Abstract
The recurrence interval statistics for regional seismicity follows a universal distribution function, independent of the tectonic setting or average rate of activity (Corral, 2004). The universal function is a modified gamma distribution with power-law scaling of recurrence intervals shorter than the average rate of activity and exponential decay for larger intervals. We employ the method of Corral (2004) to examine the recurrence statistics of a range of cellular automaton earthquake models. The majority of models has an exponential distribution of recurrence intervals, the same as that of a Poisson process. One model, the Olami-Feder-Christensen automaton, has recurrence statistics consistent with regional seismicity for a certain range of the conservation parameter of that model. For conservation parameters in this range, the event size statistics are also, consistent with regional seismicity. Models whose dynamics are dominated by characteristic earthquakes do not appear to display universality of recurrence statistics.
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
Preview
Unable to display preview. Download preview PDF.
References
Bak, P., Tang, C., and Weisenfeld (1987), Self-organised criticality: An explanation of 1/f Noise, Phys. Rev. Lett., 59(4), 381–384.
Brown, S.R., Scholz, C.H. and Rundle, J.B. (1991), A simplified spring-block model of earthquakes, Geophys. Res. Lett. 18(2), 215–218.
Bufe, C.G. and Varnes, D.J. (1993), Predictive modelling of the seismic cycle of the greater San Francisco Bay region. J. Geophys. Res. 98(B6), 9871–9883.
Burridge, R. and Knopoff, L. (1967), Model and theoretical seismology, Bull. Seismol. Soc. Am. 57(3), 341–371.
Carlson, J.M. and Langer, J.S. (1989), Mechanical model of an earthquake fault, Phys. Rev. A 40(11), 6470–6484.
Corral, A. (2004), Long-term clustering, scaling, and universality in the temporal occurrence of earthquakes, Phys. Rev. Lett. 92(10), 108501.
Gutenberg, B. and Richter, C.F., Seismicity of the Earth and Associated Phenomena (Princeton University Press, Princeton, New Jersey (1954)).
Jaumé, S.C., Weatherley, D., and Mora, P. (2000), Accelerating seismic energy release and evolution of event time and size statistics: Results from two heterogeneous cellular automaton models. Pure Appl. Geophys. 157, 2209–2226.
Marquardt, D. (1963), An algorithm for least-squares estimation of nonlinear parameters, SIAM J. Appl. Math. 11, 431–441.
Mora, P. and Place, D. (1994), Simulation of the frictional stick-slip instability, Pure Appl. Geophys. 143, 61–87.
Olami, Z., Feder, H.J.S. and Christensen, K. (1992), Self-organized criticality in a continuous, nonconservative cellular automaton modelling earthquake, Phys. Rev. Lett. 68, 1244–1247.
Pacheco, J.F., Scholz, C.H., and Sykes, L.R. (1992), Changes in frequency-size relationship from small to large earthquakes. Nature 355(6355), 71–73.
Press, W.H., Teukolsky, S.A., Vetterling, W.T., and Flannery, B.P., Numerical Recipes in C: the art of Scientific Computing (Cambridge University Press, Cambridge, New York (2002)) pp. 683–688.
Rundle, J.B. and Jackson, D.D. (1977), Numerical simulation of earthquake sequences, Bull. Seismol. Soc. Am. 67(5), 1363–1377.
Steacy, S.J. and McCloskey, J. (1998), What controls an earthquake’s size? Results from a heterogeneous cellular automaton, Geophys. J. Int. 133, F11–F14.
Steacy, S.J. and McCloskey, J. (1999), Heterogeneity and the earthquake magnitude-frequency distribution, Geophys. Res. Lett. 26(7), 899–902.
Weatherley, D. and Abe, S. (2004), Earthquake statistics in a block slider model and a fully dynamic fault model, Nonlinear Proc. Geophys. 11, 553–560.
Weatherley, D., Jaume, S.C., and Mora, P. (2000), Evolution of stress deficit and changing rates of seismicity in cellular automaton models of earthquake faults, Pure Appl. Geophys. 157, 2183–2207.
Weatherley, D. and Mora, P. (2004), Accelerating precursory activity within a class of earthquake analogue automata, Pure Appl. Geophys. 161, 2005–2019.
Weatherley, D., Mora, P., and Xia, M.F. (2002), Long-range automaton models of earthquakes: Powerlaw accelerations, correlation evolution and mode-switching, Pure Appl. Geophys. 159, 2469–2490.
Wesnousky, S.G. (1994), The Gutenberg-Richter or characteristic earthquake distribution, which is it?, Bull. Seismol. Soc. Am. 84(6), 1940–1959.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Birkhäauser Verlag
About this paper
Cite this paper
(2006). Recurrence Interval Statistics of Cellular Automaton Seismicity Models. In: Yin, Xc., Mora, P., Donnellan, A., Matsu’ura, M. (eds) Computational Earthquake Physics: Simulations, Analysis and Infrastructure, Part I. Pageoph Topical Volumes. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7992-6_13
Download citation
DOI: https://doi.org/10.1007/978-3-7643-7992-6_13
Received:
Revised:
Accepted:
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-7991-9
Online ISBN: 978-3-7643-7992-6
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)