Earthquake forecasting based on data assimilation: Sequential Monte Carlo methods for renewal point processes

Nonlinear Processes in Geophysics

Volumn 18, Issue 1, 2011, Pages 49-70

  Werner, M J ^a,c   Ide, K ^b   Sornette, D ^a  

^a ETH ZURICH   (Switzerland)

^b Bldg 142   (United States)

^c PRINCETON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; DATA ASSIMILATION; EARTHQUAKE PREDICTION; ERROR ANALYSIS; MONTE CARLO ANALYSIS; SEISMIC DATA; SEISMICITY;

EID: 79551696007     PISSN: 10235809     EISSN: 16077946     Source Type: Journal    
DOI: 10.5194/npg-18-49-2011     Document Type: Article

References (93)

1. Andrieu, C., Doucet, A., Singh, S., and Tadic, V.: Particle methods for change detection, system identification, and control, Proceedings of the IEEE, 92 (Pubitemid 40890751)
2. Arulampalam, M., Maskell, S., Gordon, N., and Clapp, T.: A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking, Signal Processing, IEEE Transactions on, 50, 174-188, doi:10.1109/78.978374, 2002. (Pubitemid 34291500)
3. Bakun, W. H., Aagaard, B., Dost, B., Ellsworth, W. L., Hardebeck, J. L., Harris, R. A., Ji, C., Johnston, M. J. S., Langbein, J., Lienkaemper, J. J., Michael, A. J., Murray, J. R., Nadeau, R. M., Reasenberg, P. A., Reichle, M. S., Roeloffs, E. A., Shakal, A., Simpson, R. W., and Waldhauser, F.: Implications for prediction and hazard assessment from the 2004 Parkfield earthquake, Nature, 437, 969-974, doi:10.1038/nature04067, 2005. (Pubitemid 41486972)
4. Biasi, G., Weldon, R., Fumal, T., and Seitz, G.: Paleoseismic event dating and the conditional probability of large earthquakes on the southern San Andreas fault, California, B. Seismol. Soc. Am., 92, 2761-2781, 2002. (Pubitemid 36689465)
5. Capṕe, O., Moulines, E., and Ryden, T.: Inference in Hidden Markov Models (Springer Series in Statistics), Springer-Verlag New York, Inc., Secaucus, NJ, USA, 2005.
6. Capṕe, O., Godsill, S., and Moulines, E.: An Overview of Existing Methods and Recent Advances in Sequential Monte Carlo, Proceedings of the IEEE, 95, 899-924, doi:10.1109/JPROC.2007. 893250, 2007.
7. Cornell, C. A.: Engineering seismic risk analysis, Bull. Seismol. Soc. Am., 58, 1583-1606, http://www.bssaonline.org/cgi/ content/abstract/58/5/1583, 1968.
8. Daley, R.: Atmospheric Data Analysis, Cambridge University Press, Cambridge, UK, 1991.
9. Daley, D. J. and Vere-Jones, D.: An Introduction to the Theory of Point Processes, vol. I, Springer, New York, USA, 2003.
10. Daley, D. J. and Vere-Jones, D.: Scoring probability forecasts for point processes: The entropy score and information gain, J. Appl. Prob., 41A, 297-312, 2004. (Pubitemid 44973186)
11. Davis, P. M., Jackson, D. D., and Kagan, Y. Y.: The longer it has been since the last earthquake, the longer the expected time till the next?, B. Seismol. Soc. Am., 79, 1439-1456, 1989.
12. de Freitas, N.: Bayesian Methods for Neural Networks, PhD thesis, Cambridge University, http://www.cs.ubc.ca/-nando/ publications.php, 1999.
13. Doucet, A., Godsill, S., and Andrieu, C.: On Sequential Monte Carlo Sampling methods for Bayesian filtering, Stat. Comput., 10, 197-208, 2000.
14. Doucet, A., de Freitas, N., and Gordon, N. (Eds.): Sequential Monte Carlo Methods in Practice, Springer-Verlag, New York, 2001.
