Predictability in the Epidemic-Type Aftershock Sequence model of interacting triggered seismicity

Journal of Geophysical Research: Solid Earth

Volumn 108, Issue 10, 2003, Pages

  Helmstetter, Agnès ^a   Sornette, Didier ^b,c  

^a UNIVERSITÉ GRENOBLE ALPES   (France)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c UNIVERSITÉ CÔTE D'AZUR   (France)

Author keywords

Aftershocks; ETAS; Foreshocks; Prediciton; Triggered seismicity

Indexed keywords

AFTERSHOCK; EARTHQUAKE PREDICTION; MARKOV CHAIN; SEISMICITY; TRIGGER MECHANISM;

EID: 1442340191     PISSN: 21699313     EISSN: 21699356     Source Type: Journal    
DOI: None     Document Type: Article

References (56)

1. Console, R., and M. Murru, A simple and testable model for earthquake clustering, J. Geophys. Res., 106, 8699-8711, 2001.
2. Feller, W., An Introduction to Probability Theory and Its Applications, vol. II, John Wiley, Hoboken, N. J., 1971.
3. W 7.3 Landers earthquake, J. Geophys. Res., 107(B9), 2190, doi:10.1029/2001JB000911, 2002.
4. Gabrielov, A., I. Zaliapin, W. I. Newman, and V. I. Keilis-Borok, Colliding cascades model for earthquake prediction, Geophys. J. Int., 143, 427-437, 2000.
5. Guo, Z., and Y. Ogata, Correlations between characteristic parameters of aftershock distributions in time, space and magnitude, Geophys. Res. Lett., 22, 993-996, 1995.
6. Guo, Z., and Y. Ogata, Statistical relations between the parameters of aftershocks in time, space and magnitude, J. Geophys. Res., 102, 2857-2873, 1997.
7. Gutenberg, B., and C. F. Richter, Frequency of earthquakes in California, Bull. Seismol. Soc. Am., 34, 185-188, 1944.
8. Hawkes, A. G., Point spectra of some mutually exciting point processes, J. R. Stat. Soc. B, 33, 438-443, 1971.
9. Hawkes, A. G., Spectra of some mutually exciting point processes with associated variables, in Stochastic Point Processes, edited by P. A. W. Lewis, pp. 261-271, John Wiley, Hoboken, N. J., 1972.
10. Helmstetter, A., Is earthquake triggering driven by small earthquakes?, Phys. Res. Lett., 91, 058501, 2003.
11. Helmstetter, A., and D. Sornette, Subcritical and supercritical regimes in epidemic models of earthquake aftershocks, J. Geophys. Res., 107(B10), 2237, doi:10.1029/2001JB001580, 2002a.
12. Helmstetter, A., and D. Sornette, Diffusion of epicenters of earthquake aftershocks, Omori's law, and generalized continuous-time random walk models, Phys. Rev. E, 66, doi:10.1103/PhysRevE.66.061104, 2002b.
13. Helmstetter, A., and D. Sornette, Importance of direct and indirect triggered seismicity in the ETAS model of seismicity, Geophys. Res. Lett., 30(11), 1576, doi:10.1029/2003GL017670, 2003.
14. Helmstetter, A., D. Sornette, and J.-R. Grasso, Mainshocks are aftershocks of conditional foreshocks: How do foreshocks statistical properties emerge from aftershock laws, J. Geophys. Res., 108(B1), 2046, doi:10.1029/2002JB001991, 2003.
15. Jaume, S. C., and L. R. Sykes, Evolving towards a critical point: A review of accelerating seismic moment/energy release prior to large and great earthquakes, Pure Appl. Geophys., 155, 279-305, 1999.
16. Kagan, Y. Y., Statistical methods in the study of the seismic process (with discussion: Comments by M. S. Bartlett, A. G. Hawkes, and J. W. Tukey), Bull. Int. Stat. Inst., 45(3), 437-453, 1973.
17. Kagan, Y. Y., Likelihood analysis of earthquake catalogues, Geophys. J. Int., 106, 135-148, 1991.
18. Kagan, Y. Y., Universality of the seismic moment-frequency relation, Pure Appl. Geophys., 155, 537-573, 1999.
19. Kagan, Y. Y., and D. D. Jackson, Probabilistic forecasting of earthquakes, Geophys. J. Int., 143, 438-453, 2000.
20. Kagan, Y., and L. Knopoff, Earthquake risk prediction as a stochastic process, Phys. Earth Planet. Inter., 14, 97-108, 1977.
21. Kagan, Y. Y., and L. Knopoff, Spatial distribution of earthquakes: The two-point correlation function, Geophys. J. R. Astron. Soc., 62, 303-320, 1980.
22. Kagan, Y. Y., and L. Knopoff, Statistical short-term earthquake prediction, Science, 236, 1467-1563, 1987.
23. Keilis-Borok, V. I., and V. G. Kossobokov, Premonitory activation of seismic flow: Algorithm M8, Phys. Earth Planet. Inter., 61, 73-83, 1990a.
24. Keilis-Borok, V. I., and V. G. Kossobokov, Times of increased probability of strong earthquakes (M ≥ 7.5) diagnosed by algorithm M8 in Japan and adjacent territories, J. Geophys. Res., 85, 12,413-12,422, 1990b.
25. Keilis-Borok, V. I., and L. N. Malinovskaya, One regularity in the occurrence of strong earthquakes, J. Geophys. Res., 69, 3019-3024, 1964.
26. Keilis-Borok, V. I., and A. Soloviev, Nonlinear Dynamics of the Lithosphere and Earthquake Prediction, 337 pp., Springer-Verlag, New York, 2003.
