Two-dimensional multivalued traveltime and amplitude maps by uniform sampling of a ray field

Geophysical Journal International

Volumn 125, Issue 2, 1996, Pages 584-598

  Lambare G ^a   Lucio, P S ^a   Hanyga, A ^b  

^a PSL RESEARCH UNIVERSITY   (France)

^b UNIVERSITY OF BERGEN   (Norway)

Author keywords

Green's functions; Numerical techniques; Ray theory; Ray tracing; Traveltime; Wave propagation

Indexed keywords

AMPLITUDE; GREEN'S FUNCTION; RAY THEORY; RAY TRACING; TRAVELTIME; WAVE PROPAGATION;

EID: 0029770069     PISSN: 0956540X     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.1365-246x.1996.tb00021.x     Document Type: Article

References (32)

1. Aki, K. & Richards, P., 1980. Quantitative seismology: Theory and methods, W.H. Freeman & Co, San Francisco, CA.
2. Burridge, R., 1976. Some mathematical topics in seismology, Courant Institut of Mathematical Sciences, New York University, NY.
3. Červený, V., 1989. Ray tracing in factorized anisotropic inhomogeneous media, Geophys. J. Int., 99, 91-100.
4. Chapman, C.H., 1985. Ray theory and its extensions: WKBJ and Maslov seismogram, J. Geophys., 58, 27-43.
5. de Boor, C., 1978. A practical guide to splines, Springer-Verlag, Berlin, Germany.
6. Ettrich, N. & Gajewski, D., 1995. Efficient prestack Kirchhoff migration using wavefront construction, extended abstract 57th EAEG Meeting, Glasgow, A023, EAEG, Zeist, Netherlands.
7. Farin, G., 1993. Curves and surfaces for computer aided geometric design: a practical guide, 3rd edn, Academic Press, San Diego, CA.
8. Farra, V. & Madariaga, R., Seismic waveform modeling in heterogeneous media by ray perturbation theory, J. geophys. Res., 92, 2697-2712.
9. Forgues, E., Lambaré, G., de Beukelaar, P., Coppens, F. & Richard, V., 1994. An application of Ray + Born inversion on real data, in SEG Ann. Meetg, Expanded Abstracts, pp. 1004-1007, Los Angeles, SEG, Tulsa, OK.
10. Geoltrain, S. & Brae, J., 1991. Can we image complex structures with finite-difference travel times?, in 61th SEG Ann. Meetg, Expanded Abstracts, pp. 1110-1113, SEG, Tulsa, OK.
11. Goldstein, H., 1980. Classical Mechanics, (1st edn 1950) Addison-Wesley, Reading, MA.
12. Guillemin, V. & Sternberg, S., 1977. Geometric Asymptotics, American Mathematical Society, Providence, RI.
13. Hanyga, A., 1984. Dynamic ray tracing on Lagrangian manifolds, Geophys. J. R. astr. Soc., 19, 51-63.
14. Hanyga, A. & Helle, H.B., 1995. Synthetic seismograms from generalized ray tracing, Geophys. Prospect., 43, 51-76.
15. Hanyga, A., Lenartowicz, E. & Pajchel, J., 1985. Seismic Waves in the Earth, Elsevier, Amsterdam.
16. Hanyga, A., Lambaré, G. & Lucio, P.S., 1995a. Asymptotic Green's functions by Maslov summation, SEG Ann. Meetg, Extended Abstracts, pp. 1297-1300, SEG, Tulsa, OK.
17. Hanyga, A., Thierry, P., Lambaré, G. & Lucio, P., 1995b. 2D and 3D asymptotic Green's functions for linear inversion, in Mathematical Methods in Geophysical Imaging III, pp. 123-137, ed. Hassanzadeh, S., Proc. SPIE, 2571, SPIE, Bellingham, WA.
18. Lambaré, G., Vineux, J., Madariaga, R. & Jin, S., 1992. Iterative asymptotic inversion in the acoustic approximation, Geophysics, 57, 1138-1154.
19. Lucio, P.S., Lambaré, G. & Hanyga, A., 1995. 3D multivalued travel time and amplitude map, in 57th EAEG Meetg, Expanded Abstracts, p. 147, EAEG, Zeist, Netherlands.
20. Maslov, V.P., 1972. Théorie des perturbations et méthodes asymptotiques, Dunod et Gauthier-Villars, Paris.
21. Moser, T.J., 1995. Inversion in a nonsmooth background, 57th EAEG Meetg, Expanded Abstracts, E036, EAEG, Zeist, Netherlands.
22. Pajchel, J., Moser, T.J., 1995. Recurcive cell raytracing, 57th EAEG Meetg, Expanded Abstracts, P092, EAEG, Zeist, Netherlands.
23. Pham, F., 1992. Géométrie et calcul différentiel sur les variétés: Cours, études et exercices pour la maîtrise de mathématiques, InterÉditions, Paris.
24. Podvin, P. & Lecomte, 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.
25. Sun, Y., 1992. Computation of 2D multiple arrival travel time fields by an interpolate shooting method, in 62th SEG Ann. Meetg, Expanded Abstracts, pp. 1320-1323, SEG, Tulsa, OK.
26. Thierry, P. & Lambaré, G., 1995. 2.5D true amplitude migration on a workstation, SEG Ann. Meetg, Extended Abstracts, pp. 156-159, SEG, Tulsa, OK.
27. Vidale, J., 1988. Finite-difference calculation of travel time, Bull. seism. Soc. Am., 78, 2062-2076.
28. Vinje, V., Iversen, E. & Gjøystdal, H., 1992. Traveltime and amplitude estimation using wavefront construction, in EAEG Ann. Meetg, Abstract, pp. 504-505, EAEG, Zeist, Netherlands.
29. Vinje, V., Iversen, E. & Gjøystdal, H., 1993a. Traveltime and amplitude estimation using wavefront construction, Geophysics, 58, 1157-1166.
30. Vinje, V., Iversen, E., Gjøystdal, H. & Åstebøl, K. 1993b. Estimation of multivalued arrivals in 3D models using wavefront construction, EAEG Ann. Meetg. Abstract, B019, EAEG, Zeist, Netherlands.
31. Vineux, J. & Farra, V., 1991. Ray tracing in 3D complex isotropic media: an analysis of the problem, Geophysics, 56, 2057-2069.
32. Weinstein, A., 1979. Lectures on symplectic manifold, AMS, Providence, RI.