Abstract
This paper deals with earthquake long term predictions based on multi-state system methodology. As a reference we consider the South America case which was examined (Tsapanos, Bull Geol Soc Gr XXXIV/4:1611–1617, 2001) in the light of the Markov model, in order to define large earthquake recurrences. In this work we make the first attempt to describe seismic zoning data as data of a multi-state system (MSS) and explore earthquake genesis by evaluating intensity rates and transition probabilities between zones using various probabilistic models. For this purpose we incorporate into the procedure discussed in Tsapanos (2001) the effect, via the underlying distribution, of sojourn times between transitions.
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References
Aki K (1984) Asperities, barriers, characteristic earthquakes and strong motion prediction. J Geophys Res 89(B7):5867–5872
Anagnos T, Kiremidjian AS (1988) A review of earthquake occurrence models for seismic hazard analysis. Probab Engin Mechanics 3(1):3–11
Andersen PK, Borgan Ø, Gill RD, Keiding N (1993) Statistical models based on counting processes. Springer
Aven T, Jensen U (1999) Stochastic Models in Reliability. Springer, New York
Balakrishnan N (2007) Permanents, order statistics, outliers, and robustness. Rev Math Comput 2(1):7–107
Balasubramanian K, Beg MI, Bapat RB (1991) On families of distributions closed under extrema. Sankhya A 53:375–388
Barlow RE, Proschan F (1965) Mathematical theory in reliability. Wiley, New York
Beck SL (1993) Variations in the rupture mode of large earthquakes along the South American subduction zone 2nd ISA. Oxford, UK 21-23/9 1993 59–62
Beck SL, Ruff L (1989) Great earthquakes and subduction along the Peru trench. Phys Earth Planet Inter 57:199–224
Beck SL, Nishenko S (1990) Variations in the mode of great earthquake rupture along the central Peru subduction zone. Geophys Res Lett 17:1969–1972
Cather H, Morris R, Philip M, Rose C (2001) Design Engineering. Butterworth-Heinemann, Oxford
Cernadas D, Osella A, Sabbione N (1998) Self-similarity in the seismicity of the South American subduction zone. Pageoph 152:57–73
Geller RJ (1997) Earthquake prediction: a critical review. Geophy J Intern 131:425–450
Hasegawa A, Sacks IS (1981) Subduction of the Nazca plate beneath Peru as determined from seismic observations. J Geophys Res 86:4971–4980
Henze N, Meintanis SG (2005) Recent and classical tests for exponentiality: a partial review with comparisons. Metrika 61:29–45
Kagan YY (1997) Are earthquakes predictable? Geophy J Intern 131:505–525
Kelleher JA (1972) Rupture zones of large South American earthquakes and sime predictions. J Geophys Res 77:2087–2103
Lawless JF (2003) Statistical Models and Methods for Lifetime Data. Wiley, New York
Lisnianski A, Frenkel I, Ding Y (2010) Multi-state system reliability analysis and optimization for engineers and industrial managers. Springer, London
Lisnianski A, Levitin G (2003) Multi-state System Reliability: Assessment. Optimization and Applications, Singapore World Scientific
Matsumura S (2008) Trends and problems in earthquake prediction research. Sci Technol:64–83
McCann WR, Nishenko SP, Sykes LR, Krause J (1979) Seismic gaps and plate tectonics: Seismic potential for Major boundaries. Pageoph 117:082–1147
Murchland J (1975) Fundamental concepts and relations for reliability analysis of Multistate systems. In: Barlow RE, Fussell JB, Singpurwalla N (eds) Reliability and fault tree analysis: theoretical and applied aspects of system reliability SIAM Philadelphia, pp 581–618
Musson RMW, Tsapanos TM, Nakas CF (2002) A power-law function for earthquake interarrival time and magnitude. Bull Seismol Soc Am 92(5):1783–1794
Natvig B (1982) Two suggestions of how to define a multistate coherent system. Adv Appl Probab 14:434–455
Natvig B (1985) Multi-state coherent systems. In: Johnson N, Kotz S (eds) Encyclopedia of statistical sciences, vol 5. Wiley, New York, pp 732–735
Natvig B (2011) Multistate Systems Reliability Theory with Applications. Wiley, New York
Natvig B, Tvete I (2007) Bayesian hierarchical space - time modeling of earthquake data. Meth Comput Applied Probab 9:89–114
Papadimitriou EE (1993) Long-term earthquake prediction along the western coast of South and Central America based on a time predictable model. Pageoph 140:301–316
Pyke R (1961a) Markov Renewal Processes: Definitions and Preliminary Processes. Ann Math Stat 32:1231–1242
Pyke R (1961b) Markov Renewal Processes with Finitely Many States. Ann Math Stat 32:1243–1259
Rice JR, Ben-Zion Y (1995) Slip complexity in earthquake fault model. In: Knooff L (ed) Proc Earthquake Prediction: The Scientific Challenge, pp 3811–3818
Tsapanos TM (2001) The Markov model as a pattern for earthquakes recurrence in South America. Bull Geol Soc Gr XXXIV/4:1611–1617
Tsapanos TM (2011) The Markov-chains as a tool for very large earthquakes in South America. STATSEI7 - Intern Workshop on Statistical Seismology 25-27 May 2011 Thera Greece
Tsapanos TM, Burton PW (1991) Seismic hazard evaluation for specific seismic regions of the world. Tectonophysics 194:153–169
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Karagrigoriou, A., Makrides, A., Tsapanos, T. et al. Earthquake Forecasting Based on Multi-State System Methodology. Methodol Comput Appl Probab 18, 547–561 (2016). https://doi.org/10.1007/s11009-015-9451-x
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DOI: https://doi.org/10.1007/s11009-015-9451-x