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Spatial pattern analysis using hybrid models: an application to the Hellenic seismicity

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Abstract

Earthquakes are one of the most destructive natural disasters and the spatial distribution of their epicentres generally shows diverse interaction structures at different spatial scales. In this paper, we use a multi-scale point pattern model to describe the main seismicity in the Hellenic area over the last 10 years. We analyze the interaction between events and the relationship with geological information of the study area, using hybrid models as proposed by Baddeley et al. (2013). In our analysis, we find two competing suitable hybrid models, one with a full parametric structure and the other one based on nonparametric kernel estimators for the spatial inhomogeneity.

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References

  • Adelfio G (2010) An analysis of earthquakes clustering based on a second-order diagnostic approach. In: Palumbo F et al (eds) Data analysis and classification. Springer, Berlin, pp 309–317

    Chapter  Google Scholar 

  • Adelfio G, Chiodi M (2009) Second-order diagnostics for space-time point processes with application to seismic events. Environmetrics 20(8):895–911

    Google Scholar 

  • Adelfio G, Chiodi M (2015a) Alternated estimation in semi-parametric space-time branching-type point processes with application to seismic catalogs. Stoch Environ Res Risk Assess 29(2):443–450

    Article  Google Scholar 

  • Adelfio G, Chiodi M (2015b) Flp estimation of semi-parametric models for space-time point processes and diagnostic tools. Spat Stat 14:119–132

    Article  Google Scholar 

  • Adelfio G, Schoenberg FP (2009) Point process diagnostics based on weighted second-order statistics and their asymptotic properties. Ann Inst Stat Math 61(4):929–948

    Article  Google Scholar 

  • Ambraseys N, Adams R (1998) The rhodes earthquake of 26 June 1926. J Seismol 2(3):267–292

    Article  Google Scholar 

  • Anwar S, Stein A, van Genderen J (2012) Implementation of the marked strauss point process model to the epicenters of earthquake aftershocks. Advances in geo-spatial information science Taylor & Francis, London, pp 125–140

    Google Scholar 

  • Baddeley A, Møller J (1989) Nearest-neighbour markov point processes and random sets. Int Stat Rev 57(2):89–121

    Article  Google Scholar 

  • Baddeley A, Turner R (2005) Spatstat: an r package for analyzing spatial point patterns. J Stat Sofw 12(6):1–42

    Google Scholar 

  • Baddeley A, Turner TR (2000) Pratical maximum pseudo likelihood for spatial point patterns (with discussion). Aust N Z J Stat 42(3):283–322

    Article  Google Scholar 

  • Baddeley A, Turner R, Møller J, Hazelton M (2005) Residual analysis for spatial point processes. J R Stat Soc Ser B 67(5):617–666

    Article  Google Scholar 

  • Baddeley A, Gregori P, Mateu J, Stoica R, Stoyan D (2006) Case studies in spatial point pattern modelling. Lecture Notes in Statistics, Springer, New York, p 185

  • Baddeley A, Rubak E, Møller J (2011) Score, pseudo-score and residual diagnostics for spatial point process models. Stat Sci 26(4):613–646

    Article  Google Scholar 

  • Baddeley A, Turner R, Mateu J, Bevan A (2013) Hybrids of gibbs point process models and their implementation. J Stat Softw 55(11):1–43

    Article  Google Scholar 

  • Baddeley A, Rubak E, Turner R (2015) Spatial point patterns: methodology and applications with R. Chapman and Hall, London

    Google Scholar 

  • Badreldin N, Uria-Diez J, Mateu J, Youssef A, Stal C, El-Bana M, Magdy A, Goossens R (2015) A spatial pattern analysis of the halophytic species distribution in an arid coastal environment. Environ Monit Assess 187(5):1–15

    Article  Google Scholar 

  • Berman M (1986) Testing for spatial association between a point process and another stochastic process. Appl Stat 35(1):54–62

    Article  Google Scholar 

  • Besag J (1975) Statistical analysis of non-lattice data. Statistician 24(3):179–195

    Article  Google Scholar 

  • Besag J (1977) Some methods of statistical analysis for spatial data. Bull Int Stat Inst 47(2):77–92

    Google Scholar 

  • Bird P (2003) An updated digital model of plate boundaries. Geochem Geophys Geosyst 4:1027

    Article  Google Scholar 

  • Bohnhoff M, Rische M, Meier T, Becker D, Stavrakakis G, Harjes HP (2006) Microseismic activity in the hellenic volcanic arc, greece, with emphasis on the seismotectonic setting of the santorini-amorgos zone. Tectonophysics 423(1):17–33

    Article  Google Scholar 

  • Caputo R, Chatzipetros A, Pavlides S, Sboras S (2013) The greek database of seismogenic sources (gredass): state-of-the-art for northern greece. Ann Geophys 55(5):859–894

    Google Scholar 

  • Chiodi M, Adelfio G (2011) Forward likelihood-based predictive approach for space-time processes. Environmetrics 22:749–757

    Article  Google Scholar 

  • Chiodi M, Adelfio G (2014) etasflp: Estimation of an etas model. mixed flp (forward likelihood predictive) and ml estimation of non-parametric and parametric components of the etas model for earthquake description. R package version 1.0.2

