Sensitivities of seismic traveltimes and amplitudes in reflection tomography

Geophysical Journal International

Volumn 131, Issue 3, 1997, Pages 618-642

  Wang, Yanghua ^a   Gerhard Pratt, R ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Fr chet derivatives; Inversion; Perturbation methods; Ray tracing; Reflection seismology; Seismic tomography

Indexed keywords

AMPLITUDE; INVERSION; PERTURBATION METHOD; RAY TRACING; SEISMIC REFLECTION; TOMOGRAPHY; TRAVELTIME;

EID: 0031422249     PISSN: 0956540X     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.1365-246X.1997.tb06603.x     Document Type: Article

References (42)

1. Aki, K. & Richards, P., 1980. Quantitative Seismology: Theory and Method, W. H. Freeman, San Francisco, CA.
2. Bishop, T.N. et al., 1985. Tomographic determination of velocity and depth in laterally varying media, Geophysics, 50, 903-923.
3. Bregman, N.D., Bailey, R.C. & Chapman, C.H., 1989. Ghosts in tomography: the effects of poor angular coverage in 2-D seismic traveltime inversion, Can. J. expl. Geophys., 25, 7-27.
4. Bube, K.P., Langan, R.T. & Resnick, J.R., 1995. Theoretical and numerical issues in the determination of reflector depths in seismic reflection tomography, J. geophys. Res., 100, 12 449-12 458.
5. Burridge, R., 1976. Some Mathematical Topics in Seismology, Courant Institute of Mathematical Sciences, New York University, New York, NY.
6. Červený, V., 1985. The application of ray tracing to numerical modelling of seismic wave fields in complex structures, in Seismic Shear Waves, Part A: Theory, pp. 1-124, ed. Dohr., G.P., Geophysical Press, London.
7. Červený, V. & Ravindra, R., 1971. Theory of Seismic Head waves, University of Toronto Press, Toronto, Canada.
8. Chapman, C.H. & Drummond, R., 1982. Body-wave seismograms in inhomogeneous media using Maslov asymptotic theory, Bull. seism. Soc. Am., 72, S277-S317.
9. Constable, S.C., Parker, R.L. & Constable, C.G., 1987. Occam's inversion: a practical algorithm for generating smooth models from electromagnetic sounding data, Geophysics, 52, 289-300.
10. Delprat-Jannaud, F. & Lailly, P., 1992. What information on the Earth model do reflection traveltimes provide?, J. geophys. Res., 97, 19 827-19 844.
11. Delprat-Jannaud, F. & Lailly, P., 1993. Ill-posed and well-posed formulations of the reflection traveltime tomography problem. J. geophys. Res., 98, 6589-6605.
12. Farra, V. & Le Bégat, S., 1995. Sensitivity of qP-wave traveltimes and polarization vectors to heterogeneity, anisotropy and interfaces, Geophys. J. Int., 121, 377-390.
13. Farra, V. & Madariaga, R., 1987. Seismic waveform modelling in heterogeneous media by ray perturbation theory, J. geophys. Res., 92, 2697-2712.
14. Farra, V. & Madariaga, R., 1988. Non-linear reflection tomography, Geophys. J., 95, 135-147.
15. Farra, V., Virieux, J. & Madariaga, R., 1989. Ray perturbation theory for interfaces, Geophys. J. Int., 99, 377-390.
16. Franklin, J. N., 1970. Well-posed stochastic extensions of ill-posed linear problems, J. Math. Anal. Appl., 31, 682-716.
17. Gajewski, D. & Psencik, I., 1990. Vertical seismic profile synthetics by dynamic ray tracing in laterally varying layered anisotropic structures, J. geophys. Res., 95, 11 301-11 315.
18. Gilbert, F. & Backus, G.E., 1966. Propagator matrices in elastic wave and vibration problems, Geophysics, 31, 326-333.
