Abstract
Investigations conducted during the last 20-30 years demonstrate some very deep, fundamental regularity in the statistics of earthquakes time and space distribution that lead to the concept that the earthquake phenomenon is a system-defined complex of interacting events.
In the final stage of earthquake preparation, the epicentral area becomes sensitive to weak global disturbances such as tides, geophysical disturbances caused by solar activity, and variations of Earth rotation rate. One can consider the earthquake source as an analogue of nonlinear relaxation oscillator, storing the energy during dozens or hundreds of years. The “discharge”, i.e., an earthquake, happens suddenly, when the stress on the fault reaches the critical value. Close to this limit, the epicentral area becomes sensitive even to weak external disturbances. The additional stresses caused by varying external factors contribute to premature “discharge” of relaxation oscillator, i.e., earthquake. In seismically active regions, varying external factors may operate as synchronizers of earthquake release moments.
Investigation of synchronizing effect of external factors in a certain region requires development of special methods, because the data of earthquakes are presented as unequally-spaced sequences of phenomena.
According to the synchronization theory of relaxation process, discharges (earthquakes) mainly happen when influencing external factor is in a certain phase. It is possible to determine these moments by means of analysis of discharge recurrence and forms of distributions of event occurrence times’ moments. The distribution corresponding to the period of an external synchronizing factor demonstrates a characteristic gap or modulation. All external influencing periodicities may be determined by an analysis of distributions for all virtual forcing periods and detection of typical characteristic forms.
A simple model describes the principles of the used approach. The stress \(P(t) = P_o+ b(t - t_0 )\) increases monotonically and undergoes the influence of external small stress with amplitude, frequency and phase denoted by \(a,\bar {\omega}\varpi,\,{\rm and}\ f\), respectively. The resulting stress and the critical stress \(P_m \), determining the discharge moment, which are connected by the equation \(P_0+ b(t - t_0 ) + a\cos (\bar {\omega} t + f) = P_m \), will be obtained. The initial moment of energy integration process is unknown. If one examines a set of N different stress accumulation starting moments separated by a step \(\varepsilon \), one will obtain N equations of type \(b(t - t_0+ \varepsilon n) = P_m- P_0- a\cos (\bar {\omega} t + f), n = 0,1,2,\ldots N.\) The solutions of equations correspond to relaxation oscillator discharge moments for stress processes, started at different time moments. Solutions obviously reveal the “gaps”, or time intervals when discharges are forbidden, and also demonstrate that the width of the gap depends on the stress growth velocity. The examination of the distribution of phases of discharges inside the period of external forcing shows that strong and slowly growing earthquakes triggered by a stable external forcing demonstrate wider gaps. Fast growth of stress gives birth to narrow gaps or modulation of distribution. An analysis of distributions for different forcing frequencies and appearance of gaps or modulation is the way for distinguishing different external synchronizing factors.
All of these considerations, and the validity of “gap” method for the discovery of external synchronizing factors, are tested and confirmed in model laboratory experiments on electromagnetic and mechanical control of slip, namely, laboratory experiments with spring-slider system.
In order to investigate the influence of external factors triggering earthquakes, the “gap” method was applied to Caucasus earthquakes. The results reveal a set of regularities for strong earthquakes (the earthquakes with \(M > 6\) that occurred during the last 100 years). The spectrum of recurrence periods of earthquakes contains 19 components which have clear astronomical and geophysical meaning; spectral distribution of time series of such earthquakes indicates that release mechanism of tectonically prepared strong earthquakes correlates with different tidal effects - the positional relationship of Sun, Earth and the Moon and periodicities of their orbital movement.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Allen M.W., The lunar triggering of earthquakes in southern California. Bull. Seism. Soc. Am. 1956. Vol.26. p. 147-157.
Becker, T. W., Deterministic Chaos in the Two State-variable Friction Sliders and the Effect of Elastic Interactions. Geocomplexity and the Physics of Earthquakes, edited by Rundle, J., Turcotte, D., and Klein, W., AGU, Washington, DC, 5–26, 2000.
