Diffusion of epicenters of earthquake aftershocks, Omori’s law, and generalized continuous-time random walk models

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 66, Issue 6, 2002, Pages 24-

  Helmstetter, A ^a   Sornette, D ^b,c  

^a UNIVERSITÉ GRENOBLE ALPES   (France)

^b UNIVERSITÉ CÔTE D'AZUR   (France)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EARTHQUAKE AFTERSHOCKS; OMORI'S LAW; RANDOM WALK MODELS; SEISMICITY;

COMPUTER SIMULATION; DIFFUSION; MATHEMATICAL MODELS; NUMERICAL ANALYSIS; PROBABILITY DISTRIBUTIONS; RANDOM PROCESSES; SEISMOLOGY; SHOCK WAVES;

EARTHQUAKES;

ARTICLE;

EID: 26544477817     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.66.061104     Document Type: Article

References (98)

1. D. Sornette, Spontaneous Formation of Space-Time Structures and Criticality, Vol. 39 of NATO Advanced Study Institute, Series B: Physics, edited by T. Riste and D. Sherrington (Kluwer, Dordrecht, 1991), pp. 57–106.
2. J. B. Rundle and W. Klein, Rev. Geophys. 33, 283 (1995).
3. I. Main, Rev. Geophys. 34, 433 (1996).
4. D. Sornette, Phys. Rep. 313, 238 (1999).
5. D. L. Turcotte, Rep. Prog. Phys. 62, 1377 (1999).
6. B. Gutenberg and C. F. Richter, Bull. Seismol. Soc. Am. 34, 185 (1944).
7. F. Omori, On the aftershocks of earthquakes, J. Coll. Sci. Imp. Univ. Tokyo 7, 111 (1894).
8. G. Ouillon, C. Castaing, and D. Sornette, J. Geophys. Res., [Solid Earth] 101 B3, 5477 (1996).
9. Y. Y. Kagan and L. Knopoff, Geophys. J. R. Astron. Soc. 62, 303 (1980).
10. V. F. Pisarenko and D. Sornette, e-print cond-mat/0011168, Pure Appl. Geophys. (to be published).
11. Y. Y. Kagan, Pure Appl. Geophys. 155, 537 (1998).
12. D. Sornette, Critical Phenomena in Natural Sciences, Springer Series in Synergetics (Springer, Heidelberg, 2000).
13. R. A. Harris, in International Handbook of Earthquake and Engineering Seismology, edited by W. H. K. Lee, H. Kanamori, P. C. Jennings, and C. Kisslinger (unpublished), Chap. 73.
14. T. Yamashita and L. Knopoff, Geophys. J. R. Astron. Soc. 91, 13 (1987).
15. M. W. Lee and D. Sornette, Eur. Phys. J. B 15, 193 (2000).
16. Y. Huang, H. Saleur, C. G. Sammis, and D. Sornette, Europhys. Lett. 41, 43 (1998).
17. T. Utsu, Y. Ogata, and S. Matsuúra, J. Phys. Earth 43, 1 (1995).
18. M. Bath and C. F. Richter, Bull. Seismol. Soc. Am. 48, 133 (1958).
19. G. C. Beroza and M. D. Zoback, Science 259, 210 (1993).
20. D. P. Hill, Science 260, 1617 (1993).
21. D. W. Steeples and D. D. Steeples, Bull. Seismol. Soc. Am. 86, 921 (1996).
22. Y. Y. Kagan and D. D. Jackson, J. Geophys. Res., [Solid Earth] 103, 24 453 (1998).
23. A. J. Meltzner and D. J. Wald, Bull. Seismol. Soc. Am. 89, 1109 (1999).
24. D. Dreger and B. Savage, Bull. Seismol. Soc. Am. 89, 1094 (1999).
25. A. Sornette and D. Sornette, Geophys. Res. Lett. 26, 1981 (1999).
