Self-similar branching of aftershock sequences

Physica A: Statistical Mechanics and its Applications

Volumn 387, Issue 4, 2008, Pages 933-943

  Holliday, James R ^a   Turcotte, Donald L ^a   Rundle, John B ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Aftershocks; Branching; Earthquakes; Epidemic type models; Hazard assessment; Scaling

Indexed keywords

MATHEMATICAL MODELS; PROBABILITY DISTRIBUTIONS; SEISMIC RESPONSE; STATISTICS;

AFTERSHOCKS; BRANCHING; EPIDEMIC TYPE MODELS; HAZARD ASSESSMENT; SCALING;

EARTHQUAKE EFFECTS;

EID: 36648999210     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2007.09.045     Document Type: Article

References (87)

1. Gutenberg B., and Richter C.F. Seismicity of the Earth and Associated Phenomena (1954), Princeton University Press, Princeton, NJ
2. Shcherbakov R., Turcotte D.L., and Rundle J.B. A generalized Omori's law for earthquake aftershock decay. Geophys. Res. Lett. 31 (2004) L11613
3. Shcherbakov R., and Turcotte D.L. A modified form of Båth's law. Bull. Seismol. Soc. Amer. 94 (2004) 1968-1975
4. Bak P., Christensen K., Danon L., and Scanlon T. Unified scaling law for earthquakes. Phys. Rev. Lett. 88 (2002) 178501
5. Davidsen J., and Paczuski M. Analysis of the spatial distribution between successive earthquakes. Phys. Rev. Lett. 94 (2005) 048501
6. Gabrielov A., Newman W.I., and Turcotte D.L. Exactly soluble hierarchical clustering model: Inverse cascades, self-similarity, and scaling. Phys. Rev. E 60 (1999) 5293
7. Working Group on California Earthquake Probabilities, Earthquake probabilities in the San Francisco Bay Region, 2002-2031, Open-File Report 2003-214, US Geological Survey, 2003
8. A.F. Frankel, C. Mueller, T. Barnhard, D. Perkins, E.V. Leyendecker, N. Dickman, S. Hanson, M. Hopper, National seismic hazard maps, Open-File Report 96-532, US Geological Survey, 1996
9. Kossobokov V.G., Keilis-Borok V.I., Turcotte D.L., and Malamud B.D. Implications of a statistical physics approach for earthquake hazard assessment and forecasting. Pure Appl. Geophys. 157 (2000) 2323-2349
10. Holliday J.R., Nanjo K.Z., Tiampo K.F., Rundle J.B., and Turcotte D.L. Earthquake forecasting and its verification. Nonlinear Process. Geophys. 12 (2005) 965-977
11. Rundle J.B., Tiampo K.F., Klein W., and Martins J.S.S. Self-organization in leaky threshold systems: The influence of near-mean field dynamics and its implications for earthquakes, neurobiology, and forecasting. Proc. Natl. Acad. Sci. USA 99 Suppl. 1 (2002) 2514-2521
12. Tiampo K.F., Rundle J.B., McGinnis S., Gross S.J., and Klein W. Eigenpatterns in southern California seismicity. J. Geophys. Res. 107 B12 (2002) 2354
13. Tiampo K.F., Rundle J.B., McGinnis S., and Klein W. Pattern dynamics and forecast methods in seismically active regions. Pure Appl. Geophys. 159 (2002) 2429-2467
14. Holliday J.R., Rundle J.B., Tiampo K.F., Klein W., and Donnellan A. Modification of the pattern informatics method for forecasting large earthquake events using complex eigenvectors. Tectonophysics 413 (2006) 87-91
15. Holliday J.R., Rundle J.B., Tiampo K.F., Klein W., and Donnellan A. Systematic procedural and sensitivity analysis of the pattern informatics method for forecasting large (M ≥ 5) earthquake events in southern California. Pure Appl. Geophys (2006)
16. Holliday J.R., Chen C.C., Tiampo K.F., Rundle J.B., Turcotte D.L., and Donnellan A. A RELM earthquake forecast based on pattern informatics. Seis. Res. Lett. 78 1 (2007) 87-93