15. Durbin, J. and Koopman, S. J.: Time Series Analysis by State Space Methods, Oxford University Press, Oxford, UK, 2001.
16. Evensen, G.: Sequential data assimilation with a nonlinear quasigeostrophic model using Monte Carlo methods to forecast error statistics, J. Geophys. Res., 99, 10143-10162, doi:10.1029/ 94JC00572, 1994.
17. Field, E. H.: A Summary of PreviousWorking Groups on California Earthquake Probabilities, B. Seismol. Soc. Am., 97, 1033-1053, doi:10.1785/0120060048, 2007a. (Pubitemid 47296566)
18. Field, E. H.: Overview of the Working Group for the Development of Regional Earthquake Likelihood Models (RELM), Seismol. Res. Lett., 78, 7-16, doi:10.1785/gssrl.78.1.7, 2007b.
19. Geller, R. J.: Earthquake prediction: A critical review, Geophys. J. Int., 131, 425-450, doi:10.1111/j.1365-246X.1997.tb06588.x, 1997. (Pubitemid 28107513)
20. Geller, R. J., Jackson, D. D., Kagan, Y. Y., and Mulargia, F.: Earthquakes cannot be predicted, Science, 275, 1616-1617, 1997. (Pubitemid 27120531)
21. Gerstenberger, M. C., Wiemer, S., Jones, L. M., and Reasenberg, P. A.: Real-time forecasts of tomorrow's earthquakes in California, Nature, 435, 328-331, 2005. (Pubitemid 40745540)
22. Ghil, M. and Malanotte-Rizzoli, P.: Data Assimilation in Meteorology and Oceanography, Adv. Geophys., 33, 141-266, doi: 10.1016/S0065-2687(08)60442-2, 1991.
23. Grant, L. B. and Gould, M. M.: Assimilation of Paleoseismic Data for Earthquake Simulation, Pure and Applied Geophysics, 161, 2295-2306, doi:10.1007/s00024-003-2564-8, 2004. (Pubitemid 39408212)
24. Hainzl, S., Enescu, B., Cocco, M., Woessner, J., Catalli, F., Wang, R., and Roth, F.: Aftershock modeling based on uncertain stress calculations, Journal of Geophysical Research Solid Earth, 114, B05309, doi:10.1029/ 2008JB006011, 2009.
25. Harte, D. and Vere-Jones, D.: The Entropy Score and its Uses in Earthquake Forecasting, Pure and Applied Geophysics, 162, 1229-1253, doi:10.1007/s00024-004-2667-2, 2005. (Pubitemid 40782255)
26. Helmstetter, A. and Sornette, D.: Subcritical and supercritical regimes in epidemic models of earthquake aftershocks, J. Geophys. Res., 107, 2237, doi:10.1029/2001JB001580, 2002.
27. Hooke, R. and Jeeves, T. A.: "Direct Search" Solution of Numerical and Statistical Problems, J. ACM, 8, 212-229, doi: 10.1145/321062.321069, 1961.
28. Ide, K., Bennett, A., Courtier, P., Ghil, M., and Lorenc, A.: Unified notation for data assimilation: Operational, sequential and variational, J. Meteor. Soc. Japan, 75, 71-79, 1997. (Pubitemid 128151955)
29. Jackson, D. D.: Hypothesis Testing and Earthquake Prediction, Proc. Natl. Acad. Sci. USA, 93, 3772-3775, 1996. (Pubitemid 26144198)
30. Jordan, T. H.: Earthquake Predictability: Brick by Brick, Seismol. Res. Lett., 77, 3-6, 2006.
31. Jordan, T. and Jones, L.: Operational Earthquake Forecasting: Some Thoughts on Why and How, Seismol. Res. Lett., 81, 571- 574, doi:10.1785/gssrl. 81.4.571, 2010.
32. Kagan, Y. Y.: Statistics of characteristic earthquakes, B. Seismol. Soc. Am., 83, 7-24, 1993. (Pubitemid 23391452)
33. Kagan, Y. Y.: Are earthquakes predictable?, Geophys. J. Int., 131, 505-525, 1997. (Pubitemid 28107520)
34. Kagan, Y. Y.: Universality of the seismic moment-frequency relation, Pure and Appl. Geophys., 155, 537-573, 1999.
