Abstract
Methods of theoretical study in seismic wave scattering are reviewed with the emphasis on the perturbation method. Detailed analysis for weak scattering using Born approximation is given. For elastic random media, the mean square amplitudes of scattered waves are derived using a new approach by working directly in the spectrum domain. The conditions for the scalar wave approximation are obtained. The problem of sensitivity of fore- and backscattering to heterogeneities with different scales and properties (velocity or impedance) is discussed.
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Bibliography
Achenbach, J. D.,Wave Propagation in Elastic Solids (North-Holland Publ. Comp., New York 1973).
Aki, K. (1973),Scattering of P waves under the Montana Lasa, J. Geophys. Res.78, 1334–1346.
Aki, K. (1980),Scattering and Attenuation of Shear Waves in the Lithosphere, J. Geophys. Res.85, 6496–9504.
Aki, K., andChouet, A. B. (1975),Origin of Coda Waves: Source, Attenuation and Scattering Effects, J. Geophys. Res.80, 3322–3342.
Aki, K., andRichards, P.,Quantitative Seismology, vol. 2 (W. H. Freeman, San Francisco 1980).
Bataille, K., Wu, R. S., andFlatté, S. M. (1989),Inhomogeneities Near the Core-mantle Boundary Evidenced from Seismic Wave Scattering—A Review, to appear in Pure Appl. Geophys.132.
Berteussen, K. A., Christofferson, A., Husebye, E. S., andDahle, A. (1975),Wave Scattering Theory in Analysis of P Wave Anomalies at NORSAR and LASA, Geophys. J. R. Astr. Soc.42, 403–417.
Capon, J. (1974),Characterization of Crust and Upper Mantle Structure under LASA as a Random Medium, Bull. Seismol. Soc. Am.64, 235–266.
Chernov, L. A.,Wave Propagation in a Random Medium (McGraw-Hill, New York 1960).
Flatté, S. M., andWu, R. S. (1988),Small Scale Structure in the Lithosphere and Asthenosphere Deduced from Arrival Time and Amplitude Fluctuations, J. Geophys. Res.93, 6601–6614.
Gilbert, T. J., andKnopoff, L. (1960),Seismic Scattering from Topographic Irregularities, J. Geophys. Res.65, 3437–3444.
Gubernatis, J. E., Domany, E., andKrumhansl, J. A. (1977a),Formal Aspects of the Theory of the Scattering of Ultrasound by Flows in Elastic Materials, J. Appl. Phys.48, 2804–2811.
Gubernatis, J. E., Domany, E., Krumhansl, J. A., andHuberman, M. (1977b),The Born Approximation in the Theory of the Scattering of Elastic Waves by Flows, J. Appl. Phys.,48, 2812–2819.
Haddon, R. A. W., andCleary, J. R. (1974),Evidence for Scattering of Seismic PKP Waves near the Mantle-core Boundary, Phys. Earth and Planet. Int.,8, 211–234.
Herrera, I., andMal, A. K. (1965),A Perturbation Method for Elastic Wave Propagation, II—Small Inhomogeneities, J. Geophys. Res.70, 871–873.
Herrera, I. (1965),A Perturbation Method for Elastic Wave Propagation, III—Thin Inhomogeneities, Geofis. Int.5, 1–14.
Hudson, J. A. (1967),Scattering Surface Waves from a Surface Obstacle, Geophys. J.13, 441–458.
Hudson, J. A. (1968),The Scattering of Elastic Waves by Granular Media, Qu. J. Mech. Appl. Math.21, 487–502.
Hudson, J. A., andKnopoff, L. (1967),Statistical Properties of Rayleigh Waves due to Scattering by Topography, Null. Seis. Soc. Am.57, 83–90.
Hudson, J. A. (1977),Scattered Waves in the Coda of P, J. Geophys.43, 359–374.
Knopoff, L., andHudson, J. A. (1964),Scattering of Elastic Waves by Small Inhomogeneities, J. Acoust. Soc. Am.36, 338–343.
Knopoff, L., andHudson, J. A. (1967),Frequency Dependence of Scattered Elastic Waves, J. Acoust. Soc. Am.42, 18–20.
Miles, J. W. (1980),Scattering of Elastic Waves by Small Inhomogeneities, Geophysics25, 642–648.
Morse, P. M., andFeshbach, H.,Methods of Theoretical Physics, Ch. 13 (McGraw-Hill Book Comp., New York 1953).
Pao, Y. H., andMow, C. C.,Diffraction of Elastic Waves and Dynamic Stress Concentrations (Crane Russak, New York 1973).
Sato, H. (1984),Attenuation and Envelope Formation for Three-component Seismograms of Small Local Earthquakes in Randomly Inhomogeneous Lithosphere, J. Geophys. Res.89, 1221–1241.
Tatarskii, V. I.,Wave Propagation in a Turbulent Medium (Dover, New York 1961).
Tatarskii, V. I. (1971),The Effects of the Turbulent Atmosphere on Wave Propagation. (Translated from Russian) National Technical Information Service, Springfield, VA.
Wu, R. S., andAki, K. (1985a),Scattering Characteristics of Elastic Waves by an Elastic Heterogeneity, Geophysics50, 582–595.
Wu, R. S., andAki, K., (1985b),Elastic Wave Scattering by a Random Medium and the Small Scale Inhomogeneities in the Lithosphere, J. Geophys. Res.90, (B12), 10261–10273.
Wu, R. S., andFlatté, S. M. (1989),Transmission Fluctuation Across an Array and the Heterogeneities in the Crust and Upper Mantle, to appear in Pure Appl. Geophys.132.
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Wu, RS. The perturbation method in elastic wave scattering. PAGEOPH 131, 605–637 (1989). https://doi.org/10.1007/BF00876266
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DOI: https://doi.org/10.1007/BF00876266