creep deformations, J. geophys. Res., 101, 5677-5706.
4. Ben-Zion, Y., 2003. Key Formulas in Earthquake Seismology, in International Handbook of Earthquake and Engineering Seismology, Part B, pp. 1857-1875, eds Lee, W.H.K., Kanamori, H., Jennings, P.C., Kisslinger, C., Academic Press, Boston.
5. Ben-Zion, Y. & Rice, J.R., 1995. Slip patterns and earthquake populations along different classes of faults in elastic solids, J. geophys. Res., 100, 12959-12983.
6. Ben-Zion, Y., Dahmen, K., Lyakhovsky, V., Ertas, D. & Agnon, A., 1999. Self driven mode switching of earthquake activity on a fault system, Earth planet. Sci. Lett., 172 (1-2), 11-21.
7. Blanpied, M.L., Lockner, D.A. & Byerlee, J.D., 1991. Fault stability inferred from granite sliding experiments at hydrothermal conditions, Geophys. Res. Lett., 18 (4), 609-612.
8. Carlson, J.M., Langer, J.S. & Shaw, B.E., 1994. Dynamics of earthquake faults, Rev. Mod. Phys., 66, 658-670.
9. Chester, F.M., 1994. Effects of temperature on friction: Constitutive equations and experiments with quartz Gouge, J. geophys. Res., 99 (B4), 7247-7261.
10. Chester, F.M. & Higgs, N.G., 1992. Multimechanism friction constitutive model for ultrafine quartz Gouge at hypocentral conditions, J. geophys. Res., 97 (B2), 1859-1870.
11. Ciliberto, S., Guarino, A. & Scorretti, R., 2001. The effect of disorder on the fracture nucleation process, Physica D, 158, 83-104.
12. Dahmen, K., Ertas, D. & Ben-Zion, Y., 1998. Gutenberg-Richter and characteristic earthquake behaviour in a simple mean-field model of heterogeneous faults, Phys. Rev. E, 58, 1494-501.
13. Dieterich, J., 1994. A constitutive law for rate of earthquake production and its application to earthquake clustering, J. geophys. Res., 99 (B2), 2601-2618.
14. Felzer, K.R., Becker, T.W., Abercrombie, R.E., Ekstrm, G. & Rice, J.R., 2002. Triggering of the 1999 Mw 7.1 Hector mine earthquake by aftershocks of the 1992 Mw 7.3 Landers earthquake, J. geophys. Res., 107, 2190.
15. Habermann, R.E. & Wyss, M., 1984. Background seismicity rates and precursory seismic quiescence: Imperial Valley, California, Bull. seism. Soc. Am., 74 (5), 1743-1755.
16. Helmstetter, A., 2003. Is earthquake triggering driven by small earthquakes? Phys. Rev. Lett., 91 (5) 05850.
17. Helmstetter, A. & Shaw, B.E., 2006. Relation between stress heterogeneity and aftershock rate in the rate-and-state model, J. geophys. Res., 111, B07304.
18. Helmstetter, A. & Sornette, D., 2003. Foreshocks explained by cascades of triggered seismicity, J. geophys. Res. (Solid Earth) 108 (B10), 2457.
19. Helmstetter, A., Ouillon, G. & Sornette, D., 2003. Are aftershocks of large californian earthquakes diffusing? J. geophys. Res., 108, 2483.
20. Helmstetter, A., Kagan, Y. & Jackson, D., 2005. Importance of small earthquakes for stress transfers and earthquake triggering, J. geophys. Res., 110, B05S08.
21. Heslot, F., Baumberger, T., Perrin, B., Caroli, B. & Caroli, C., 1994. Creep, stick-slip, and dry friction dynamics: Experiments and a heuristic model, Phys. Rev. E, 49, 4973-4988.
22. Jones, L.M. & Molnar, P., 1979. Some characteristics of foreshocks and their possible relationship to earthquake prediction and premonitory slip on fault, J. geophys. Res., 84, 3596-3608.