17. Keilis-Borok V.I. The lithosphere of the earth as a nonlinear system with implications for earthquake prediction. Rev. Geophys. 28 (1990) 19-34
18. Keilis-Borok V. Earthquake predictions: State-of-the-art and emerging possibilities. An. Rev. Earth Planet. Sci. 30 (2002) 1-33
19. Shebalin P., Keilis-Borok V., Zaliapin I., Uyeda S., Nagao T., and Tsybin N. Advance short-term prediction of the large Tokachi-oki earthquake, September 25, M = 8.1: A case history. Earth Planets Space 56 (2004) 715-724
20. Keilis-Borok V., Shebalin P., Gabrielov A., and Turcotte D. Reverse tracing of short-term earthquake precursors. Phys. Earth Planet. Int. 145 (2004) 75-85
21. Buffe C.G., and Varnes D.J. Predictive modeling of the seismic cycle of the greater San Francisco Bay region. J. Geophys. Res. 98 (1993) 9871-9883
22. Bowman D.D., Ouillon G., Sammis C.G., Sornette A., and Sornette D. An observational test of the critical earthquake concept. J. Geophys. Res. 103 (1998) 24359-24372
23. Sammis C.G., Bowman D.D., and King G. Anomalous seismicity and accelerating moment release preceding the 2001-2002 earthquakes in northern Baha California, Mexico. Pure Appl. Geophys. 161 (2004) 2369-2378
24. Kagan Y.Y., and Knopoff L. Stochastic synthesis of earthquake catalogs. J. Geophys. Res. 86 4 (1981) 2853-2862
25. Ogata Y. Statistical models for earthquake occurrences and residual analysis for point processes. J. Amer. Statist. Assoc. 83 (1988) 9-27
26. Ogata Y. Statistical model for standard seismicity and detection of anomalies by residual analysis. Tectonophysics 169 (1989) 159-174
27. Ogata Y. Detection of precursory relative quiescence before great earthquakes through a statistical model. J. Geophys. Res. 97 (1992) 19845-19871
28. Ogata Y. Space-time point process models for earthquake occurrences. Ann. Inst. Statist. Math. 50 (1998) 379-402
29. Ogata Y. Seismicity analysis through point-process modeling: A review. Pure Appl. Geophys. 155 (1999) 471-507
30. Ogata Y. Exploratory analysis of earthquake clusters by likelihood-based trigger models. J. Appl. Probab. 38A (2001) 202-212
31. Ogata Y. Increased probability of large earthquakes near aftershock regions with relative quiescence. J. Geophys. Res. 106 (2001) 8729-8744
32. Ogata Y. Space-time model for regional seismicity and detection of crustal stress changes. J. Geophys. Res. 109 (2004) B06308
33. Ogata Y., Matsuura R.S., and Katsura K. Fast likelihood computation of epidemic type aftershock-sequence model. Geophys. Res. Lett. 20 (1993) 2143-2146
34. Ogata Y., Jones L.M., and Toda S. When and where the aftershock activity was depressed: Contrasting decay patterns of the proximate large earthquakes in southern California. J. Geophys. Res. 108 (2003) 2318
35. Guo Z.Q., and Ogata Y. Statistical relations between the parameters of aftershocks in time, space, and magnitude. J. Geophys. Res. 102 B2 (1997) 2857-2873
36. Ogata Y., and Zhuang J. Space-time ETAS models and an improved extension. Tectonophysics 413 (2006) 13-23
37. Zhuang J., and Ogata Y. Properties of the probability distribution associated with the largest event in an earthquake cluster and their implications to foreshocks. Phys. Rev. E 73 (2006) 046134
38. Zhuang J., Ogata Y., and Vere-Jones D. Stochastic declustering of space-time earthquake occurrences. J. Amer. Statist. Assoc. 97 (2002) 369-380
39. Zhuang J., Ogata Y., and Vere-Jones D. Analyzing earthquake clustering features by using stochastic reconstruction. J. Geophys. Res. 109 (2004) B05301
40. Vere-Jones D. A class of self-similar random measure. Adv. Appl. Probab. 37 (2005) 908-914