27. Kisslinger, C., The stretched exponential function as an alternative model for aftershock decay rate, J. Geophys. Res., 98, 1913-1921, 1993.
28. Kossobokov, V. G., J. H. Healy, and J. W. Dewey, Testing an earthquake prediction algorithm, Pure Appl. Geophys., 149, 219-232, 1997.
29. Kossobokov, V. G., L. L. Romashkova, V. I. Keilis-Borok, and J. H. Healy, Testing earthquake prediction algorithms: Statistically significant advance prediction of the largest earthquakes in the Circum-Pacific, 1992-1997, Phys. Earth Planet. Inter., 111, 187-196, 1999.
30. Lomnitz, C., Modelling the earthquake process, in Global Tectonics and Earthquake Risk, chap. 7, Elsevier Sci., New York, 1974.
31. Molchan, G. M., Structure of optimal strategies in earthquake prediction, Tectonophysics, 193, 267-276, 1991.
32. Molchan, G. M., Earthquake prediction as a decision-making problem, Pure Appl. Geophys., 149, 233-247, 1997.
33. Molchan, G. M., and Y. Y. Kagan, Earthquake prediction and its optimization, J. Geophys. Res, 97, 4823-4838, 1992.
34. Morse, P. M., and H. Feshbach, Methods in Theoretical Physics, McGraw-Hill, New York, 1953.
35. Ogata, Y., Statistical models for earthquake occurrences and residual analysis for point processes, Res. Memo. Tech. Rep. 288, Inst. of Stat. Math., Tokyo, 1985.
36. Ogata, Y., Long-term dependence of earthquake occurrences and statistical models for standard seismic activity (in Japanese), in Mathematical Seismology, vol. II, edited by M. Saito, pp. 115-125, Inst. of Stat. Math., Tokyo, 1987.
37. Ogata, Y., Statistical models for earthquake occurrence and residual analysis for point processes, J. Am. Stat. Assoc., 83, 9-27, 1988.
38. Ogata, Y., Statistical model for standard seismicity and detection of anomalies by residual analysis, Tectonophysics, 169, 159-174, 1989.
39. Ogata, Y., Detection of precursory relative quiescence before great earthquakes though a statistical model, J. Geophys. Res., 97, 19,845-19,871, 1992.
40. Ogata, Y., Seismicity analysis through point-process modeling: A review, Pure Appl. Geophys., 155, 471-507, 1999.
41. Ogata, Y., Increased probability of large earthquakes near aftershock regions with relative quiescence, J. Geophys. Res., 106, 8729-8744, 2001.
42. Omori, F., On the aftershocks of earthquakes, J. College Sci. Imp. Univ. Tokyo, 7, 111-120, 1894.
43. Pepke, S. L., and J. L. Carlson, Predictability of self-organizing systems, Phys. Rev. E, 50, 236-242, 1994.
44. Pepke, S. L., J. L. Carlson, and B. E. Shaw, Prediction of large events on a dynamical model of a fault, J. Geophys. Res., 99, 6769-6788, 1994.
45. Reasenberg, P. A., and L. M. Jones, Earthquake hazard after a mainshock in California, Science, 243, 1173-1176, 1989.
46. Rundle, P. B., J. B. Rundle, K. F. Tiampo, J. S. S. Martins, S. McGinnis, and W. Klein, Nonlinear network dynamics on earthquake fault systems, Phys. Rev. Lett., 87, 141-143, 2001.
47. Rundle, J. B., K. F. Tiampo, W. Klein, and J. S. S. Martins, Self-organization in leaky threshold systems: The influence of near-mean field dynamics and its implications for earthquakes, neurobiology, and forecasting, Proc. Nat. Acad. Sci. USA, 99, 2514-2521, 2002.
48. Sammis, S. G., and D. Sornette, Positive feedback, memory and the predictability of earthquakes, Proc. Nat. Acad. Sci. USA, 99(suppl.), 2501-2508, 2002.
49. Sornette, A., and D. Sornette, Renormalization of earthquake aftershocks, Geophys. Res. Lett., 26, 1981-1984, 1999.
50. Sornette, D., and A. Helmstetter, On the occurrence of finite-time-singularity in epidemic models of rupture, earthquakes and starquakes, Phys. Res. Lett., 89, 15,801, 2002.
51. Sornette, D., and C. G. Sammis, Complex critical exponents from renormalization group theory of earthquakes: Implications for earthquake predictions, J. Phys. I Fr., 5, 607-619, 1995.
52. Utsu, T., Aftershocks and earthquake statistics II: Further investigation of aftershocks and other earthquake sequence based on a new classification of earthquake sequences, J. Facul. Sci. Hokkaido Univ. Ser. VII, 3, 379-441, 1970.
53. Utsu, T., A review of seismicity (in Japanese), in Mathematical Seismology, vol. II, edited by M. Saito, pp. 139-157, Inst. of Stat. Math., Tokyo, 1992.
54. Utsu, T., Y. Ogata, and S. Matsu'ura, The centenary of the Omori Formula for a decay law of aftershock activity, J. Phys. Earth, 43, 1-33, 1995.
55. Vere-Jones, D., Probabilities and information gain for earthquake forecasting, Comput. Seismol., 30, 248-263, 1998.
56. Wiemer, S., Introducing probabilistic aftershock hazard mapping, Geophys. Res. Lett., 27, 3405-3408, 2000.