Skip to main content
Log in

Scattering and dissipation of seismic waves in the presence of nonlinearity

  • Published:
pure and applied geophysics Aims and scope Submit manuscript

Abstract

The processes of seismic wave scattering and dissipation are examined in a medium that, in addition to being inhomogeneous and anelastic, is nonlinear and seismically active (seismic emission). In such a medium, there is a complex interrelation between the effects of nonlinearity, scattering and dissipation. Thus, nonlinear interactions between the various components (primary, scattered and induced) of a developing wavefield cause nonlinear (or wave-on-wave) scattering and, by transferring part of the wave energy to the high-frequency region, contribute to its scattering and dissipation. On the other hand, whereas dissipation opposes the accumulation of nonlinear effects by reducing the wave amplitudes, scattering assists it by increasing the propagation distance (and hence the interaction time).

Estimates based on results of field experiments involving vibrators indicate that, as a rule, scattering on inhomogeneities is much stronger than nonlinear scattering, and that nonlinear effects may often dominate dissipative ones.

The nonlinearity of the transmitting medium explains observedQ-value anomalies, and its seismic activity explains the existence ofP coda and the temporal changes in codaQ.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Aki, K. (1969),Analysis of the Seismic Coda of Local Earthquakes as Scattered Waves, J. Geophys. Res.74, 615–631.

    Google Scholar 

  • Aki, K. (1980),Attenuation of Shear Waves in the Lithosphere from Frequency 0.5 to 25 Hz, Phys. Earth Plan. Inter.21, 50–60.

    Google Scholar 

  • Aki, K., andChouet, B. (1975),Origin of Coda Waves: Source, Attenuation and Scattering Effects, J. Geophys. Res.21, 3322–3342.

    Google Scholar 

  • Antonova, L. V., Apitkaen, F. F., Kurochkina, R. I., et al. (1978),Experimental'nye seismicheskie issledovanija nedr Zemli, Nauka, Moskva, p. 203 (in Russian).

    Google Scholar 

  • Beresnev, I. A., andNikolaev, A. V.,Kachestvennaja kartina formirovantija nelinejnyh effektov pri rasprostranenii seismicheskih voln, InProblemy nelinejnoj seismiki (eds. Nikolaev, A., and Galkin, I.) (Nauka, Moskva 1987), pp. 86–94 (in Russian).

    Google Scholar 

  • Beresnev, I. A., Solov'ev, V. S., andShalashov, G. M.,Nelinejnye parametricheskie javlenija v seismike garmonicheskih signalov, InProblemy nelinejnoj seismiki (eds. Nikolaev, A., and Galkin, I.) (Nauka, Moskva 1987a) pp. 180–186 (in Russian).

    Google Scholar 

  • Beresnev, I. A., Shalashov, G. M., andGurevich, B. Ja.,Kombinatsionnoe vzaimodejsvie seismicheskih voln v nelinejnoj pjatikonstantnoj srede, InProblemy nelinejnoj seismiki (eds. Nikolaev, A., and Galkin, I.), (Nauka, Moskva 1987b) pp. 120–128 (in Russian).

    Google Scholar 

  • Berzon, I. S., Epinat'eva, A. M., Starodubrovskaja, B. Ja, et al. (1962),Dinamicheskie harakteristiki seismicheskih voln v real'nih sredah, Izdat. Akad. Nauk SSSR, Moskva, p. 605 (in Russian).

    Google Scholar 

  • Chelidze, T. L., andChergoleishvili, T. T.,Teorija neuporjadochennyh sred i nekotoryje problemy nelinejnoj seismiki, InProblemy nelinejnoj seismiki (eds. Nikolaev, A., and Galkin, I.) (Nauka, Moskva 1987) pp. 41–50 (in Russian).

    Google Scholar 

  • Chernov, L. A.,Wave Propagation in a Random Medium (McGraw-Hill, New York 1972) (English Translation).

    Google Scholar 

  • Clymer, R. W., andMcEvilly, T. V. (1981),Travel Time Monitoring with Vibrosis, Bull. Seism. Soc. Am71, 1903–1920.

    Google Scholar 

  • DeFacio, T., Aki, K., andAlba, I. (1973),Solid Earth Tide and Observed Change of in situ Seismic Velocity, J. Geophys. Res.78, 1973–1322.