41. Helmstetter A. Is earthquake triggering driven by small earthquakes?. Phys. Rev. Lett. 91 (2003) 0585014
42. Helmstetter A., Sornette D., and Grasso J.R. Mainshocks are aftershocks of conditional foreshocks: How do foreshock statistical properties emerge from aftershock laws. J. Geophys. Res. 108 B1 (2003) 2046
43. Helmstetter A.S., Ouillon G., and Sornette D. Are aftershocks of large California earthquakes diffusing?. J. Geophys. Res. 108 B10 (2003) 2483
44. Helmstetter A., Hergarten S., and Sornette D. Properties of foreshocks and aftershocks of the non-conservative self-organized critical Olami-Feder-Christensen model. Phys. Rev. E 70 (2004) 046120
45. Helmstetter A., Kagan Y.Y., and Jackson D.D. Comparison of short-term and time-independent earthquake forecast models for southern California. Bull. Seismol. Soc. Amer. 96 (2006) 90-106
46. Helmstetter A., and Sornette D. Diffusion of epicenters of earthquake aftershocks, Omori's law, and generalized continuous-time random walk models. Phys. Rev. E 66 6 (2002) 061104
47. Helmstetter A., and Sornette D. Subcritical and supercritical regimes in epidemic models of earthquake aftershocks. J. Geophys. Res. 107 B10 (2002) 2237
48. Helmstetter A., and Sornette D. Foreshocks explained by cascades of triggered seismicity. J. Geophys. Rev. 108 B10 (2003) 2457
49. Helmstetter A., and Sornette D. Predictability in the epidemic-type aftershock sequence model of interacting triggered seismicity. J. Geophys. Rev. 108 B10 (2003) 2482
50. Helmstetter A.S., and Sornette D. Båth's law derived from the Gutenberg-Richter law and from aftershock properties. Geophys. Res. Lett. 30 20 (2003) 2069
51. Helmstetter A.S., and Sornette D. Importance of direct and indirect triggered seismicity in the ETAS model of seismicity. Geophys. Res. Lett. 30 11 (2003) 1576
52. Saichev A., Helmstetter A., and Sornette D. Power-law distributions of offspring and generation numbers in branching models of earthquake triggering. Pure Appl. Geophys. 162 (2005) 1113-1134
53. Saichev A., and Sornette D. Anomalous power law distribution of total lifetimes of branching processes: Application to earthquake aftershock sequences. Phys. Rev. E 70 4 (2004) 046123
54. Saichev A., and Sornette D. Distribution of the largest aftershocks in branching models of triggered seismicity: Theory of the universal Båth's law. Phys. Rev. E 71 5 (2005) 056127
55. Saichev A., and Sornette D. Vere-Jones' self-similar branching model. Phys. Rev. E 72 (2005) 056122
56. Saichev A., and Sornette D. Power law distribution of seismic rates: Theory and data analysis. Eur. Phys. J. B49 (2006) 377-401
57. Saichev A., and Sornette D. Renormalization of branching models of triggered seismicity from total to observed seismicity. Eur. Phys. J. B51 (2006) 443-459
58. Saichev A., and Sornette D. "Universal" distribution of interearthquake times explained. Phys. Rev. Lett. 97 (2006) 078501
59. Saichev A., and Sornette D. Power law distributions of seismic rates. Tectonophysics 431 (2007) 7-13
60. Sornette D., and Helmstetter A. Occurrence of finite-time singularities in epidemic models of rupture, earthquakes, and starquakes. Phys. Rev. Lett. 89 15 (2002) 158501
61. Sornette D., and Werner M.J. Apparent clustering and apparent background earthquakes biased by undetected seismicity. J. Geophys. Res. 110 (2005) B09303
62. Sornette D., and Werner M.J. Constraints on the size of the smallest triggering earthquake from the epidemic-type aftershock sequence model, Båth's law, and observed aftershock sequences. J. Geophys. Res. 110 B8 (2005) B08304
