Parameter estimation in the ETAS model: Approximations and novel methods

Bulletin of the Seismological Society of America

Volumn 104, Issue 2, 2014, Pages 985-994

  Lippiello, E ^a   Giacco, F ^a   de Arcangelis, L ^a   Marzocchi, W ^b   Godano, C ^a  

^a SECOND UNIVERSITY OF NAPLES   (Italy)

^b ISTITUTO NAZIONALE DI GEOFISICA E VULCANOLOGIA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

SEISMOLOGY;

BRANCHING PROCESS; EARTHQUAKE OCCURRENCES; EPIDEMIC-TYPE AFTERSHOCK SEQUENCES; LOG LIKELIHOOD; NOVEL METHODS; NOVEL TECHNIQUES; NUMERICAL CODE; PARAMETER INVERSION;

GEOPHYSICS;

ACCURACY ASSESSMENT; AFTERSHOCK; EARTHQUAKE CATALOGUE; EARTHQUAKE EVENT; ESTIMATION METHOD; NUMERICAL MODEL;

EID: 84897529275     PISSN: 00371106     EISSN: 19433573     Source Type: Journal    
DOI: 10.1785/0120130148     Document Type: Article

References (43)

1. Bottiglieri, M., E. Lippiello, C. Godano, and L. de Arcangelis (2011). Comparison of branching models for seismicity and likelihood maximization through simulated annealing, J. Geophys. Res. 116, no. B02303, doi: 10.1029/2009JB007060.
2. Console, R., M. Murru, and G. Falcone (2010). Probability gains of an epidemic-type aftershock sequence model in retrospective forecasting of M 5 earthquakes in Italy, J. Seismol. 14, 9-26.
3. Daley, D., and D. Vere-Jones (2003). An Introduction to the Theory of Point Processes, Volume I: Elementary Theory and Methods, Second Ed., Springer-Verlag, Berlin, Vol. XXI, 471 pp.
4. Felzer, K. R., and E. E. Brodsky (2006). Decay of aftershock density with distance indicates triggering by dynamic stress, Nature 441, 735-738.
5. Gutenberg, B., and C. F. Richter (1944). Frequency of earthquakes in California, Bull. Seismol. Soc. Am. 34, 185-188.
6. Harte, D. S. (2013). Bias in fitting the ETAS model: A case study based on New Zealand seismicity, Geophys. J. Int. 192, 390-412, doi: 10.1093/ gji/ggs026.
7. Hawkes, A. G., and L. Adamopoulos (1973). Cluster models for earthquakes-Regional comparisons, Bull. Int. Statist. Inst. 45, no. 3, 454-461.
8. Helmstetter, A., and D. Sornette (2003). Predictability in the epidemic-type aftershock sequence model of interacting triggered seismicity, J. Geophys. Res. 108, 2482-2499.
9. Jordan, T. H., Y.-T. Chen, P. Gasparini, R. Madariaga, I. Main, W. Marzocchi, G. Papadopoulos, G. Sobolev, K. Yamaoka, and J. Zschau (2011). Operational earthquake forecasting: State of knowledge and guidelines for utilization, Ann. Geophys. 54, 315-391, doi: 10.4401/ag-5350.
10. Kagan, Y. Y. (1973). Statistical methods in the study of seismic processes, Bull. Int. Statist. Inst. 45, 437-453.
11. Kagan, Y. Y. (1991). Likelihood analysis of earthquake catalogues, Geophys. J. Int. 106, 135-148.
12. Kagan, Y. Y. (2002). Aftershock zone scaling, Bull. Seismol. Soc. Am. 92, 641-655.
13. Lippiello, E., L. de Arcangelis, and C. Godano (2008). Influence of time and space correlations on earthquake magnitude, Phys. Rev. Lett. 100, 038501-04.
14. Lippiello, E., L. de Arcangelis, and C. Godano (2009). The role of static stress diffusion in the spatio-temporal organization of aftershocks, Phys. Rev. Lett. 103, 038501-04.
15. Lippiello, E., M. Bottiglieri, C. Godano, and L. de Arcangelis (2007). Dynamical scaling and generalized Omori law, Geophys. Res. Lett. 34, L23301, doi: 10.1029/2007GL030963.
16. Lippiello, E., C. Godano, and L. de Arcangelis (2007). Dynamical scaling in branching models for seismicity, Phys. Rev. Lett. 98, 098501-04.
17. Lippiello, E., W. Marzocchi, L. de Arcangelis, and C. Godano (2013). Spatial organization of foreshocks as a tool to forecast large earthquakes, Sci. Rept. 2, no. 846, doi: 10.1038/srep00846.
18. Marzocchi, W., and J. Zhuang (2011). Statistics between mainshocks and foreshocks in Italy and southern California, Geophys. Res. Lett. 38, L09310, doi: 10.1029/2011GL047165.
