Inverse Statistics Method: Spatial and Temporal Dependence in Earthquake

Document Type : Seismology and Engineering Seismology

Authors

1 International Institute of Earthquake Engineering and Seismology

2 Shahid Beheshti University

Abstract

The aim of this work is to understand the relation between time and place that an earthquake takes place. In order to answer this question, the Modified Level Crossing (MLC) technique has been implemented. By studying two earthquakes, one in Iran and one in California we came to the conclusion that there is a relation between time and place of an earthquake occurrence. As a matter of fact, this relation is quite decisive. By performing MLC analysis and comparing the two regions, we can state that geographical effects play an effective role due to geophysical differences between Iran and California. Indeed, by comparing the readings of Iran and California, one could come to understand the geophysical differences between the two domains.The so-called level crossing analysis has been used to investigate the spatial and temporal fluctuations of earthquake form time series. In this paper, we calculated the average frequency of up-crossing for original and shuffled data of Iran and California earthquakes in spatial and temporal series. This analysis showed a significant difference between the original data and shuffled data. By introducing the relative change of the total number of up-crossings for original data with respect to the so-called shuffled data, R, and calculate the Hurst exponent, Iran and California earthquakes are compared.

Keywords

References

  1. Park, S.K. (1997) Monitoring resistivity change in Parkfield, California: 1988-1995. J. Geophys. Res., 102, 24545.
  2. Raleigh, B., Bennet, G., Craig, H., Hanks, T., Molnar, P., Nur, A., Savage, J., Scholz, C., Turner,
  3. R., and Wu, F. (1977) EOS. Trans. Am. Geophys. Union, 58, 236.
  4. Tabar, M., Sahimi, M., Kaviani, K., Allamehzadeh, M., Peinke, J., and Mokhtari, M. (2005) Dynamics
  5. of the Markov time scale of seismic activity may provide a short-term alert for earthquakes. arXiv preprint physics/0510043.
  6. Shadkhoo, S. and Jafari, G.R. (2005) Multifractal detrended cross-correlation analysis of temporal and spatial seismic data. The European Physical Journal B-Condensed Matter and Complex Systems.
  7. Rahimi Tabar, M., Sahimi, M., Kaviani, K., Allamehzadeh, M., Peinke, J., Mokhtari, M., Vesaghi, M., Niry, M.D., Ghasemi, F., Bahraminasab, A., Tabatabai, S., and Fayazbakhsh, F., Akbari, M. (2007) Modelling critical and catastrophic phenomena in geoscience: a statistical physics approach. Lecture Notes in Physics, 705, 281-301, Springer Verlag, Berlin-Heidelberg.
  8. Simonsen, I., Jensen, M.H., and Johansen, A. (2002) Optimal investment horizons. Eur. Phys. J., 27, 583.
  9. Jensen, M.H., Johansen A., and Simonsen, I. (2003) Statistical Mechanics and its Applications. Physica A 324-338.
  10. Jensen, M.H., Johansen, A., Petroni F., and Simonsen, I. (2004) Statistical Mechanics and its Applications. Physica A., 340, 678-684.
  11. Rice, S.O. (1944) Mathematical analysis of random noise. Bell Syst. Tech. J., 23, 282
  12. Newland, D.E. (1993) An Introduction to Random Vibrations, Spectral and Wavelet Analysis.
  13. rd ed., Harlow, UK, Longman Scientific and Technical.
  14. Shahbazi, F., Sobhanian, S., Reza Rahimi Tabar, M., Khorram, S., Frootan, G.R., and Zahed, H.
  15. (2003) Level crossing analysis of growing surfaces. J. Phys. A: Math. Gen., 36, 2517.
  16. Vahabi, M. and Jafari, G.R. (2007) Global Privatization and Its Impact. Nova Science, Chapter 7.
  17. Ghasemi, F., Sahimi, M., Peinke, J., Friedrich, R., Jafari, G.R., and Rahimi Tabar, M. (2007) Phys. Rev. E., 75 060102(R).
  18. Jensen, M.H., Johansen, A., Petroni, F., and Simonsen, I. (2004) Synchronization model for stock market asymmetry. Physica A., 340, 678.
  19. Jafari, G.R., Movahed, M.S., Fazeli, S.M., and Rahimi Tabar, M.R. (2006) Stochastic features of rough surfaces: analysis of laser-induced silicon surface modification, J. Stat. Mech., P06008.
  20. Simonsen, I., Jensen, M.H., and Johansen, (2002) A Optimal investment horizons. Eur. Phys. J. B., 27, 583.
  21. Bunde, A., Eichner, J.F., Kantelhardt, J.W. and Havlin, Sh. (2005) Analysis of fractional Gaussian noises using level crossing method. Phys. Rev. Lett., 94, 048701.
  22. Newell, G.F. and Rosenblatt, M. (1962) Zero crossing probabilities for Gaussian stationary processes, Ann. Math. Stat., 33, 1306.
  23. Vahabi, M. and Jafari, G.R. (2007) Stochastic features of rough surfaces: analysis of laser induced silicon surface modification, Physica A, 385, 583.
  24. Peitgen, H.-O., Saupe, D. (1988) The Science of Fractal Images, New York: Plenum.
  25. Peng, C.-K., Havlin, S., Schwartz, M., and Stanley, H.E. (1991) Directed-polymer and ballistic-deposition growth with correlated noise. Phys. Rev. A., 44, R2239.
  26. Prakash, S., Havlin, S., Schwartz, M., and Stanley, H.E. (1991) Structural and dynamical properties of long-range correlated percolation. Phys. Rev. A., 46, R1724.
  27. Hamzehpour, H. and Sahimi, M. (2006) Development of optimal models of porous media by
  28. combining static and dynamic data: The permeability and porosity distributions, Phys. Rev. E., 73, 056121.
  29. Pang, N.-N., Yu, Y.-K., and Halpin-Healy, T. (1995) Analysis of fractional Gaussian noises using level crossing method, Phys. Rev. E., 52, 3224.
  30. Makse, H.A., Havlin, S., Schwartz, M., and Stanley, H.E. (1996) Method for generating long-range correlations for large systems. Phys. Rev. E., 53, 5445.
  31. Mehrabi, A.R., Rassamdana, H., and Sahimi, M. (1997) Characterization of long-range correlations
  32. in complex distributions and profiles, Phys. Rev. E., 56, 712.
  33. Voss, R.F. (1985) Fundamental Algorithms for Computer Graphics. NATO ASI Series Vol. 17, edited by R.A. Earnshaw, Heidelberg: Springer, p.p. 805.
  34. Ausloos, M. and Berman, D.H. (1985) A Multi variate Weierstrass-Mandelbrot Function. Proc.
  35. R. Soc. A., 400, 331.
  36. Data was downloaded from http://www.iiees.ac.ir/ and http://www.usgs.gov.

Files

Share

How to cite

Statistics