Summary
The concept of diffracted rays introduced by Keller (1962) opened the way for a ray approach in the numerical modeling of the diffraction phenomena frequently seen in the seismic field records. Unlike the computation of travel times, which has never caused any difficulties being governed by the same eikonal equation as are the rays of ordinary seismic body waves, the evaluation of the diffracted ray amplitude has been another story. In this paper we give a tutorial account of a highly promising technique for the computation of the ray amplitude of seismic waves diffracted by linear edges on seismic interfaces originally presented by Klem-Musatov (1980, 1995). We demonstrate the adequacy of this technique on a series of SH synthetic traces containing diffracted arrivals, some of them diffracted more than once. Our computer program is based on a successful combination of Klem-Musatov's approach with the zero order approximation of the Asymptotic Ray Theory (Červený and Hron, 1980). We showed in the paper that both techniqúes are ideally suited for such a combination, since the ray amplitude evaluation in each of them is based on the same transport equation. In our tutorial review we present all formulae which are needed for a practical implementation of the method and provide their physical interpretation, wherver possible, by using the numerical examples presented in the paper.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abramowitz, M. and Stegun, I.A., 1972:Handbook of Mathematical Functions, Dover Publications, Inc. New York.
Alekseev, A.S., Babich, V.M. and Gelchinsky, B.Y., 1961: Ray Method of Calculating the Intensity of Wave Fronts, In: G.I. Petrashen (Ed.),Problems of Dynamic Theory of Propagation of Seismic Waves,5, Leningrad University Press, 3–24, (in Russian).
Babich, V.M. and Buldyrev, V.S., 1972:Asymptotic Methods in the Problems of Short Wave Diffraction, Nauka, Moscow (in Russian).
Babich, V.M. and Kirpichnikova, N.Ya., 1974:The Boundary Layer Method in the Diffraction Problems, Leningrad University Press, Leningrad, (in Russian).
Červený, V. and Ravindra, R., 1971:Theory of Seismic Head Waves, University of Toronto Press, Toronto.
Červený, V., Molotkov, I.A. and Pšenčík, I., 1977:Ray Method in Seismology, Univerzita Karlova, Praha.
Červený, V. and Hron, F., 1980: The Ray Series Method and Dynamic Ray Tracing System for Three-Dimensional Inhomogeneous Media.Bull. Seism. Soc. Am. 70, 47–77.
Chan, G.H., 1986:Seismic Diffraction from Wedges, Ph.D. Thesis, University of Alberta, Edmonton.
Fock, V.A., 1965:Electromagnetic Diffraction and Propagation Problems, Pergamon Press, New York.
Hagedoorn, J.G., 1954: A process of Seismic Reflection Interpretation.Geophys. Prosp. 2, 85–127.
Hoffmann, H.J., Klaeschen, D., Rabbel, W. and Flueh, E.R., 1993: Raytracing Based Migration Operators for Complex Media and Discontinuities by the Edge-Wave Method, EAEG 1993, Paper No. B038, Stavanger.
Hron, F., 1968: Introduction to the Ray Theory in a Broader Sense: Application to Seismology,Textbook of Laboratoire de Physique de l'École Normale Supérieure, Université de Paris, Paris.
Hron, F. and Kanasewich, E., 1971: Synthetic Seismograms for Deep Seismic Sounding Studies Using Asymptotic Ray Theory.Bull. Seism. Soc. Am. 61, 1169–1200.
Hron, F. and Covey, J.D., 1988: Theory of Seismic Waves Diffracted by the Linear Edges of Seismic Interfaces.Tech. Report F88-E-13, AMOCO Research Centre, Tulsa.
James, G.L., 1976:Geometrical Theory of Diffraction for Electromagnetic Waves, Peregrinus, Southgate House, Stevenage.
Keller, J.B., 1962: A Geometrical Theory of Diffraction.J. Opt. Soc. Am. 52, 116–130.
Klaeschen, D., Rabbel, W. and Flueh, R.E., 1994: An Automated Ray Method for Diffraction Modelling in Complex Media.Geophys. J. Int. 116, 23–38.
Klem-Musatov, K.D., 1980:The Theory of Edge Waves and its Application in Seismics, Nauka, Novosibirsk (in Russian).
Klem-Musatov, K.D. and Aizenberg, A.M., 1985: Seismic Modelling by Methods of the Theory of Edge Waves.J. Geophys. 57, 90–105.
Klem-Musatov, K.D. and Aizenberg, A.M., 1989: The Edge Wave Superposition Method (2-D Scalar Problem).Geophys. J. Int. 99, 351–367.
Klem-Musatov, K., Aizenberg, A., Pajchel, J. and Helle, H.B., 1994:Edge and Tip Diffractions: Theory and Applications in Seismic Prospecting, Norsk Hydro Research Centre, Bergen.
Klem-Musatov, K.D., 1995:Theory of Seismic Diffractions, S.E.G., Tulsa.
Kravtsov, Y.A. and Orlov, Y.I., 1980:The Geometric Optics of Inhomogeneous Media, Nauka, Moscow, (in Russian).
Krey, T., 1952: The Significance of Diffractions in the Investigation of Faults.Geophysics 17, 843–858.
Kunz, B.F.J., 1960: Diffraction Problems in Fault Interpretation.Geophys. Prosp. 8, 381–388.
Landa, E., Shtivelman, V. and Gelchinsky, B., 1987: A Method for Detection of Diffracted Waves on Common Offset Sections.Geophys. Prosp. 35, 359–373.
Mikhailenko, B.G., 1984: Synthetic Seismograms for Complex Three-Dimensional Geometries Using an Analytical-Numerical Algorithm.Geophys. J.R. Astr. Soc. 79, 963–986.
Pajchel, J., Helle, H.B. and Froyland, L.A., 1989: The Theory of Edge Waves Applied to the Modelling of Seismic Diffraction in VSP, EAEG 1989, Paper No. C-39, Berlin.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hron, F., Chan, G.H. Tutorial on the numerical modeling of edge diffracted waves by the ray method. Stud Geophys Geod 39, 103–137 (1995). https://doi.org/10.1007/BF02296070
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02296070