35. Kagan, Y. Y. and Jackson, D. D.: Seismic gap hypothesis: Ten years after, J. Geophys. Res., 96, 21419-21431, 1991.
36. Kagan, Y. Y. and Jackson, D. D.: New Seismic Gap Hypothesis: Five Years After, J. Geophys. Res., 100, 3943-3959, 1995. (Pubitemid 26464527)
37. Kagan, Y. Y. and Jackson, D. D.: Probabilistic forecasting of earthquakes, Geophys. J. Int., 143, 483-453, 2000.
38. Kagan, Y. Y. and Knopoff, L.: Statistical Short-Term Earthquake Prediction, Science, 236, 1563-1567, 1987.
39. Kalman, R. E.: A new Approach to Linear Filtering and Predictive Problems, Transactions ASME, J. Basic Eng., 82D, 35-45, 1960.
40. Kalman, R. E. and Bucy, R. S.: New Results in Linear Filtering and Prediction Theory, Transactions ASME, J. Basic Eng., 83, 95-108, 1961.
41. Kalnay, E.: Atmospheric Modeling, Data Assimilation and Predictability, Cambridge Univ. Press, Cambridge, UK, 2003.
42. Kong, A., Liu, J., and Wong, W.: Sequential Imputations and Bayesian Missing Data Problems, J. Am. Stat. Assoc., 89, 278-288, 1994.
43. K̈unsch, H. R.: State space and hidden Markov models, in: Complex stochastic systems (Eindhoven, 1999), vol. 87 of Monogr. Statist. Appl. Probab., pp. 109-173, Chapman & Hall/CRC, Boca Raton, FL, 2001.
44. Laherr̀ere, J. and Sornette, D.: Stretched exponential distributions in nature and economy: "Fat tails" with characteristic scales, European Physical Journal B, 2, 525-539, doi:10.1007/ s100510050276, 1998. (Pubitemid 128437418)
45. Lewis, R. M. and Torczon, V.: Pattern Search Algorithms for Bound Constrained Minimization, SIAM J. Optimization, 9, 1082-1099, doi:http://dx.doi.org/10.1137/S1052623496300507, 1999. (Pubitemid 129489318)
46. Liu, J. S.: Monte Carlo Strategies in Scientific Computing, Springer-Verlag, New York, 2001.
47. Liu, J. S. and Chen, R.: Sequential Monte Carlo Methods for Dynamic Systems, J. Am. Stat. Assoc., 93, 1032-1044, 1998.
48. Lovett, W.: Banking and Financial Institutions Law in a Nutshell, West Publishing Co., second edn., 1988.
49. McCann,W., Nishenko S. Sykes L. Krause J.: Seismic Gaps and plate tectonics: Seismic Potential for major boundaries Pure Appl. Geophys. 117, 1082-1147, 1979.
50. McGuire, J. J.: Seismic Cycles and Earthquake Predictability on East Pacific Rise Transform Faults, B. Seismol. Soc. Am., 98, 1067-1084, doi:10.1785/0120070154, 2008. (Pubitemid 351902776)
51. Ḿezard, M., Parisi, G., and Virasoro, M.: Spin glass theory and beyond, World Scientific Lecture Notes in Physics Vol. 9, Cambridge Univ. Press, Cambridge, UK, 1987.
52. Miller, R. N., Carter, E. F., and Blue, S. T.: Data Assimilation into Nonlinear Stochastic Models, Tellus, 51A, 167-194, 1999.
53. Nadeau, R. and Johnson, L.: Seismological studies at Parkfield VI: Moment release rates and estimates of source parameters for small repeating earthquakes, B. Seismol. Soc. Am., 88, 790-814, 1998. (Pubitemid 28438000)
54. Nishenko, S. P.: Circum-Pacific seismic potential 1989-1999, Pure Appl. Geophys., 135, 169-259, 1991.
55. Nishenko, S. P. and Buland, R.: A generic recurrence interval distribution for earthquake forecasting, B. Seismol. Soc. Am., 77, 1382-1399, 1987.
56. Ogata, Y.: Statistical models for earthquake occurrence and residual analysis for point processes, J. Am. Stat. Assoc., 83, 9-27, 1988.
57. Ogata, Y.: Space-time Point-process Models for Earthquake Occurrences, Ann. Inst. Stat. Math., 5, 379-402, 1998. (Pubitemid 128487986)