23. Kagan, Y.Y., 1994. Distribution of incremental static stress caused by earthquakes, Nonlin. Proc. Geophys., 1, 171-181.
24. Kagan, Y.Y., 2003. Accuracy of modern global earthquake catalogues, Phys. Earth planet. Int., 135 (2-3), 173-209.
25. Kagan, Y.Y., 2004. Short-term properties of earthquake catalogues and models of earthquake source, Bull. seism. Soc. Am., 94 (4), 1207-1228.
26. Kagan, Y.Y. & Knopoff, L., 1978. Statistical study of the occurrence of shallow earthquakes, Geophys. J. R. astr. Soc., 55, 67-86.
27. Kagan, Y.Y. & Knopoff, L., 1981. Stochastic synthesis of earthquake catalogues, J. geophys. Res., 86, 2853-2862.
28. King, G.C.P., Stein, R.S. & Lin, J., 1994. Static stress changes and the triggering of earthquakes, Bull. seism. Soc. Am., 84 (3), 935-953.
29. Klein, W., Rundle, J.B. & Ferguson, C.D., 1997. Scaling and nucleation in models of earthquake faults, Phys. Rev. Lett., 78, 3793-3796.
30. Lapusta, N. & Rice, J.R., 2003. Nucleation and early seismic propagation of small and large events in a crustal earthquake model, J. geophys. Res., 108 (B4), 2205.
31. Lockner, D.A., 1998. A generalized law for brittle deformation of Westerly granite, J. geophys. Res., 103 (B3), 5107-5123.
32. Lyakhovsky, V., Ben-Zion, Y. & Agnon, A., 2001. Earthquake cycle, fault zones, and seismicity patterns in a rheologically layered lithosphere, J. geophys. Res., 106, 4103-4120.
33. Marsan, D., 2005. The role of small earthquakes in redistributing crustal elastic stress. Geophys. J. Int., 163 (1), 141-145.
34. Marsan, D., 2006. Can coseismic stress variability suppress seismicity shadows? Insights from a rate-and-state friction model, J. geophys. Res., 111, B06305.
35. Marsan, D. & Lengliné, O., 2008. Extending earthquakes' reach through cascading, Science, 319, 1076.
36. Miltenberger, P., Sornette, D. & Vanneste, C., 1993. Fault self-organization as optimal random paths selected by critical spatio-temporal dynamics of earthquakes, Phys. Rev. Lett., 71, 3604-3607.
37. Ogata, Y., 1988. Statistical models for earthquake occurrence and residual analysis for point processes, J. Am. stat. Assoc., 83, 9-27.
38. Ouillon, G. & Sornette, D., 2005. Magnitude-Dependent Omori Law: Theory and Empirical Study, J. geophys. Res., 110, B04306.
39. Pacheco, J.F., Scholz, C.H. & Sykes, L.R., 1996. Changes in frequency-size relationship from small to large earthquakes, Nature, 355, 71-73.
40. Peng, Z., Vidale, J.E., Ishii, M. & Helmstetter, A., 2007. Seismicity rate immediately before and after main shock rupture from high-frequency waveforms in Japan, J. geophys. Res., 112, B03306.
41. Pisarenko, V.F. & Sornette, D., 2004. Statistical detection and characterization of a deviation from the Gutenberg-Richter distribution above magnitude 8, Pure appl. Geophys., 161 (4), 839-864.
42. Rice, J.R. & Ben-Zion, Y., 1996. Slip complexity in earthquake fault models, Proc. Natl. Acad. Sci. USA, 93, 3811-3818.
43. Rousseeuw, P.J. & Leroy, A.M., 1987. Robust Regression and Outlier Detection. John Wiley and Sons, Inc., New York.
44. Saichev, A. & Sornette, D., 2005. Andrade, Omori and time-to-failure laws from thermal noise in material rupture, Phys. Rev. E, 71, 016608.