19. Musmeci, F., and D. Vere-Jones (1992). A space-time clustering model for historical earthquakes, Ann. Inst. Statist. Math. 44, 1-11.
20. Ogata, Y. (1978). The asymptotic behavior of maximum likelihood estimators for stationary point processes, Ann. Inst. Statist. Math. 30, no. 2, 243-261.
21. Ogata, Y. (1988). Statistical models for earthquake occurrence and residual analysis for point processes, J. Am. Statist. Assoc. 83, 9-27.
22. Ogata, Y. (1998). Space-time point-process models for earthquake occurrence, Ann. Inst. Statist. Math. 50, 379-402.
23. Ogata, Y., and H. Akaike (1982). On linear intensity models for mixed doubly stochastic Poisson and self-exciting processes, J. Roy. Stat. Soc. 44, 102-107.
24. Ogata, Y., and D. Vere-Jones (1984). Inference for earthquake models: A self-correcting model, Stoch. Proc. Appl. 17, 337-347.
25. Ogata, Y., and J. Zhuang (2006). Space-time ETAS models and an improved extension, Tectonophysics 413, 13-23.
26. Ogata, Y., L. M. Jones, and S. Toda (2003). When and where the aftershock activity was depressed: Contrasting decay patterns of the proximate large earthquakes in southern California, J. Geophys. Res. 108, 2318.
27. Omori, F. (1894). On the after-shocks of earthquakes, J. Coll. Sci. Imp. Univ. Tokyo 7, 111-200.
28. Ozaki, T. (1979). Maximum likelihood estimation of Hawkes self-exciting point process, Ann. Inst. Statist. Math. B31, 145-155.
29. Schoenberg, F. P. (2013). Facilitated estimation of ETAS, Bull. Seismol. Soc. Am. 103, no. 1, 601-605, doi: 10.1785/0120120146.
30. Sornette, D., and M. J. Werner (2005). Apparent clustering and apparent background earthquakes biased by undetected seismicity, J. Geophys. Res. 110, no. B09303, doi: 10.1029/2005JB003621.
31. Tiampo, K. R., and R. Shcherbakov (2012). Seismicity-based earthquake forecasting techniques: Ten years of progress, Tectonophysics 522, 89-121.
32. Turcotte, D. L., J. R. Holliday, and J. B. Rundle (2007). BASS, an alternative to ETAS, Geophys. Res. Lett. 34, doi: 10.1029/2007GL029696.
33. Utsu, T. (1969). Aftershocks and earthquake statistics (I) source parameters which characterize an aftershock sequence and their interrelations, J. Fac. Sci. Hokkaido Univ., Series VII, 3, 129-195.
34. Utsu, T., and A. Seki (1954). A relation between the area of aftershock region and the energy of mainshock, Zisin 7, 233-240.
35. Veen, A., and F. P. Schoenberg (2008). Estimation of space-time branching process models in seismology using an EM-type algorithm, J. Am. Stat. Assoc. 103, no. 482, 614-624.
36. Vere-Jones, D. (1970). Stochastic models for earthquake occurrence, J. Roy. Stat. Soc. 32, 1-62.
37. Vere-Jones, D., and J. Zhuang (2008). Distribution of the largest event in the critical epidemic-type aftershock-sequence model, Phys. Rev. E 78, 047102.
38. Wang, Q., D. D. Jackson, and J. Zhuang (2010). Missing links in earthquake clustering models, Geophys. Res. Lett. 37, L21307, doi: 10.1029/ 2010GL044858.
39. Wang, Q., F. P. Schoenberg, D. D. Jackson, and Y. Y. Kagan (2010). Standard errors of parameter estimates in the ETAS model, Bull. Seismol. Soc. Am. 100, 1989-2001.
40. Zhuang, J. (2006). Second-order residual analysis of spatiotemporal point processes and applications in model evaluation, J. Roy. Stat. Soc. 68, no. 4, 635-653, doi: 10.1111/j.1467-9868.2006.00559.x.
41. Zhuang, J., D. Harte, M. J. Werner, S. Hainzl, and S. Zhou (2012). Basic models of seismicity: Temporal models, Community Online Resource for Statistical Seismicity Analysis, doi: 10.5078/corssa-79905851.
42. Zhuang, J., Y. Ogata, and D. Vere-Jones (2002). Stochastic declustering of space-time earthquake occurrences, J. Am. Stat. Assoc. 97, 369-380.
43. Zhuang, J., Y. Ogata, and D. Vere-Jones (2004). Analyzing earthquake clustering features by using stochastic reconstruction, J. Geophys. Res. 109, no. B05301, 117.