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On the statistics of the linked stress release model

  • Mark Bebbington (a1) and David S. Harte (a2)

The paper reviews the formulation of the linked stress release model for large scale seismicity together with aspects of its application. Using data from Taiwan for illustrative purposes, models can be selected and verified using tools that include Akaike's information criterion (AIC), numerical analysis, residual point processes and Monte Carlo simulation.

Corresponding author
1 Postal address: Institute of Information Sciences and Technology, Massey University, Private Bag 11222, Palmerston North, New Zealand. Email:
2 Postal address: Statistics Research Associates, PO Box 12 649, Thorndon, Wellington, New Zealand. Email:
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Aalen, O. O. and Hoem, J. M. (1978). Random time changes for multivariate counting processes. Scand. Actuarial J. 1978, 81101.
Akaike, H. (1977). On entropy maximization principle. In Applications of Statistics , ed. Krishnaiah, P. R., North Holland, Amsterdam, 2741.
Daley, D. J. and Vere-Jones, D. (1988). An Introduction to the Theory of Point Processes. Springer, New York.
Gardner, J. K. and Knopoff, L. (1974). Is the sequence of earthquakes in southern California, with aftershocks removed, Poissonian? Bull. Seismol. Soc. Amer. 64, 13631367.
Harte, D. S. (1999). Documentation for the Statistical Seismology Library. Research Report 98/10 (revised edition), School of Mathematical and Computing Sciences, Victoria University of Wellington.
Hill, D. P. et al. (1993). Seismicity remotely triggered by the magnitude 7.3 Landers, California, earthquake. Science 260, 16171623.
Imoto, M., Maeda, K. and Yoshida, A. (1999). Use of statistical models to analyze periodic seismicity observed for clusters in the Kanto region, central Japan. Pure Appl. Geophys. 155, 609624.
Kagan, Y. Y. (1991). Seismic moment distribution. Geophys. J. Int. 106, 123134.
Kanamori, H. and Anderson, D. L. (1975). Theoretical basis of some empirical relations in seismology. Bull. Seismol. Soc. Amer. 65, 10731095.
Kanaori, Y., Kawakami, S. and Yairi, K. (1993). Space-time correlations between inland earthquakes in central Japan and great offshore earthquakes along the Nankai trough: Implication for destructive earthquake prediction. Engrg. Geol. 33, 289303.
Knopoff, L. (1971). A stochastic model for the occurrence of main sequence events. Rev. Geophys. and Space Phys. 9, 175188.
Liu, J., Chen, Y., Shi, Y. and Vere-Jones, D. (1999). Coupled stress release model for time dependent seismicity. Pure Appl. Geophys. 155, 649667.
Lu, C., Harte, D. and Bebbington, M. (1999). A linked stress release model for historical Japanese earthquakes: Coupling among major seismic regions. Earth Planets Space 51, 907916.
Ogata, Y. (1981). On Lewis's simulation method for point processes. IEEE Trans. Inf. Theory 27, 2331.
Ogata, Y. (1988). Statistical models for earthquake occurrences and residual analysis for point processes. J. Amer. Statist. Assoc. 83, 927.
Pollitz, F. F. and Sacks, I. S. (1997). The 1995 Kobe, Japan earthquake: A long-delayed aftershock of the offshore 1944 Tonokai and 1946 Nankaido earthquakes. Bull. Seismol. Soc. Amer. 87, 110.
Press, W. H., Flannery, B. P., Teukolsky, S. A. and Vetterling, W. T. (1986). Numerical Recipes. Cambridge University Press.
Shimazaki, K. (1976). Intra-plate seismicity and inter-plate earthquakes: Historical activity in southwest Japan. Tectonophysics 33, 3342.
Vere-Jones, D. (1978). Earthquake prediction: a statistician's view. J. Phys. Earth 26, 129146.
Vere-Jones, D. (1988). On the variance properties of stress-release models. Austral. J. Statist. 30A, 123135.
Zheng, X. (1991). Ergodic theorems for stress release processes. Stoch. Proc. Appl. 37, 239258.
Zheng, X. and Vere-Jones, D. (1991). Applications of stress release models to earthquakes from North China. Pure Appl. Geophys. 135, 559576.
Zheng, X. and Vere-Jones, D. (1994). Further applications of the stochastic stress release model to historical earthquake data. Tectonophysics 229, 101121.
Zhuang, J. and Ma, L. (1998). The stress release model and results from modelling features of some seismic regions in China. Acta Seismologica Sinica 11, 5970.
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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
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