Beeler, N. M. and Lockner, D. A.: Why earthquakes correlate weakly with the solid Earth tides: Effects of periodic stress on the rate and probability of earthquake occurrence, J. Geophys. Res., B108, 2391–2405, 2003.
Blechman I.I., Synchronization of Dynamical Systems, 1971. (Sinchronizatzia Dinamicheskich Sistem, Nauka, Moscow, in Russian.)
Bocaletti, S., Grebogi, C., Lay Y.-C.: The control of chaos; theory and applications, Physics Reports, 329, 103–197, 2000.
Chelidze, T. and Lursmanashvili, O.: Electromagnetic and mechanical control of slip: laboratory experiments with slider system, Nonlin. Proc. Geophys., 20, 1–8, 2003.
Chelidze, T., T. Matsharashvili, J. Gogiashvili, O. Lursmanashvili and M. Devidze (2005): Phase synchronization of slip in laboratory slider system, Nonlinear Processes Geophys., 12, pp. 163-170.
Chelidze, T., T. Matcharashvili, J. Gogiashvili, O. Lursmanashvili and M. Devidze (2006) Electromagnetic Synchronization of Slip. Nonlinear Dynamics, v 44, pp. 293-298.
Custodio, S., Fonseca, J., Faria, B., and d’Oreye, N.: Tidal modulation of volcanic tremor in Fogo Island, Cape Verde, Book of Abstracts, European Seismological Commission XXVIII Assembly, Genoa, 236, 2002.
Dieterich, J.: Nucleation and triggering of earthquake slip: Effect of periodic stresses, Tectonophysics, 144, 127–139, 1987.
Grasso, J.-R.: Mechanics of Seismic Instabilities Induced by the Recovery of Hydrocarbons, Pageoph, 139, 507–534, 1992.
Grebennikov E.A., Ryabov Y.A. Resonances and small denominators in celestial mechanics. 1978, Moscow, Nauka, 126 p.
Gulyaev V.P., On the synchronization of thyratron generator. Journal of Technical Physics, v 9, No.18, 1939.
Heaton T.N., Tidal triggering of earthquakes. Geoph. J. of the Royal Astr. Soc. 1975, vol.43. p. 307-326.
Hoffman R.B., Aftershock-energy release versus tidal effects, Hebgen Lake earthquakes, Montana. US.Geol.Survey Prpf. Paper 1961, 424-C. p. 267-270.
Kartvelishvili K., Kartvelishvili N. Tidal triggering of earthquakes. Journal of Georgian Geophysical Society. Issue(A), Solid Earth, v.2. 1996.
Knopoff L., Earth tides as triggering mechanism for earthquakes. Bull. Seism. Soc. Am., 1964. vol.54. p. 1865-1870.
Knopoff L. Earthquake prediction: The scientific Challenge. Proc.Nat. Acad. Sci. USA, vol 93, pp. 3719-3720, 1996.
Lursmanashvili, O.V., On periodicity of strong earthquakes in the Caucasus, Izv. AN SSSR, Fiz. Zemli, No. 2, in Russian, 1973.
Lursmanashvili, O.V., Gakhokidze L.D., Nikoladze, I.E., Ruda L.G., Results of calculations of the recurrence spectrum of earthquakes in the Caucasus, Soobshch. AN GSSR, 1926, No.1, in Russian, 1987a.
Lursmanashvili, O.V Gakhokidze L.D, Ruda L.G., Recurrence spectrum of strong earthquakes in some seismically active regions of the Eurasia, Soobshch. AN GSSR, 126, No.1, in Russian, 1987b.
Lursmanashvili O. Role of exogenous factors in initiation of Caucasus earthquakes. Journal of the Georgian Geophysical Society. Issue (A), Physics of Solid Earth, v. 6. 2001.
Matcharashvili, T., Chelidze, T., and Javakhishvil, Z.: Nonlinear analysis of magnitude and interevent time interval sequences for earthquakes of the Caucasian region, Nonlin. Proc. Geophys., v 7, pp. 9–19, 2000.