    Google Scholar 

  • Dimitriu, P. P. (1988),Self-modulation and Recurrence Phenomena in Vibratory Induced Steady-state Sinusoidal Ground Vibration, Phys. Earth Planet. Inter.50, 74–82.

    Google Scholar 

  • Engelbrecht, Yu. K. (1984),K probleme opisanja nelinejnyh voln v aktivnoj srede, Doklady Akad. Nauk SSSR278, 591–594 (in Russian).

    Google Scholar 

  • Engelbrecht, Yu. K., andFeldman, M. V.,Izmenenie spektral'nogo sostava seismicheskih impulsov pri rasprostranenii v nelinejnoj srede, InProblemy nelinejnoj seismiki (eds. Nikolaev, A., and Galkin, I.) (Nauka, Moskva 1987), pp. 103–108 (in Russian).

    Google Scholar 

  • Everden, J. F., Archambeau, C. B., andCranswick, E. (1986),An Evaluation of Seismic Decoupling and Underground Nuclear Test Monitoring Using High-frequency Seismic Data, Rev. Geophys. Space Phys.24, 143–215.

    Google Scholar 

  • Gurevitch, G. I. (1974),Deformiruemost'sredi i rasprostranenie seismicheskih voln, Nauka, Moskva, 530 pp. (in Russian).

    Google Scholar 

  • Gusev, A. A., andLemsikov, V. K. (1985),Properties of Scattering Elastic Waves in Lithosphere of Kamchatka: Parameters and Temporal Variations, Tectonophysics112, 137–153.

    Google Scholar 

  • Gustchin, V. V., andShalashov, G. M.,O vozmozjnosti ispol'zovanija nelinejnyh seismicheskih effektov v zadachah vibratsionnovo prosvechivanija Zemli, InIssledovanie Zemli nevzryvnymi seismicheskimi istochnikami (Nauka, Moskva 1981) pp. 144–155.

    Google Scholar 

  • Hjørtenberg, E., andRisbø, T. (1975),Monochromatic Components of Seismic Noise in NORSAR Area, Geoph. J. Roy. Astr. Soc.42, 547–554.

    Google Scholar 

  • Jim, A., andAki, K. (1986),Temporal Changes of Coda Q Before the Tangshan Earthquake of 1976 and the Haicheng Earthquake of 1975, J. Geophys. Res.91, 665–673.

    Google Scholar 

  • Khavroshkin, O. B., Nikolaev, A. V., Rykunov, L. N., andTsyplakov, V. V.,Methods, Results and Perspectives of the High Frequency Seismic and Vibrosignals Study, 6th Rep. IASPEI Comm. Microseisms (XVIII Assembly IUGG, Hamburg 1983) pp. 143–149.

  • Kopvillem, U. H., andKholodkevich,Nelinejnyj seismicheskij otklik sistemy geoblokov InProblemy nelinejnoj seismologii (eds. Nikolaev, A., and Galkin, I.) (Nauka, Moskva 1987) pp. 64–75 (in Russian).

    Google Scholar 

  • Landau, L. D., andLifshitz, E. M. (1965),Teorija Uprugosti, Nauka, Moskva, p. 203 (in Russian).

    Google Scholar 

  • Litvin, A. A., andTsvankin, I. D.,Vzaimodejstvie ploskih voln s granitsej nelinejno-uprugoj sredy, InProblemy nelinejnoj seismiki (eds. Nikolaev, A., and Galkin, I.) (Nauka, Moskva 1987), pp. 128–137 (in Russian).

    Google Scholar 

  • Nevskij, M. V., Nikolaev, A. V., andRiznichenko, O. Yu. (1982),Rasseyanie i pogloschenie seismicheskoj energil v zemnoj kore, Izv. Akad. Nauk, Fizika Zemli10, 20–30 (in Russian).

    Google Scholar 

  • Nevskij, M. V., Morozova, L. A., Starchenko, A. I., andBezgodkov, V. I.,Zavisimost' vremennyh variatsij seismicheskih voln ot variatsii deformatsii vsledstvie geodinamicheskih protsessov, InProblemy nelinejnoj seismiki (eds. Nikolaev, A., and Galkin, I.) (Nauka, Moskva 1987) pp. 203–215 (in Russian).

    Google Scholar 

  • Nikolaev, A. V.,Seismics of Heterogeneous and Turbid Media (Nauka, Moscow 1975) 139 pp. (English translation), 186 pp. (Russian original).

