Abstract
When reverberations between heterogeneities or resonance scattering can be neglected but accumulated effects of forward scattering are strong, the Born approximation is not valid but the De Wolf approximation can be applied in such cases. In this paper, renormalized MFSB (multiple-forescattering single-backscattering) equations and the dual-domain expression for scalar, acoustic and elastic waves are derived by a unified approach. Two versions of the one-return method (using MFSB approximation) are given: One is the wide-angle dual-domain formulation (thin-slab approximation); the other is the screen approximation. In the screen approximation, which involves a small-angle approximation for the wave-medium interaction, it can be seen clearly that the forward scattered, or transmitted waves are mainly controlled by velocity perturbations; while the backscattered or reflected waves, by impedance perturbations. The validity of the method and the wide-angle capability of the dual-domain implementation are demonstrated by numerical examples. Reflection coefficients of a plane interface derived from numerical simulations by the wide-angle method match the theoretical curves well up to critical angles. For the reflections of a low-velocity slab, the agreement between theory and synthetics only starts to deteriorate for angles greater than 70°. The accuracy of the wide-angle version of the method could be further improved by optimizing the wave-number filtering for the forward propagation and shrinking the step length along the propagation direction.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aki, K., andRichards, P. G. (1980),Quantitative Seismology: Theory and Methods, Vol. 1 (W. H. Freeman, New York, NY 1980).
Claerbout, J. F. (1970),Coarse Grid Calculations of Waves in Inhomogeneous Media with Applications to Delineation of Complicated Seismic Structure, Geophysics35, 407–418.
Claerbout, J. F.,Fundamentals of Geophysical Data Processing, (McGraw-Hill, New York 1976).
De Wolf, D. A. (1971),Electromagnetic Reflection from an Extended Turbulent Medium: Cumulative Forward-scatter Single-backscatter Approximation, IEEE Trans. Ant. and Propag.AP-19, 254–262.
De Wolf, D. A. (1985),Renormalization of EM Fields in Application to Large-angle Scattering from Randomly Continuous Media and Sparse Particle Distribution, IEEE Trans. Ant. and Propag.AP-33, 608–615.
Feit, M. D., andFleck, J. A., Jr. (1978),Light Propagation in Graded-index Optical Fibers, Appl. Opt.17, 3990–3998.
Flatté, S. M., andTappert, F. D. (1975),Calculation of the Effect of Internal Waves on Oceanic Sound Transmission, J. Acoust. Soc. Am.58, 1151–1159.
Hudson, A. (1980).A Parabolic Approximation for Elastic Waves, Wave Motion2, 207–214.
Landers, T., andClaerbout, J. F. (1972),Numerical Calculation of Elastic Waves in Laterally Inhomogeneous Media, J. Geophys. Res.77, 1476–1482.
Martin, J. M., andFlatté, S. M. (1988),Intensity Images and Stastistics from Numerical Simulation of Wave Propagation in 2-D Random Media, Appl. Opt.17, 211–2126.
McCoy, J. J. (1977),A Parabolic Theory of Stress Wave Propagation through Inhomogeneous Linearly Elastic Solids, J. Appl. Mech.44, 462–468.
Stoffa, P. L., Fokkema, J. T., Freire, R. M. D., andKessinger, W. P. (1990),Split-step Fourier Migration, Geophysics55, 410–421.
Tappert, F. D.,The Parabolic equation method. InWave Propagation and Underwater Acoustics (eds. Keller and Papadakis) (Springer, New York 1977).
Thomson, D. J., andChapman, N. R. (1989),A Wide-angle Split-step Algorithm for the Parabolic Equation, J. Acoust. Soc. Am.74, 1848–1854.
Wales, S. C.,A vector parabolic equation model for elastic propagation. InOcean Seismo-Acoustics (eds.) Akal and Berkson) (Plenum, New York 1986).
Wales, S. C., andMcCoy, J. J. (1983),A Comparison of Parabolic Wave Theories for Linearly Elastic Solids, Wave Motion5, 99–113.
Wu, R. S. (1994),Wide-angle Elastic Wave One-way Propagation in Heterogeneous Media and an Elastic Wave Complex-screen Method, J. Geophys. Res.99, 751–766.
Wu, R. S., andAki, K. (1985),Scattering Characteristics of Waves by an Elastic Heterogeneity, Geophysics50, 582–595.
Wu, R. S., andHuang, L. J. (1992),Second field calculation in heterogeneous media using phase-screen poopagator. InExpanded Abstracts of the Technical Program, SEG 62nd Annual Meeting (Society of Exploration Geophysicists, Tulsa) pp. 1289–1292.
Wu, R. S., andHuang, L. J. (1995a),Reflected wave modeling in heterogeneous acoustic media using the De Wolf approximation. InMathematical Methods in Geophysical Imaging III (ed. Hassanzadeh, S.) (SPIE-The International Society for Optical Engineering, Bellingham, Washington, USA 1995) pp. 176–186.
Wu, R. S., Huang, L. J., andXie, X. B. (1995b),Backscattered wave calculation using the De Wolf approximation and a phase-screen propagator. InExpanded Abstracts of the Technical Program, SEG 65th Annual Meeting (Society of Exploration Geophysicists, Tulsa) pp. 1293–1296.
Wu, R. S., andXie, X. B. (1993),A complex-screen method for elastic wave one-way propagation in heterogeneous media. InExpanded Abstracts of the 3rd International Congress of the Brazilian Geophysical Society.
Wu, R. S., andXie, X. B. (1994),Multi-screen backpropagator for fast 3-D elastic prestack migration. InMathematical Methods in Geophysical Imaging II (ed. Hassanzadeh, S.) (SPIE-The International Society for Optical Engineering, Bellingham, Washington, USA 1994) pp. 181–193.
Xie, X. B., andWu, R. S. (1995),A complex-screen method for modeling elastic wave reflections. InExpanded Abstracts of the Technical Program, SEG 65th Annual Meeting (Society of Exploration Geophysicists, Tulsa)pp. 1269–1272.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Wu, RS. Synthetic seismograms in heterogeneous media by one-return approximation. PAGEOPH 148, 155–173 (1996). https://doi.org/10.1007/BF00882059
Received:
Revised:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00882059