A Moore's cellular automaton model to get probabilistic seismic hazard maps for different magnitude releases: A case study for Greece

Abstract Cellular automata are simple mathematical idealizations of natural systems and they supply useful models for many investigations in natural science. Examples include sandpile models, forest fire models, and slider block models used in seismology. In the present paper, they have been used for establishing temporal relations between the energy releases of the seismic events that occurred in neighboring parts of the crust. The catalogue is divided into time intervals, and the region is divided into cells which are declared active or inactive by means of a threshold energy release criterion. Thus, a pattern of active and inactive cells which evolves over time is determined. A stochastic cellular automaton is constructed starting with these patterns, in order to simulate their spatio-temporal evolution, by supposing a Moore's neighborhood interaction between the cells. The best model is chosen by maximizing the mutual information between the past and the future states. Finally, a Probabilistic Seismic Hazard Map is given for the different energy releases considered. The method has been applied to the Greece catalogue from 1900 to 1999. The Probabilistic Seismic Hazard Maps for energies corresponding to m  = 4 and m  = 5 are close to the real seismicity after the data in that area, and they correspond to a background seismicity in the whole area. This background seismicity seems to cover the whole area in periods of around 25–50 years. The optimum cell size is in agreement with other studies; for m  > 6 the optimum area increases according to the threshold of clear spatial resolution, and the active cells are not so clustered. The results are coherent with other hazard studies in the zone and with the seismicity recorded after the data set, as well as provide an interaction model which points out the large scale nature of the earthquake occurrence.

[1]  D. Wells,et al.  New empirical relationships among magnitude, rupture length, rupture width, rupture area, and surface displacement , 1994, Bulletin of the Seismological Society of America.

[2]  Tang,et al.  Self-Organized Criticality: An Explanation of 1/f Noise , 2011 .

[3]  P. Burton,et al.  A catalogue of seismicity in Greece and the adjacent areas for the twentieth century , 2004 .

[4]  Fraser,et al.  Independent coordinates for strange attractors from mutual information. , 1986, Physical review. A, General physics.

[5]  Antoni M. Correig,et al.  Spatio-temporal seismicity patterns using mutual information application to southern Iberian peninsula (Spain) earthquakes , 2000 .

[6]  Keisuke Ito,et al.  Earthquakes as self-organized critical phenomena , 1990 .

[7]  Melanie Mitchell,et al.  Computation in Cellular Automata: A Selected Review , 2005, Non-standard Computation.

[8]  T. Vicsek.  Fractal Growth Phenomena , 1989 .

[9]  J. Drakopoulos,et al.  A revised and extended earthquake catalogue for Greece since 1900 , 1989 .

[10]  John von Neumann,et al.  Theory Of Self Reproducing Automata , 1967 .

[11]  Daryl J. Daley,et al.  Scoring probability forecasts for point processes: the entropy score and information gain , 2004, Journal of Applied Probability.

[12]  Dicing with earthquakes , 1996 .

[13]  Tommaso Toffoli,et al.  Cellular Automata Machines , 1987, Complex Syst..

[14]  Konrad Zuse,et al.  Rechnender Raum , 1991, Physik und Informatik.

[15]  B. Papazachos,et al.  Geophysical and tectonic features of the Aegean Arc , 1971 .

[16]  Antonio M. Posadas,et al.  A probabilistic seismic hazard model based on cellular automata and information theory , 2005 .

[17]  B. Papazachos,et al.  Time-Independent and Time-Dependent Seismic Hazard in Greece Based on Seismogenic Sources , 2000 .

[18]  B. Papazachos.  Seismicity of the Aegean and surrounding area , 1990 .

[19]  B. Papazachos,et al.  Earthquakes in Greece , 1940, Nature.

[20]  Michael R. Frater,et al.  Communications and Information Systems , 2002 .

[21]  P. Burton,et al.  Extreme Earthquake and Earthquake Perceptibility Study in Greece and its Surrounding Area , 2004 .

[22]  B. S. Papazachos.  Large seismic faults in the Hellenic arc , 1996 .

[23]  P. Bak,et al.  Self-organized criticality. , 1988, Physical review. A, General physics.

[24]  H. Akaike,et al.  Information Theory and an Extension of the Maximum Likelihood Principle , 1973 .

[25]  A scale‐invariant cellular‐automata model for distribited seismicity , 1991 .

[26]  T. Tsapanos,et al.  The seismic potential assessment for some seismogenic sources in the central northern Greece and its adjacent areas based on the maximum credible magnitude , 2002 .

[27]  Antonio Posadas,et al.  Information Theory to Characterize Spatiotemporal Patterns of Seismicity in the Kanto Region , 2002 .

[28]  Theodoros M. Tsapanos,et al.  Estimation of the seismic hazard parameters for various sites in Greece using a probabilistic approach , 2004 .

[29]  P. Burton,et al.  A catalogue of seismicity in Greece and adjacent areas , 1981 .

[30]  P. Burton,et al.  An evaluation of seismic hazard parameters in southern Turkey , 1999 .

[31]  P. Burton,et al.  Strong ground acceleration seismic hazard in Greece and neighboring regions , 2003 .

[32]  Christensen,et al.  Self-organized criticality in a continuous, nonconservative cellular automaton modeling earthquakes. , 1992, Physical review letters.

[33]  Daniel Ray Upper,et al.  Theory and algorithms for hidden Markov models and generalized hidden Markov models , 1998 .

[34]  J. R. Wallis,et al.  Noah, Joseph, and Operational Hydrology , 1968 .

[35]  One-dimensional discrete computer model of the subduction erosion phenomenon (plate tectonics process) , 1998 .