Abstract
An algorithm for computing multivalued maps for travel time, amplitude and any other ray related variable in 3D smooth velocity models is presented. It is based on the construction of successive isochrons by tracing a uniformly dense discrete set of rays by fixed travel-time steps. Ray tracing is based on Hamiltonian formulation and includes computation of paraxial matrices. A ray density criterion ensures uniform ray density along isochrons over the entire ray field including caustics. Applications to complex models are shown.
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References
Aki, K., andRichards, P.,Quantitative Seismology: Theory and Methods (W. H. Freeman and Co, New York 1980).
Aminzadeh, F., Burehard, N., Nicoletis, L., Rocca, F., andWyatt, K. (1994a),SEG/EAEG 3-D Modeling Project: First Report, The Leading Edge13, 110–111.
Aminzadeh, F., Burehard, N., Nicoletis, L., Rocca, F., andWyatt, K. (1994b),SEG/EAEG 3-D Modeling Project: Second Report, The Leading Edge13, 949–952.
Aminzadeh, F., Burehard, N., Nicoletis, L., Rocca, F., andWyatt, K. (1995).SEG/EAEG 3-D Modeling Project: Third Report, The Leading Edge14, 125–128.
Chapman, C. (1985),Ray Theory and its Extensions: WKBJ and Maslov Seismogram, J. Geophys.58, 27–43.
de Boor, C.,A Practical Guide to Splines (Springer-Verlag, New York 1978).
Ettrich, N., andGajewski, D. (1995),Efficient prestack Kirchhoff migration using wave-front construction. In57th Annual EAEG Meeting, Extended Abstracts, Glasgow, A023. Also article in this issue.
Farin, G.,Curves and Surfaces for Computer-aided Geometric Design: A Practical Guide,Third edition (Academic Press, Inc., San Diego 1993).
Farra, V. (1993),Ray Tracing in Complex Media, J. Appl. Geophys.30, 55–73.
Farra, V., andMadariaga, R. (1987),Seismic Waveform Modeling in Heterogeneous Media by Ray Perturbation Theory, J. Geophys. Res.92, 2697–2712.
Forgues, E., Lambaré, G., de Beukelaar, P., Coppens, F., andRichard, V. (1994),An application of Ray + Born inversion on real data. In64th SEG Annual Meeting and Exposition, Expanded Abstracts, Los Angeles, pp. 1004–1007.
Geoltrain, S., andBrac, J. (1991),Can we image complex structures with finite-difference travel times? In61st Annual SEG meeting and Exposition, Expanded Abstracts, Houston, pp. 1110–1113.
Goldstein, H.,Classical Mechanics (Addison-Wesley Publishing Company, Inc., Reading, Massachusetts 1980).
Guillemin, V., andSternberg, S.,Geometric Asymptotics (AMS, Providence, R.I. 1977).
Hanyga, A., andHelle, H. B. (1994),Synthetic Seismograms from Generalized Ray Tracing, Geophys. Prosp.43, 51–76.
Hanyga, A., Lenartowicz, E., andPajchel, J.,Seismic Wave Propagation in the Earth (Elsevier, Amsterdam 1984).
Lambaré, G., Lucio, P., andHanyga, A. (1996),Two-dimensional Multivalued Travel Time and Amplitude Maps by Uniform Sampling of Ray Field, Geophys. J. Int.125, 584–598.
Lambaré, G., Virieux, J., Madariaga, R., andJin, S. (1992),Iterative Asymptotic Inversion of Seismic Profiles in the Acoustic Approximation, Geophysics57, 1138–1154.
Moser, T., andFajchel, J. (1995),Recursive Ray Modeling: Applications in Inversion and VSP, submitted to Geophysical Prospecting.
Pham, F.,Géométric et calcul différentiel sur les variétés: cours, études et execrices pour la maîtrise de mathématiques (InterÉditions, Paris 1992).
Podvin, P., andLecomte, I. (1991),Finite-difference Computation of Travel Times in Very Contrasted Velocity Models: A Massively Parallel Approach and its Associated Tools, Geophys. J. Int.105, 271–284.
Sun, Y. (1992),Computation of 2D multiple arrival traveltime fields by an interpolative shooting method. In62nd Annual SEG Meeting and Exposition, Expanded Abstracts, New Orleans, pp. 1320–1323.
Thierry, P., andLambaré, G. (1995),2.5D true amplitude migration on a workstation. In66th Annual SEG Meeting and Exposition, Expanded Abstracts, Houston, pp. 156–159.
Versteeg, R. J. (1991),Analyse du problème de la détermination du modèle de vitesse pour l'imagerie sismique, Ph.D. Thesis, Université Paris 7.
Vidale, D. (1988),Finite-difference Calculation of Travel Time, Bull. Seismol. Soc. Am.78, 2062–2076.
Vinje, V., Iversen, E., andGjøystdal, H. (1992),Travel time and amplitude estimation using wave front construction. In54th Annual EAEG Meeting, Extended Abstracts, Paris, pp. 504–505.
Vinje, V., Iversen, E., andGjøystdal, H. (1993a),Travel time and Amplitude Estimation Using Wave Front Construction, Geophysics58, 1157–1166.
Vinje, V., Iversen, E., Gjøystdal, H., andÄstebøl, K. (1993b),Estimation of multivalued arrivals in 3D models using wave front construction. In55th Annual EAEG Meeting, Extended Abstracts, Stavanger, B019.
Weinstein, A.,Lectures on Symplectic Manifolds (AMS, Providence, R.I. 1979).
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Lucio, P.S., Lambaré, G. & Hanyga, A. 3D multivalued travel time and amplitude maps. PAGEOPH 148, 449–479 (1996). https://doi.org/10.1007/BF00874575
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DOI: https://doi.org/10.1007/BF00874575