26. A. Helmstetter and D. Sornette, e-print http://arXiv.org/abs/ cond-mat/0109318, J. Geophys. Res. (to be published).
27. D. Sornette and A. Helmstetter, Phys. Rev. Lett. 89, 158501 (2002).
28. K. Mogi, J. Phys. Earth 16, 30 (1968).
29. M. Imoto, On migration phenomena of aftershocks following large thrust earthquakes in subduction zones, Report of the National Research Center for Disaster Prevention, No. 25, 1981, pp. 29–71.
30. J. L. Chatelain, R. K. Cardwell, and B. L. Isacks, Geophys. Res. Lett. 10, 385 (1983).
31. F. Tajima and H. Kanamori, Phys. Earth Planet. Inter. 40, 77 (1985).
32. F. Tajima and H. Kanamori, Geophys. Res. Lett. 12, 345 (1985).
33. R.L. Wesson, Tectonophysics 144, 214 (1987).
34. T. Ouchi and T. Uekawa, Phys. Earth Planet. Inter. 44, 211 (1986).
35. J. Noir, E. Jacques, S. Bekri, P. M. Adler, P. Tapponnier, and G. C. P. King, Geophys. Res. Lett. 24, 2335 (1997).
36. E. Jacques, J. C. Ruegg, J. C. Lepine, P. Tapponnier, G. C. P. King, and A. Omar, Geophys. J. Int. 138, 447 (1999).
37. P. A. Rydelek and I. S. Sacks, Geophys. Res. Lett. 28, 3079 (2001).
38. A. Nur and J. R. Booker, Science 175, 885 (1972).
39. K. W. Hudnut, L. Seeber, and J. Pacheco, Geophys. Res. Lett. 16, 199 (1989).
40. J. Dieterich, J. Geophys. Res., [Solid Earth] 99, 2601 (1994).
41. Y. Y. Kagan and L. Knopoff, Science 236, 1563 (1987).
42. Y. Ogata, Am. Stat. 83, 9 (1988).
43. Y. Yamanaka and K. Shimazaki, J. Phys. Earth 38, 305 (1990).
44. G. Drakatos and J. Latoussakis, Journal of Seismology 5, 137 (2001).
45. Z. Guo, and Y. Ogata, J. Geophys. Res., [Solid Earth] 102, 2857 (1997).
46. A. Helmstetter, Geophys. Res. Lett. (to be published).
47. K. R. Felzer, T. W. Becker, R. E. Abercrombie, G. Ekström, and J. R. Rice, J. Geophys. Res., [Solid Earth] (to be published).
48. M. Bath, Tectonophysics 2, 483 (1965).
49. R. Console, A. M. Lombardi, M. Murru, and D. Rhoades, J. Geophys. Res. (to be published).
50. Y. Ogata, Tectonophysics 169, 159 (1989).
51. Y. Ogata, J. Geophys. Res., [Solid Earth] 97, 19 845 (1992).
52. Y. Ogata, Pure Appl. Geophys. 155, 471 (1999).
53. Y. Ogata, J. Geophys. Res., [Solid Earth] 106, 8729 (2001).
54. Y. Y. Kagan, Geophys. J. Int. 106, 135 (1991).
55. Y. Y. Kagan and D. D. Jackson, Geophys. J. Int. 143, 438 (2000).
56. R. Console and M. Murru, J. Geophys. Res., [Solid Earth] 166, 8699 (2001).
57. E. W. Montroll and G. H. Weiss, J. Math. Phys. 6, 167 (1965).
58. S. Krishnamurthy, A. Tanguy, P. Abry, and S. Roux, Europhys. Lett. 51, 1 (2000).
59. Y. Ogata, Ann. Inst. Stat. Math. 50, 379 (1998).
60. C. H. Scholz and B. B. Mandelbrot, Fractals in Geophysics (Birkhäuser Verlag, Boston, 1989).
61. A. Sornette, P. Davy, and D. Sornette, J. Geophys. Res. [Solid Earth] 98, 12 111 (1993).