    Google Scholar 

  • Nikolaev, A. V.,Vibratsionnoe prosvechivanie—Metod issledovanija Zemli, InProblemy vibratsionnovo prosvechivanija Zemli (eds. Nikolaev, A., and Galkin, I.) (Nauka, Moskva 1977) pp. 5–29 (in Russian).

    Google Scholar 

  • Nikolaev, A. V. (1981),Methods and Some Results of Investigations of the Scattering Properties of the Crust and Mantle, Phys. Earth Plan. Inter.26, 285–291.

    Google Scholar 

  • Nikolaev, A. V. (1984),Seismicheskie issledovanija Zemli vibratsionnymi istochnikami, Vestnik Akad. Nauk SSSR10, 76–87 (in Russian)

    Google Scholar 

  • Nikolaev, A. V. (Editor),Seismicheskij monitoring zemnoj kory (Nauka, Moskva 1986), p. 286 (in Russian).

    Google Scholar 

  • Nikolaev, A. V.,Problemy nelinejnoj seismiki, InProblemy nelinejnoj seismiki (eds. Nikolaev, A., and Galkin, I.) (Nauka, Moskva 1987), pp. 5–19 (in Russian).

    Google Scholar 

  • Ponomarev, V. S.,Gornye porody kak sredy sø sobstvennymi istochnikami uprugoj energii, InProblemy nelinejnoj seismiki (eds. Nikolaev, A., and Galkin, I.) (Nauka, Moskva 1987) pp. 50–64 (in Russian).

    Google Scholar 

  • Rykunov, L. N., Khavroshkin, O. B., andTsyplakov, V. V. (1979),Vremennye izmenenija visokochastonyh seismicheskih shumov, Izv. Akad. Nauk, Fizika Zemli11, 72–77 (in Russian).

    Google Scholar 

  • Sadovskij, M. A. (1983),O raspredelenii razmerov tvjerdyh otdel'nostei, Dokl. Akad. Nauk SSSR269, 69–73 (in Russian).

    Google Scholar 

  • Sato, H. (1977),Energy Propagation Including Scattering Effects, Signal Isotropic Approximation, J. Phys. Earth25, 27–41.

    Google Scholar 

  • Solov'ev, V. S.,Experimental'noe issledovanie nelinejnih seismicheskih effektov, InProblemy nelinejnoj seismiki (eds. Nikolaev, A., and Galkin, I.) (Nauka, Moskva 1987), pp. 164–179, (in Russian).

    Google Scholar 

  • Troitskij, P. A.,Issledovanie shumovovo otklika litosfery na zemletrjasenija, InProblemy nelinejnoj seismiki (eds. Nikolaev, A., and Galkin, I.) (Nauka, Moskva 1987) pp. 164–179 (in Russian).

    Google Scholar 

  • Unger, R., van Kampen, W. A., Berkout, A. J.,et al., (1987),New Possibilities in Controlled-source Seismology with a Magnetic-levitation Vibrator, Geophys. J. Roy. Astr. Soc., in press.

  • Usseinova, P. (1986),Monolog zemletrjasenij, Znanie-Sila6, 12–15 (in Russian).

    Google Scholar 

  • Vasil'ev, Yu. I. (1959),Dve svodki konstant zatuhaniya gornyh porod, Izv. Akad. Naud, Fizika Zemli5, 565–602 (in Russian).

    Google Scholar 

  • Wesson, R. L., Nersessov, I. L., Nikolaev, A. V., andSedova, E. N. (1979),Issledovanie vremennyh izmenenij skorosti prodol'nyh voln v Severnoj Kalifornii, InZbornik Sovetsko-Amerikanskih rabot po prognozu zemletrjasenij, Donish, Dushanbe2 (1), 57–80.

  • Wu, R. S. (1982),Attenuation of Short Period Seismic Waves Due to Scattering in Lithosphere, Geophys. Res. Lett.9, 9–12.

    Google Scholar 

  • Zhadin, V. V. (1975),Spektral'nyj sostav kolebanij, soprovojhdajuschih vstuplenija P-voln, Izv. Akad, Nauk SSSR, Fizika Zemli5, 10–15 (in Russian).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nikolaev, A.V. Scattering and dissipation of seismic waves in the presence of nonlinearity. PAGEOPH 131, 687–702 (1989). https://doi.org/10.1007/BF00876268

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00876268

Key words

Navigation