A stochastic two-node stress transfer model reproducing Omori's law

Pure and Applied Geophysics

Volumn 160, Issue 8, 2003, Pages 1429-1445

  Borovkov, K ^a   Bebbington, M S ^b  

^a UNIVERSITY OF MELBOURNE   (Australia)

^b MASSEY UNIVERSITY   (New Zealand)

Author keywords

Aftershocks; Constitutive law; Markov model; Modified Omori formula; Stress release

Indexed keywords

AFTERSHOCK; EARTHQUAKE; MARKOV CHAIN; MODELING; STRESS CHANGE;

EID: 0037789575     PISSN: 00334553     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00024-003-2354-8     Document Type: Article

References (38)

1. AKAIKE, H., On entropy maximization principle. In Applications of Statistics (ed. Krishnaiah, P.R.) (North-Holland, Amsterdam 1977) pp. 27-41.
2. BEBBINGTON, M. and HARTE, D. (2001), On the Statistics of the Linked Stress Release Process, J. Appl. Probab. 38A, 176-187.
3. BOROVKOV, K. and VERE-JONES, D. (2000), Explicit Formulae for Stationary Distributions of Stress Release Processes, J. Appl. Probab. 37, 315-321.
4. DALEY, D. J. and VERE-JONES, D., An Introduction to the Theory of Point Processes (Springer, Berlin 1988).
5. DAVIS, S. D. and FROHLICH, C. (1991), Single-link Cluster Analysis of Earthquake Aftershocks: Decay Laws and Regional Variations, J. Geophys. Res. 96, 6335-6350.
6. DIETERICH, J. (1994), A Constitutive Law for Rate of Earthquake Production and its Application to Earthquake Clustering, J. Geophys. Res. 99, 2601-2618.
7. FROHLICH, C. (1987), Aftershocks and Temporal Clustering of Deep Earthquakes, J. Geophys. Res. 92, 13,944-13,956.
8. JAUM S. C. and SYKES, L. R. (1999), 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.
9. JONES, L. M. (1994), Foreshocks, Aftershocks, and Earthquake Probabilities: Accounting for the Landers Earthquake, Bull. Seismol. Soc. Am. 84, 892-899.
10. KANAMORI, H. and ANDERSON, D. L. (1975), Theoretical Basis of Some Empirical Relations in Seismology, Bull. Seismol. Soc. Am. 65, 1073-1095.
11. KISSLINGER, C. (1988), Seismicity Patterns and the Stress State in Subduction-type Seismogenic Zones, Geol. Surv. Open-File Rep. (U.S.) 88-16, 84-90.
12. KISSLINGER, C. (1996), Aftershocks and Fault-zone Properties, Adv. Geophys. 38, 1-36.
13. KISSLINGER, C. and JONES, L. M. (1991), Properties of Aftershock Sequences in Southern California, J. Geophys. Res. 96, 11,947-11,958.
14. KNOPOFF, L. (1996), A Selective Phenomenology of the Seismicity of Southern California, Proc. Natl. Acad. Sci. USA 93, 3756-3763.
15. KOSSOBOKOV, V. G., User manual for M8. In Algorithms for Earthquake Statistics and Prediction (eds. Healy, J.H., Kellis-Borok, V.I., and Lee, W.H.K.) (IASPEI, Menlo Park 1997) pp. 167-222.
16. KURTZ, T. G. Approximation of Population Processes (SIAM, Philadelphia, 1981).
17. LIU, J. VERE-JONES, D. MA, L. SHI, Y. and ZHUANG, J. (1998), The Principle of Coupled Stress Release Model and its Applications, Acta Seismologica Sinica II, 273-281.
18. LU, C., HARTE, D. S., and BEBBINGTON, M. S. (1999), A Linked Stress Release Model for Historical Japanese Earthquakes: Coupling Among Major Seismic Regions, Earth Planets Space 51, 907-916.
19. MATSU'URA, R. S. (1993), Median values of parameters in the modified Omori formula - for main shocks in and near Japan of M 6.0 and larger (1969-1991), Abstracts, 1993 Japan Earth Planet. Sci. Joint Meeting 224 (in Japanese).
20. MENDOZA, C. and HARTZELL, S. H. (1988), Aftershock Patterns and Main Shock Faulting, Bull. Seismol. Soc. Am. 77, 1382-1399.
21. MIKUMO, T. and MIYATAKE, T. (1979), Earthquake Sequences on a Frictional Fault Model with Non-uniform Strengths and Relaxation Times, Geophys. J. R. astr. Soc. 59, 497-522.
22. OGATA, Y. (1983), Estimation of the Parameters in the Modified Omori Formula for Aftershock Sequences, J. Phys. Earth 31, 115-124.
23. OGATA, Y. (1988), Statistical Models for Earthquake Occurrences and Residual Analysis for Point Processes, JASA 83, 9-27.
24. OMORI, F. (1894a), On Aftershocks, Rep. Imp. Earthq. Inv. Com. 2, 103-138 (in Japanese).
25. OMORI, F. (1894b), On Aftershocks of Earthquakes, J. Coll. Sci. Imp. Univ. Tokyo 7, 111-200 (in Japanese).
26. PAPAZACHOS, B. C. (1974), On the Time Distribution of Aftershocks and Foreshocks in the Area of Greece, Pure Appl. Geophys. 112, 627-631.
27. UTSU, T. (1957), Magnitudes of Earthquakes and Occurrence of their Aftershocks, Zisin, Ser. 2 10, 35-45 (in Japanese).
28. UTSU, T. (1961), A Statistical Study on the Occurrence of Aftershocks, Geophys. Mag. 30, 521-605.
29. UTSU, T. (1969), Aftershocks and Earthquake Statistics (I) -Some Parameters which Characterize an Aftershock Sequence and their Interaction, J. Fac. Sci. Hokkaido Univ., Ser. VII, 2, 129-195.
30. UTSU, T. (1970), Aftershocks and Earthquake Statistics (II) -Further Investigation of Aftershocks and Other Earthquake Sequences Based on a New Classification of Earthquake Sequences, J. Fac. Sci. Hokkaido Univ., Ser. VII, 3, 197-266.
31. UTSU, T., OGATA, Y., and MATSU'URA, R. S. (1995), The Centenary of the Omori Formula for a Decay Law of Aftershock Activity, J. Phys. Earth 43, 1-33.
32. VERE-JONES, D. (1978), Earthquake Prediction: a Statistician's View, J. Phys. Earth 26, 129-146.
33. VERE-JONES, D. (1988), On the Variance Properties of Stress-release Models, Austral. J. Statist. 30 A, 123-135.
34. VERE-JONES, D. (1995), Forecasting Earthquakes and Earthquake Risk, Internat. J. Forecasting II, 503-538.
35. ZHAO, Z.-X., OIKE, O., MATSUMURA, K., and XU, J.-R.(1992), p Values of Continental Aftershock Activity in China, Acta Seismol. Sin., 5, 683-690.
36. ZHENG, X. (1991), Ergodic Theorems for Stress Release Processes, Stoch. Proc. Appl. 37, 239-258.
37. ZHENG, X. and VERE-JONES, D. (1991), Applications of Stress Release Models to Earthquakes from North China, Pure Appl. Geophys. 135, 559-576.
38. ZHENG, X. and VERE-JONES, D. (1994), Further Applications of the Stochastic Stress Release Model to Historical Earthquake Data, Tectonophysics 229, 101-121.