19. Jackson, D.D., 1979. The use of a priori data to resolve nonuniqueness in linear inversion, Geophys. J. R. astr. Soc., 57, 137-157.
20. Kline, M. & Kay, I.W., 1965. Electromagnetic Theory ana Geometrical Optics, John Wiley & Sons, New York, NY.
21. Neele, F., VanDecar, J.C. & Snieder, R., 1993a. A formalism for including amplitude data in tomographic inversions, Geophys. J. Int., 115, 482-496.
22. Neele, F., VanDecar, J.C. & Snieder, R., 1993b. The use of P-wave amplitude data in a joint tomographic inversion with travel times for upper-mantle velocity structure, J. geophys. Res., 98, 12 033-12 054.
23. Nowack, R.L. & Lutter, W.J., 1988. Linearized rays, amplitude and inversion, Pure appl. Geophys., 128, 401-421.
24. Nowack, R.L. & Lyslo, J.A., 1989. Fréchet derivatives for curved interfaces in the ray approximation, Geophys. J., 97, 497-509.
25. Ory, J. & Pratt, R.G., 1995. Are our parameter estimators biased? The significance of finite-difference regularization operators, Inverse Problem 11, 397-424.
26. Pratt, R.G. & Chapman, C.H., 1992. Traveltime tomography in anisotropic media - II. Application, Geophys. J. Int., 109, 20-37.
27. Sambridge, M.S., 1990. Non-linear arrival time inversion: constraining velocity anomalies by seeking smooth models in 3-D, Geophys. J. Int., 102, 653-677.
28. Sheriff, R.E. & Geldart, L.P., 1995. Exploration Seismology, 2nd edn, Cambridge University Press, Cambridge.
29. Snieder, R. & Sambridge, M., 1992. Ray perturbation theory for traveltimes and ray paths in 3-D heterogeneous media, Geophys. J. Int., 109, 294-322.
30. Snieder, R. & Sambridge, M., 1993. The ambiguity in ray perturbation theory, J. geophys. Res., 98, 22 012-22 034.
31. Snieder, R. & Lomax, A., 1996. Wavefield smoothing and the effect of rough velocity perturbations on arrival times and amplitudes, Geophys. J. Int., 125, 796-812.
32. Snieder, R. & Spencer, C., 1993. A unified approach to ray bending, ray perturbation and paraxial ray theories, Geophys. J. Int., 115, 456-470.
33. Stork, C., 1992a. Singular value decomposition of the velocity-reflector depth tradeoff, Part 1: Introduction using a two-parameter model, Geophysics, 57, 927-932.
34. Stork, C., 1992b. Singular value decomposition of the velocity-reflector depth tradeoff, Part 2: High-resolution analysis of a generic model, Geophysics, 57, 933-943.
35. Tarantola, A., 1987. Inverse Problem Theory, Methods for Data Fitting and Model Parameter Estimation, Elsevier, Amsterdam.
36. Tarantola, A. & Vallette B., 1982. Generalized nonlinear inverse problems solved using the least squares criterion, Rev. Geophys. Space Phys., 20, 219-232.
37. Thomson, C.J., 1983. Ray-theoretical amplitude inversion for laterally varying velocity structure below NORSAR, Geophys. J. R. astr. Soc., 74, 525-558.
38. Thomson, C.J. & Chapman, C.H., 1985. An introduction to Maslov's asymptotic method, Geophys. J. R. astr. Soc., 83, 143-168.
39. Wang, Y. & Houseman, G.A., 1994. Inversion of reflection seismic amplitude data for interface geometry, Geophys. J. Int., 117, 92-110.
40. Wang, Y. & Houseman, G.A., 1995. Tomographic inversion of reflection-seismic amplitude data for velocity variation, Geophys. J. Int., 123, 355-372.
41. Wang, Y., White, R.E. & Pratt, R.G., 1998. Geometrical inversion of seismic amplitudes from real, migrated reflection gathers, Geophysics, submitted.
42. Williamson, P.R., 1990. Tomographic inversion in reflection seismology, Geophys. J. Int., 100, 255-274.