Meerovich L.A. and Zelichenko L.G., Impulse technique. Moscow, 600 p, 1954.
Melchior P., Physics and dynamics of planets, Mir, Moscow, in Russian, 1976.
Nikolaev, A. V. (Ed.): Induced Seismicity, Moscow, “Nauka”, in Russian, 220, 1994.
Ott, E., Grebogi, C., and Yorke, J. A. Controlling chaos, Phys. Rev. Lett., 64, 1196–1199, 1990.
Perfettini, H. and Schmittbuhl, J.: Periodic loading on a creeping fault: Implications for tides, Geophys. Res. Lett., 28, 435–438, 2001.
Pikovsky, A., Rosenblum, M. G., and Kurth, J.: Synchronization: Universal Concept in Nonlinear Science, Cambridge University Press, Cambridge, 411, 2003
Polumbo A., Lunar and solar tidal components in the occurance of earthquakes in Italy. Geophys. J. Roy. Astron. Soc. 1986. Vol. 84. #1. p. 93-99.
Ryall A., Van Wormer J.D., Jones A.E., Trigering of microearthquakes by earth tides, and other features of the Truckee, California earthquake sequences of September, 1966. Bull. Seism. Soc. Am. 1968. 58. p. 215-248.
Scholz, C. H.: Good tidings, Nature, 425, 670–671, 2003.
Shlien S., Earthquake-tide correlation. Geoph. J. R. Astr. Soc. 1972. vol.28. p. 27-34.
Simpson J.F., Earth tides as a triggering mechanism for earthquakes. Earth. Planet. Sci. Lett., 1967. vol.2. p. 473.
Sobolev, G. A. and Ponomarev, A. V.: Physics of Earthquakes and Precursors, Moscow, “Nauka”, in Russian, 270, 2003.
Tamrazian G.P., Principal regularities in the distribution of major earthquakes relative to solar and lunar tides and other cosmic sources. Icarus 9. 1968. p. 574-592.
Tarasov, N. G., Tarasova, N. V., Avagimov, A. A., and Zeigarnik, V. A.: The effect of high-power electromagnetic pulses on the seismicity of the central Asia and Kazakhstan, Vulkanologia I seismologia, in Russian, 4–5, 152–160, 1999
Ulomov, V., Danilova, T., Medvedeva, N., Polyakova, T. Seismogeodynamics of Lineament Structures in the Mountainous Regions Bordering the Scythian-Turan Plate. Physics of the Solid Earth, 2006, v 42, No 7, pp. 551-566.
Ulomov, V., Danilova, T., Medvedeva, N., Polyakova, T. Shumilina L.S. Assessment of Seismic Hazard in the North Caucasus. Physics of the Solid Earth, 2007, v 43, No 7, pp. 559-572.
Vidale, J., Agnew, D., Johnston, M., and Oppenheimer, D.: Absence of earthquake correlation with earth tides: an indication of high preseismic fault stress rate, J. Geophys. Res., 103, 24 567–24 572, 1998.
Vitkevich V.V., Geometrical theory of relaxation generator synchronization. Journal of Technical Physics, v 15, No 18, 1945.
Wang, Y., Mora, P., Yin, C., and Place, D.: Statistical tests of load/unload response ratio signals by lattice solid model, Pure Appl. Geophys., 161, 1829–1839, 2004.
Weems R. E., Perry W.H., Strong correlation of major earthquakes with solid-earth tides in part of the eastern United States. Geology. 1989. Vol.17. p. 661-664.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Lursmanashvili, O., Paatashvili, T., Gheonjian, L. (2010). Detecting Quasi-Harmonic Factors Synchronizing Relaxation Processes: Application to Seismology. In: de Rubeis, V., Czechowski, Z., Teisseyre, R. (eds) Synchronization and Triggering: from Fracture to Earthquake Processes. Geoplanet: Earth and Planetary Sciences. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12300-9_18
Download citation
DOI: https://doi.org/10.1007/978-3-642-12300-9_18
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-12299-6
Online ISBN: 978-3-642-12300-9
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)