Detection of Long-Range Correlations and Trends Between Earthquakes in California

Document Type : Research Note

Authors

1 Alzahra University

2 International Institute of Earthquake Engineering and Seismology

Abstract

In this paper, we investigate the long-range correlations and trends between
consecutive earthquakes by means of the scaling parameter so-called locally Hurst
parameter, H(t), and examine its variations in time, to find a specific pattern that
exists between Earthquakes. The long-range correlations are usaully detected
by calculating a constant Hurst parameter. However, the multi-fractal structure of
earthquakes caused that more than one scaling exponent is needed to account
for the scaling properties of such processes. Thus, in this paper, we consider the
time-dependent Hurst exponent to realize scale variations in trend and correlations
between consecutive seismic activities, for all times. We apply the Hilbert-Huang
transform to estimate H(t) for the time series extracted from seismic activities
occurred in California during 12 years, from 2/24/2007 to 9/29/2017. The superiority
of the method is discovering some specific hidden patterns that exist between
consecutive earthquakes, by studying the trend and variations of H(t). Estimationg
H(t) only as a measure of dependency, may lead to misleading results, but using this
method, the trend and variations of the parameter is studying to discover hidden
dependencies between consecutive earthquakes. Recognizing such dependency
patterns can help us in prediction of future main shocks.

Keywords


1. Martin-Montoya, L.A., Aranda-Camachob, N.M.,
and Quimbayc, C.J. (2014) Long-range correlations
and trends in Colombian seismic time
series. Physica A: Statistical Mechanics and its
Applications, 421, 124-133.
2. Flandrin, P. and Abry, P. (1999) Wavelets for
scaling processes. Fractals, Springer , 47-64,
London.
3. Borgnat, P., Amblard, P.O., and Flandrin, P. (2005)
Scale invariances and lamperti transformations
for stochastic processes. J. Phys. A., 38(10),
2081-2101.
4. Bardet, J.M., Lang, G., Oppenheim, G., Philippe,
A., Stoev, S., and Taqqu, M.S. (2003)
Semiparametric estimation of the long-range
dependence parameter: a survey. Theory and
applications of long-range dependence. Birkhuser
Boston, Boston, MA.
5. Beran, J. (1994) Statistics for Long-Memory
Processes. Monographs on Statistics and Applied
Probability. Chapman and Hall, New York.
6. Coeurjolly, J.F. (2001) Estimating the parameters
of a fractional Brownian motion by discrete
variations of its sample paths. Stat. Inference
Stoch. Process, 4(2), 199-227.
7. Main, I. (1996) Statistical physics, seismogenesis,
and seismic hazard. Rev. Geophys., 34(4), 433-
462.
8. Sammonds, P.R., Meredith, P.G., and Main, I.G.
(1992) Role of pore fluids in the generation of
seismic precursors to shear fracture. Nature, 359,
228-230.
9. Turcotte, D.L. (1997) Fractals and Chaos in
Geology and Geophysics. Cambridge University
Press, Cambridge, UK, 2nd Ed.
10. Michas, G., Vallianatos, F., and Sammonds, P.
(2013) Non-extensivity and long-range correlations
in the earthquake activity at the West
Corinth rift (Greece), Nonlin, Processes
Geophys., 20, 713-724.
11. Mandelbrot, B.B. and Wallis, J.R. (1968) Noah,
Joseph and the operational hydrology. Water
Resour. Res., 4(5), 909-918.
12. Cajueiro, D.O. and Tabak, B.M. (2004) The
Hurst exponent over time: testing the assertion
that emerging markets are becoming more
efficient. Physica A: Stat. Mech. Appl. ,
336(3-4), 521-537.
13. Cavanaugh, J.E., Wang, Y., and Davis, J.W.
(2003) Locally Self-Similar Processes and
Their Wavelet Analysis. Stochastic Processes:
Modelling and Simulation, Handbook of
Statist. North-Holland, Amsterdam.
14. Goncalves, P. and Abry, P. (1997) Multiplewindow
wavelet transform and local scaling
exponent estimation. IEEE Int. Conf. on Acoust.
Speech and Sig. Proc., Munich, Germany.
15. Kent, J.T. and Wood, A.T.A. (1997) Estimating
the fractal dimension of a locally self-similar
Gaussian process by using increments. J. Roy.
Statist. Soc. Ser. B, 59(3), 679-699.
16. Stoev, S., Taqqu, M.S., Park, C., Michailidis, G.,
and Marron, J.S. (2006) LASS: a tool for the
local analysis of self-similarity. Comput. Statist.
Data Anal., 50(9), 2447-2471.
17. Hurst, H.E. (1951) Long-term storage capacity
of reservoirs. Transactions of the American
Society of Civil Engineers, 116, 770-808.
18. Huang, N. E. (2014) Introduction to the Hilbert
Huang Transform and Its Related Mathematical
Problems, Hilbert-Huang Transform and Its
Applications, World Scientific.
19. Carmona, R., Hwang, W.L., and Torresani, B.
(1998) Practical Time-Frequency Analysis:
Gabor and Wavelet Transform with an Implementation
in S, Academic . San Diego,
California.
20. Noemi, N., Tiziana, D.M., and Tomaso, A. (2016)
Time-dependent scaling patterns in high
frequency financial data. Eur. Phys. J. Special
Topics, 225, 1997-2016.
21. Huang, N.E., Shen, Z., Long, S.R., Wu, M.C.,
Shih, H.H., Zheng, Q., Yen, N.C., Tung, C.C.,
and Liu, H.H. (1998) The empirical mode
decomposition and the Hilbert spectrum for
nonlinear and non-stationary time series
analysis. Proc. R. Soc. London, A, 454(1971),
903-998.
22. King, F. (1997) Encyclopedia of Mathematics
and its Applications. Cambridge University
Press, Cambridge.
23. Farrokhi, M., Hamzehloo, H., Rahimi, H., and
AllamehZadeh, M. (2016) Separation of intrinsic
and scattering attenuation in the crust of central
and eastern Alborz region. Physics of the Earth
and Planetary Interiors, 253, 88-96.
24. Farrokhi, M., Hamzehloo, H., Rahimi, H., and
AllamehZadeh, M. (2015) Estimation of codawave
attenuation in the central and Eastern
Alborz. Seismol. Soc. Am., Bull., 105(3), doi:
10.1785/012014049.
25. AllamehZadeh, M., Farahbod, A.M., Hatzfeld, D.,
Mokhtari, M., Moradi, A.S., Mostafazadeh, M.,
Paul, A., and Tatar, M. (2004) Seismological
aspects of 26 December 2003 Bam earthquake
and its aftershock analysis. Ear thquake
Spectra , Special Issue.
26. Vazirzade, S.M., Nozhati, S., and AllamehZadeh,
M. (In Press) Seismic reliability assessment of
structures using artificial neural network.
Journal of Building Engineering, http://doi.
org/10.1016/j.jobe.2017.04.001.