62. C. C. Barton and P. R. La Pointe, Fractals in the Earth Sciences (Plenum Press, New York, 1995).
63. K. Nanjo and H. Nagahama, Pure Appl. Geophys. 157, 575 (2000).
64. G. Ouillon and D. Sornette, Geophys. Res. Lett. 23, 3409 (1996).
65. D. Hamburger, O. Biham, and D. Avnir, Phys. Rev. E 53, 3342 (1996).
66. M. Eneva, Geophys. J. Int. 124, 773 (1996).
67. O. Malcai, D. A. Lidar, O. Biham, and D. Avnir, Phys. Rev. E 56, 2817 (1997).
68. A. Helmstetter, D. Sornette, and J.-R. Grasso, e-print http://arXiv.org/abs/ cond-mat/0205499, J. Geophys. Res. (to be published).
69. E. W. Montroll and H. Scher, J. Stat. Phys. 9, 101 (1973).
70. H. Scher and E. W. Montroll, Phys. Rev. B 12, 2455 (1975).
71. V.M. Kenkre, E. W. Montroll, and M. F. Shlesinger, J. Stat. Phys. 9, 45 (1973).
72. M. F. Shlesinger, J. Stat. Phys. 10, 421 (1974).
73. G. H. Weiss, Aspects and Applications of Random Walk (North-Holland, Amsterdam, 1994).
74. B. D. Hughes, Random Walks and Random Environments (Oxford University Press, New York, 1995).
75. R. Metzler and J. Klafter, Phys. Rep. 339, 1 (2000).
76. G. Margolin and B. Berkowitz, J. Phys. Chem. 104, 3942 (2000).
77. B. Berkowitz and H. Scher, Transp. Porous Media 42, 241 (2001).
78. S. Redner, Am. J. Phys. 58, 267 (1990).
79. H. Scher, H. G. Margolin, R. Metzler, J. Klafter, and B. Berkowitz, Geophys. Res. Lett. 29, 5 (2002).
80. J. W. Kirchner, X. Feng, and C. Neal, Nature (London) 403, 524 (2000).
81. E. Barkai, R. Metzler, and J. Klafter, Phys. Rev. E 61, 132 (2000).
82. A. M. Mathai and R. K. Saxena, The H-function with Applications in Statistics and Other Disciplines (Wiley Eastern Limited, New Delhi, 1978).
83. H. E. Roman and P. A. Alemany, J. Phys. A 27, 3407 (1994).
84. E. Barkai, Phys. Rev. E 63, 046118 (2001).
85. C. Budde, D. Prato, and M. Re, Phys. Lett. A 283, 309 (2001).
86. M. Kotulski, J. Stat. Phys. 81, 777 (1995).
87. E. Barkai, e-print cond-mat/0108024.
88. A. I. Saichev and G. M. Zaslavsky, Chaos 7, 753 (1997).
89. C. M. Bender and S. Orzag, Advanced Mathematical Methods for Scientists and Engineers (McGraw-Hill, New York, 1978).
90. G. H. Weiss and P. P. Calabrese, Physica A 234, 443 (1996).
91. I. M. Sokolov, A. Blumen, and J. Klafter, e-print cond-mat/0107632.
92. I. M. Sokolov, Phys. Rev. E 63, 011104 (2001).
93. C. M. Bender, S. Boettcher, and P. N. Meisinger, Phys. Rev. Lett. 75, 3210 (1995).
94. B. E. Shaw, Geophys. Res. Lett. 20, 907 (1993).
95. D. Marsan, C. J. Bean, S. Steacy, and J. McCloskey, J. Geophys. Res. [Solid Earth] 105, 28 (2000).
96. D. Marsan, C. J. Bean, S. Steacy, and J. McCloskey, Geophys. Res. Lett. 26, 3697 (1999).
97. D. Marsan and C. J. Bean, Geophys. J. Int. (to be published).
98. O. Sotolongo-Costa, J. C. Antoranz, A. Posadas, F. Vidal, and A. Vásquez, Geophys. Res. Lett. 27, 1965 (2000).