Abstract
In this paper we propose a clustering technique set up to separate and find out the two main components of seismicity: the background seismicity and the triggered one. We suppose that a seismic catalogue is the realization of a non homogeneous space–time Poisson clustered process, with a different parametrization for the intensity function of the Poisson-type component and of the clustered (triggered) component. The method here proposed assigns each earthquake to the cluster of earthquakes, or to the set of independent events, according to the increment to the likelihood function, computed using the conditional intensity function estimated by maximum likelihood methods and iteratively changing the assignment of the events; after a change of partition, MLE of parameters are estimated again and the process is iterated until there is no more improvement in the likelihood.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Adelfio, G., Chiodi, M., De Luca, L, & Luzio, D. (2006a). Nonparametric clustering of seismic events. In S. Zani, A. Cerioli, M. Riani, & M. Vichi (Eds.), Data analysis, classification and the forward search (pp. 397–404). Berlin: Springer.
Adelfio, G., Chiodi, M., De Luca, L., Luzio, D., & Vitale, M. (2006b). Southern-tyrrhenian seismicity in space–time-magnitude domain. Annals of Geophysics, 49(6), 1139–1151.
Adelfio, G., & Chiodi, M. (2008). Second-order diagnostics for space–time point processes with application to seismic events. Environmetrics, doi:10.1002/env.961.
Daley, D. J., & Vere-Jones, D. (2003). An introduction to the theory of point processes (2nd edition). New York: Springer.
Gutenberg, B., & Richter, C. F. (1944). Frequency of earthquakes in California. Bulletin of the Seismological Society of America, 34, 185–188.
Ogata, Y. (1988). Statistical models for earthquake occurrences and residual analysis for point processes. Journal of the American Statistical Association, 83(401), 9–27.
Ogata, Y. (1998). Space–time point-process models for earthquake occurrences. Annals of the Institute of Statistical Mathematics, 50(2), 379–402.
Ogata, Y. (2001). Exploratory analysis of earthquake clusters by likelihood-based trigger models. Journal of Applied Probability, 38(A), 202–212.
Ogata, Y., Zhuang, J., & Vere-Jones, D. (2004). Analyzing earthquake clustering features by using stochastic reconstruction. Journal of Geophysical Research, 109(B05301), 1–17.
R Development Core Team. (2005). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing.
Silverman, B. W. (1986). Density estimation for statistics and data analysis. London: Chapman and Hall.
Utsu, T. (1961). A statistical study on the occurrence of aftershocks. Geophysical Magazine, 30, 521–605.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Adelfio, G., Chiodi, M., Luzio, D. (2010). An Algorithm for Earthquakes Clustering Based on Maximum Likelihood. In: Palumbo, F., Lauro, C., Greenacre, M. (eds) Data Analysis and Classification. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03739-9_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-03739-9_3
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-03738-2
Online ISBN: 978-3-642-03739-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)