  • Cox DR, Isham V (1980) Point processes. Chapman and Hall, London

    Google Scholar 

  • D’Alessandro A, Papanastassiou D, Baskoutas I (2011) Hellenic unified seismological network: an evaluation of its performance through snes method. Geophys J Int 185(3):1417–1430

    Article  Google Scholar 

  • Daley DJ, Vere-Jones D (2007) An introduction to the theory of point processes: general theory and structure. Springer Science & Business Media, New York

    Google Scholar 

  • Dimitriadis I, Karagianni E, Panagiotopoulos D, Papazachos C, Hatzidimitriou P, Bohnhoff M, Rische M, Meier T (2009) Seismicity and active tectonics at coloumbo reef (aegean sea, greece): monitoring an active volcano at santorini volcanic center using a temporary seismic network. Tectonophysics 465(1):136–149

    Article  Google Scholar 

  • Geyer CJ (1999) Likelihood inference for spatial point processes. Stoch Geom 80:79–140

    Google Scholar 

  • Hawkes A, Adamopoulos L (1973) Cluster models for erthquakes-regional comparison. Bull Int Stat Inst 45(3):454–461

    Google Scholar 

  • Illian J, Penttinen A, Stoyan H, Stoyan D (2008) Statistical analysis and modelling of spatial point patterns. Wiley, New York

    Google Scholar 

  • Jensen JL, Moller J et al (1991) Pseudolikelihood for exponential family models of spatial point processes. Ann Appl Probab 1(3):445–461

    Article  Google Scholar 

  • Le Pichon X, Angelier J (1979) The hellenic arc and trench system:a key to the neotectonic evolution of the eastern mediterranean area. Tectonophysics 60(1):1–42

    Article  Google Scholar 

  • Meulenkamp J, Wortel M, Van Wamel W, Spakman W, Strating EH (1988) On the hellenic subduction zone and the geodynamic evolution of crete since the late middle miocene. Tectonophysics 146(1):203–215

    Article  Google Scholar 

  • Møller J, Waagepetersen R (2004) Statistical inference and simulation for spatial point processes. Chapman & Hall/CRC, London

    Google Scholar 

  • Muggeo VM (2003) Estimating regression models with unknown break-points. Stat Med 22(19):3055–3071

    Article  Google Scholar 

  • Muggeo VM (2008) Segmented: an R package to fit regression models with broken-line relationships. R News 8(1):20–25

    Google Scholar 

  • Ogata Y (1988) Statistical models for earthquake occurrences and residual analysis for point processes. J Am Stat Assoc 83(401):9–27

    Article  Google Scholar 

  • Papazachos V, Papazachos B, Papazachou C, Papazachou K (1997) The earthquakes of Greece. Ziti, Thessaloniki

    Google Scholar 

  • R Development Core Team (2005) R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna. http://www.R-project.org, ISBN 3-900051-07-0

  • Ripley BD (1976) The second-order analysis of stationary point processes. J Appl Probab 13(2):255–266

    Article  Google Scholar 

  • Ripley BD (1988) Statistical inference for spatial processes. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Ripley BD, Kelly FP (1977) Markov point processes. J Lond Math Soc 15:188–192

    Article  Google Scholar 

  • Siebert L, Simkin T (2014) Volcanoes of the world: an illustrated catalog of holocene volcanoes and their eruptions. Smithsonian Institution, Global Volcanism Program Digital Information Series, GVP-3. http://volcano.si.edu/search_volcano.cfm

  • Silverman BW (1986) Density estimation for statistics and data analysis. Chapman and Hall, London

    Book  Google Scholar 

  • Sokos E, Kiratzi A, Gallovič F, Zahradník J, Serpetsidaki A, Plicka V, Janskỳ J, Kosteleckỳ J, Tselentis GA (2015) Rupture process of the 2014 cephalonia, greece, earthquake doublet (mw6) as inferred from regional and local seismic data. Tectonophysics 656:131–141

    Article  Google Scholar 

  • Strauss DJ (1975) A model for clustering. Biometrika 62(2):467–475

    Article  Google Scholar 

  • Vere-Jones D (1978) Earthquake prediction: a statistician’s view. J Phys Earth 26:129–146

    Article  Google Scholar 

  • Ye X, Yu J, Wu L, Li S, Li J (2015) Open source point process modeling of earthquake. In: Bian F, Xie Y (eds) Geo-informatics in resource management and sustainable ecosystem. Springer, Berlin, pp 548–557

    Chapter  Google Scholar 

Download references

Acknowledgments

This research was partially developed during the traineeship at the Istituto Nazionale di Geofisica e Vulcanologia funded by “PROGRAMMA OPERATIVO CONVERGENZA 2007-2013 FONDO SOCIALE EUROPEO (MISURA 3)” and this work was partially funded by Grant MTM2013-43917-P from the Spanish Ministry of Science and Education. We thank the reviewers for providing constructive comments and helping in improving the quality of this paper.

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Correspondence to Marianna Siino.

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Siino, M., Adelfio, G., Mateu, J. et al. Spatial pattern analysis using hybrid models: an application to the Hellenic seismicity. Stoch Environ Res Risk Assess 31, 1633–1648 (2017). https://doi.org/10.1007/s00477-016-1294-7

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