58. Ogata, Y.: Estimating the Hazard of Rupture Using Uncertain Occurrence Times of Paleoearthquakes, J. Geophys. Res., 104, 17995-18014, 1999.
59. Ogata, Y.: Slip-Size-Dependent Renewal Processes and Bayesian Inferences for Uncertainties, J. Geophys. Res., 107, 2268, doi: 10.1029/2001JB000668, 2002.
60. Olsson, J. and Ryd́en, T.: Asymptotic properties of particle filterbased maximum likelihood estimators for state space models, Stoc. Proc. Appl., 118, 649-680, doi:10.1016/j.spa.2007.05.007, 2008. (Pubitemid 351258212)
61. Parsons, T.: Monte Carlo method for determining earthquake recurrence parameters from short paleoseismic catalogs: Example calculations for California, J. Geophys. Res. (Solid Earth), 113, B03302, doi:10.1029/ 2007JB004998, 2008.
62. Pham, D. T.: Stochastic Methods for Sequential Data Assimilation in Strongly Nonlinear Systems, Mon. Weather Rev., 129, 1194-1207, 2001. (Pubitemid 32554953)
63. Polakoff, M. and Durkin, T.: Financial institutions and markets, Houghton Mifflin Boston, second edn., 1981.
64. Reid, H.: The Mechanics of the Earthquake, The California Earthquake of April 18, 1906, Report of the State Investigation Commission, Vol. 2, Carnegie Institution ofWashington,Washington, D.C., pp. 16-28, 1910.
65. Rhoades, D. A. and Evison, F. F.: Long-range Earthquake Forecasting with Every Earthquake a Precursor According to Scale, Pure Appl. Geophys., 161, 47-72, doi:10.1007/s00024-003-2434-9, 2004. (Pubitemid 38070129)
66. Rhoades, D. A., Dissen, R. V., and Dowrick, D.: On the Handling of Uncertainties in Estimating the Hazard of Rupture on a Fault Segment, J. Geophys. Res., 99, 13701-13712, 1994.
67. Robert, C. P. and Casella, G.: Monte Carlo Statistical Methods (Springer Texts in Statistics), Springer-Verlag New York, Inc., Secaucus, NJ, USA, 2004.
68. Rong, Y., Jackson, D. D., and Kagan, Y. Y.: Seismic gaps and earthquakes, J. Geophys. Res. (Solid Earth), 108, 2471, doi: 10.1029/2002JB002334, 2003.
69. Sambridge, M. and Mosegaard, K.: Monte Carlo Methods in Geophysical Inverse Problems, Rev. Geophys., 40, 1009, doi: 10.1029/2000RG000089, 2002.
70. Scholz, C. H.: The Mechanics of Earthquakes and Faulting, Cambridge University Press, Cambridge, 2nd edn., 2002.
71. Schorlemmer, D., Gerstenberger, M. C.,Wiemer, S., Jackson, D. D., and Rhoades, D. A.: Earthquake Likelihood Model Testing, Seismol. Res. Lett., 78, 17, 2007.
72. Schorlemmer, D., Zechar, J. D., Werner, M. J., Field, E., Jackson, D. D., and Jordan, T. H.: First Results of the Regional Earthquake Likelihood Models Experiment, Pure and Appl. Geophys.: The Frank Evison Volume, 167(8/9), doi:10.1007/s00024-010- 0081-5, 2010.
73. Snyder, C., Bengtsson, T., Bickel, P., and Anderson, J.: Obstacles to High-Dimensional Particle Filtering, Mon.Weather Rev., 136, 4629-4640, 2008.
74. Sornette, D.: Critical Phenomena in Natural Sciences: Chaos, Fractals, Selforganization and Disorder: Concepts and Tools, Springer, Berlin, 2nd edn., 2004.
75. Sornette, D. and Ide, K.: The Kalman-Ĺevy filter, Physica D Nonlinear Phenomena, 151, 142-174, 2001.
76. Sornette, D., Knopoff, L., Kagan, Y., and Vanneste, C.: Rankordering statistics of extreme events: application to the distribution of large earthquakes, J. Geophys. Res., 101, 13883-13893, 1996.
