Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-20T16:30:57.596Z Has data issue: false hasContentIssue false

On the statistics of the linked stress release model

Published online by Cambridge University Press:  14 July 2016

Mark Bebbington*
Affiliation:
Massey University
David S. Harte*
Affiliation:
Statistics Research Associates Ltd
*
1Postal address: Institute of Information Sciences and Technology, Massey University, Private Bag 11222, Palmerston North, New Zealand. Email: [email protected]
2Postal address: Statistics Research Associates, PO Box 12 649, Thorndon, Wellington, New Zealand. Email: [email protected]

Abstract

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.

Type
Models and statistics in seismology
Copyright
Copyright © Applied Probability Trust 2001 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aalen, O. O. and Hoem, J. M. (1978). Random time changes for multivariate counting processes. Scand. Actuarial J. 1978, 81101.CrossRefGoogle Scholar
Akaike, H. (1977). On entropy maximization principle. In Applications of Statistics , ed. Krishnaiah, P. R., North Holland, Amsterdam, 2741.Google Scholar
Daley, D. J. and Vere-Jones, D. (1988). An Introduction to the Theory of Point Processes. Springer, New York.Google Scholar
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.CrossRefGoogle Scholar
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.Google Scholar
Hill, D. P. et al. (1993). Seismicity remotely triggered by the magnitude 7.3 Landers, California, earthquake. Science 260, 16171623.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
Kagan, Y. Y. (1991). Seismic moment distribution. Geophys. J. Int. 106, 123134.CrossRefGoogle Scholar
Kanamori, H. and Anderson, D. L. (1975). Theoretical basis of some empirical relations in seismology. Bull. Seismol. Soc. Amer. 65, 10731095.Google Scholar
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.CrossRefGoogle Scholar
Knopoff, L. (1971). A stochastic model for the occurrence of main sequence events. Rev. Geophys. and Space Phys. 9, 175188.CrossRefGoogle Scholar
Liu, J., Chen, Y., Shi, Y. and Vere-Jones, D. (1999). Coupled stress release model for time dependent seismicity. Pure Appl. Geophys. 155, 649667.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Ogata, Y. (1981). On Lewis's simulation method for point processes. IEEE Trans. Inf. Theory 27, 2331.CrossRefGoogle Scholar
Ogata, Y. (1988). Statistical models for earthquake occurrences and residual analysis for point processes. J. Amer. Statist. Assoc. 83, 927.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Press, W. H., Flannery, B. P., Teukolsky, S. A. and Vetterling, W. T. (1986). Numerical Recipes. Cambridge University Press.Google Scholar
Shimazaki, K. (1976). Intra-plate seismicity and inter-plate earthquakes: Historical activity in southwest Japan. Tectonophysics 33, 3342.CrossRefGoogle Scholar
Vere-Jones, D. (1978). Earthquake prediction: a statistician's view. J. Phys. Earth 26, 129146.CrossRefGoogle Scholar
Vere-Jones, D. (1988). On the variance properties of stress-release models. Austral. J. Statist. 30A, 123135.CrossRefGoogle Scholar
Zheng, X. (1991). Ergodic theorems for stress release processes. Stoch. Proc. Appl. 37, 239258.Google Scholar
Zheng, X. and Vere-Jones, D. (1991). Applications of stress release models to earthquakes from North China. Pure Appl. Geophys. 135, 559576.CrossRefGoogle Scholar
Zheng, X. and Vere-Jones, D. (1994). Further applications of the stochastic stress release model to historical earthquake data. Tectonophysics 229, 101121.Google Scholar
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.CrossRefGoogle Scholar