63. w 7.3 landers earthquake. J. Geophys. Res. 107 B9 (2002) 2190
64. Felzer K.R., Abercrombie R.E., and Ekstrom G. Secondary aftershocks and their importance for aftershock forecasting. Bull. Seismol. Soc. Amer. 93 4 (2003) 1433-1448
65. Felzer K.R., Abercrombie R.E., and Ekstrom G. A common origin for aftershocks, foreshocks, and multiplets. Bull. Seismol. Soc. Amer. 94 (2004) 88-98
66. Console R., and Murru M. A simple and testable model for earthquake clustering. J. Geophys. Res. 106 (2001) 8699-8711
67. Console R., Murru M., and Lombardi A.M. Refining earthquake clustering models. J. Geophys. Res. 108 (2003) 2468
68. Console R., Murru M., and Catalli F. Physical and stochastic models of earthquake clustering. Tectonophysics 417 (2006) 141-153
69. M. Gersterberger, S. Wiemer, L. Jones, Real-time forecasts of tomorrow's earthquakes in California: A new mapping tool, Open-File Report 2004-1390, US Geological Survey, 2004
70. Gersterberger M.C., Wiemer S., Jones L.M., and Reasenberg P.A. Real-time forecasts of tomorrow's earthquakes in California. Nature 435 (2005) 328-331
71. Lombardi A.M., and Marzocchi W. Evidence of clustering and nonstationarity in the time distribution of large worldwide earthquakes. J. Geophys. Res. 112 (2007) B02303
72. Båth M. Lateral inhomogeneities in the upper mantle. Tectonophysics 2 (1965) 483-514
73. Vere-Jones D. A note on the statistical interpretation of Båth's law. Bull. Seismol. Soc. Amer. 59 (1969) 1535-1541
74. Shcherbakov R., Turcotte D.L., and Rundle J.B. Aftershock statistics. Pure Appl. Geophys. 162 (2005) 1051-1076
75. Console R., Lombardi A.M., Murru M., and Rhoades D. Bath's law and the self-similarity of earthquakes. J. Geophys. Res. 108 B2 (2003) 2128
76. Kisslinger C., and Jones L.M. Properties of aftershock sequences in Southern California. J. Geophys. Res. 96 (1991) 11947-11958
77. Tsapanos T.M. Spatial distribution of the difference between the magnitudes of the main shock and the largest aftershock in the circum-Pacific belt. Seis. Soc. Am. Bull. 80 (1990) 1180-1189
78. Turcotte D.L., Holliday J.R., and Rundle J.B. BASS, an alternative to ETAS. Geophys. Res. Lett. 34 (2007) L12303
79. Turcotte D.L., and Newman W.I. Symmetries in geology and geophysics. Proc. Natl. Acad. Sci. 93 (1996) 14295-14300
80. Tokunaga E. Consideration on the composition of drainage networks and their evolution. Geographical Rep. Tokya Metro. Univ. 13 (1978) 1-27
81. Pelletier J.D. Self-organization and scaling relationships of evolving river networks. J. Geophys. Res. 104 (1999) 7359-7375
82. Ossadnik P. Branch order and ramification analysis of large diffusion limited aggregation clusters. Phys. Rev. A 45 (1992) 1058-1066
83. Reasenberg P.A., and Jones L.M. Earthquake hazard after a mainshock in California. Science 243 4895 (1989) 1173-1176
84. Yamanaka Y., and Shimazaki K. Scaling relationship between the number of aftershocks and the size of the main shock. J. Phys. Earth 38 4 (1990) 305-324
85. Nanjo K.Z., Enescu B., Shcherbakov R., Turcotte D.L., Iwata T., and Ogata Y. The decay of aftershock activity for Japanese earthquakes. J. Geophys. Res. 112 (2007) B08309 10.1029/2006JB004754
86. Felzer K.R., and Brodsky E.E. Decay of aftershock density with distance indicates triggering by dynamic stress. Nature 441 (2006) 735-738
87. Reasenberg P.A. Foreshock occurrence rates before large earthquake worldwide. Pure. Appl. Geophys. 155 (1999) 355-379