77. Sykes, L. R. and Menke, W.: Repeat Times of Large Earthquakes: Implications for Earthquake Mechanics and Long-Term Prediction, B. Seismol. Soc. Am., 96, 1569-1596, doi:10.1785/ 0120050083, 2006. (Pubitemid 44612989)
78. Talagrand, O.: Assimilation of Observations, J. Meteorol. Soc. Japan, 75, 191-209, 1997.
79. Tarantola, A.: Inverse Problem Theory, Elsevier Science Publishers B. V., Amsterdam, The Netherlands, 1987.
80. Tippett, M. K., Anderson, J. L., Bishop, C. H., Hamill, T. M., and Whitaker, J. S.: Ensemble Square Root Filters, Mon. Weather Rev., 131, 1485-1490, doi:10.1175/1520-0493(2003)131h1485: ESRFi2.0.CO;2, http://journals.ametsoc.org/doi/abs/10.1175/ 1520- 0493282003291313C14853AESRF3E2.0.CO3B2, 2003. (Pubitemid 36953823)
81. Torczon, V.: On the Convergence of Pattern Search Algorithms, SIAM J. on Optimization, 7, 1-25, doi:http://dx.doi.org/10.1137/ S1052623493250780, 1997.
82. Van Aalsburg, J., Grant, L. B., Yakovlev, G., Rundle, P. B., Rundle, J. B., Turcotte, D. L., and Donnellan, A.: A feasibility study of data assimilation in numerical simulations of earthquake fault systems, Phys. Earth Planet. In., 163, 149-162, doi:10.1016/j. pepi.2007.04.020, 2007. (Pubitemid 47250421)
83. Varini, E.: Sequential Estimation Methods in Continuous-Time State Space Models, PhD thesis, Universit̀a Commerciale "Luigi Bocconi" - Milano, 2005.
84. Varini, E.: A Monte Carlo method for filtering a marked doubly stochastic Poisson process, Stat. Method Appl., 17, 183-193, 2008.
85. Vere-Jones, D.: Stochastic Models for Earthquake Occurrence, J. Roy. Stat. Soc. Series B (Methodological), 32, 1-62 (with discussion), 1970.
86. Vere-Jones, D.: Forecasting Earthquakes and earthquake risk, Intern. J. Forecasting, 11, 503-538, 1995.
87. Werner, M. J. and Sornette, D.: Magnitude Uncertainties Impact Seismic Rate Estimates, Forecasts and Predictability Experiments, J. Geophys. Res. Solid Earth, 113, B08302, doi: 10.1029/2007JB005427, 2008.
88. Werner, M. J., Helmstetter, A., Jackson, D. D., and Kagan, Y. Y.: High Resolution Long- and Short-Term Earthquake Forecasts for California, B. Seismol. Soc. Am., accepted, preprint available at http://arxiv.org/abs/0910.4981, 2010a.
89. Werner, M. J., Helmstetter, A., Jackson, D. D., Kagan, Y. Y., and Wiemer, S.: Adaptively Smoothed Seismicity Earthquake Forecasts for Italy, Annals of Geophysics, 53, 107-116, doi: 10.4401/ag-4839, 2010b.
90. Werner, M. J., Zechar, J. D., Marzocchi, W., and Wiemer, S.: Retrospective Evaluation of the Five-year and Ten-year CSEP-Italy Earthquake Forecasts, Annals of Geophysics, 53, 11-30, doi: 10.4401/ag-4840, 2010c.
91. Wesnousky, S. G.: The Gutenberg-Richter or characteristic earthquake distribution, which is it?, B. Seismol. Soc. Am., 84, 1940- 1959, 1994.
92. Wikle, C. K. and Berliner, L. M.: A Bayesian tutorial for data assimilation, Physica D Nonlinear Phenomena, 230, 1-2, doi: 10.1016/j.physd. 2006.09.017, 2007. (Pubitemid 46776909)
93. Zechar, J. D., Schorlemmer, D., Liukis, M., Yu, J., Euchner, F., Maechling, P. J., and Jordan, T. H.: The Collaboratory for the Study of Earthquake Predictability perspective on computational earthquake science, Concurrency and Computation: Practice and Experience, 22(12), 1836-1847, doi:10.1002/cpe.1519, 2010.