45. Saichev, A. & Sornette, D., 2006a. Power law distribution of seismic rates: Theory and data, Eur. Phys. J. B, 49, 377-401.
46. Saichev, A. & Sornette, D., 2006b. Generic multifractality in exponentials of long memory processes, Phys. Rev. E, 74, 011111.
47. Sornette, D., 1991. Self-organized criticality in plate tectonics, in the proceedings of the NATO ASI 'Spontaneous formation of space-time structures and criticality, 'Geilo, Norway 2-12 April 1991, Vol. 349, pp. 57-106, eds Riste, T. & D. Sherrington, Kluwer Academic Press, Dordrecht, Boston.
48. Sornette, D., 2006. Critical Phenomena in Natural Sciences, (Chaos, Fractals, Self-organization and Disorder: Concepts and Tools) 2nd edn, 2nd reprint, Springer Series in Synergetics, Heidelberg.
49. Sornette, D. & Helmstetter, A., 2003. Endogeneous versus exogeneous shocks in systems with memory, Physica A, 318 (3-4), 577-591.
50. Sornette, D. & Ouillon, G., 2005. Multifractal scaling of thermally-activated rupture processes, Phys. Rev. Lett., 94, 038501.
51. Sornette, D. & Virieux, J., 1992. Linking short-timescale deformation to long-timescale tectonics, Nature, 357, 401-404.
52. Sornette, D. & Werner, M.J., 2005. Apparent clustering and apparent background earthquakes biased by undetected seismicity, J. geophys. Res., 110 (B9), B09303.
53. Sornette, D., Davy, Ph. & Sornette, A., 1990. Structuration of the lithosphere in plate tectonics as a self-organized critical phenomenon, J. geophys. Res., 95, 17353-17361.
54. Sornette, D., Miltenberger, P. & Vanneste, C., 1994. Statistical physics of fault patterns self-organized by repeated earthquakes, Pure appl. Geophys., 142 (3/4), 491-527.
55. Sornette, D., Malevergne, Y. & Muzy, J.F., 2003. Tail risk: What causes crashes? Risk, 16 (2), 67-71 (e-print at http://arXiv.org/abs/ cond-mat/0204626).
56. Stein, R.S., 2003. Earthquake conversations, Sci. Am., 288 (1), 72-79.
57. Toda, S., Stein, R.S. & Sagiya, T., 2002. Evidence from the ad 2000 Izu islands earthquake swarm that stressing rate governs seismicity, Nature, 419, 58-61.
58. Wells, D.L. & Coppersmith, K.J., 1994. New empirical relationships among magnitude, rupture length, rupture width, rupture area, and surface displacement, Bull. seism. Soc. Am., 84 (4), 974-1002.
59. Werner, M. & Sornette, D., 2008. Magnitude uncertainties impact seismic rate estimates, forecasts and predictability experiments, J. geophys. Res., 113, B08302.
60. Zhuang, J., Ogata, Y. & Vere-Jones, D., 2004. Analyzing earthquake clustering features by using stochastic reconstruction, J. geophys. Res., 109, B05301.
61. Zhurkov, S.N., 1965. Kinetic concept of the strength of solids, Int. J. Fract. Mech., 1, 311-323.
62. Ziv, A. & Rubin, A.M., 2003. Implications of rate-and-state friction for properties of aftershock sequence: Quasi-static inherently discrete simulations, J. geophys. Res., 108 (B1), 2051.
63. Zoller, G., Holschneider, M. & Ben-Zion, Y., 2004. Quasi-static and Quasi-dynamic modeling of earthquake failure at intermediate scales, Pure appl. Geophys., 161, 2103-2118.
64. Zolotarev, V.M., 1986. One-dimensional stable distributions, Amer. Mmath. Soc. Providence R.I.
65. Zolotarev, V.M. & Strunin, B.M., 1971. Internal stress distribution for a random distribution of point defects, Soviet Phys. Solid State, 13, 481-482.