Accounting for the definition domain of the forward map in traveltime tomography - Application to the inversion of prismatic reflections

Inverse Problems

Volumn 23, Issue 1, 2007, Pages 139-164

  Cavalca, Maud ^a   Lailly, Patrick ^a  

^a IFP ENERGIES NOUVELLES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; INVERSE KINEMATICS; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; NUMERICAL METHODS; PROBLEM SOLVING;

COMPLEX KINEMATICS; PRISMATIC REFLECTIONS; TRAVELTIME TOMOGRAPHY;

TOMOGRAPHY;

EID: 33947660491     PISSN: 02665611     EISSN: 13616420     Source Type: Journal    
DOI: 10.1088/0266-5611/23/1/007     Document Type: Article

References (47)

1. Bécache E 1992 Reflection tomography: how to cope with multiple arrivals? Part II. A new gradient computation method: continuous and discrete problems PSI Annual Report Institut Francais du Pétrole, Rueil-Malmaison, France
2. Berkhout A J 1985 Seismic Migration-Theoretical Aspects (Amsterdam: Elsevier)
3. Billette F and Lambaré G 1998 Velocity macro model estimation by stereotomography Geophys. J. Int. 135 671-80
4. Bishop T N, Bube K P, Cutler R T, Langan R T, Love P L, Resnick J R, Shuey R T, Spindler D A and Wyld H W 1985 Tomographic determination of velocity and depth in laterally varying media Geophysics 50 903-23
5. Bleistein N 1987 On the imaging of reflectors in the earth Geophysics 52 931-42
6. Bois P, La-Porte M, Lavergne M and Thomas G 1971 Essai de détermination automatique des vitesses sismiques par mesures entre puits Geophys. Prospect. 19 42-83
7. Broto K and Lailly P 2001 Towards the tomographic inversion of prismatic reflections 71st Ann. Int. Mtg, Soc. Expl. Geophys. pp 726-9 (Expanded abstracts)
8. Bube K P 1998 Seismic traveltime tomography Lecture Notes of the 1998 Mathematical Geophysics Summer School (Palo Alto, CA: Stanford University Press)
9. Cavalca M and Lailly P 2001 Towards the tomographic inversion of prismatic reflections KIM Ann. Report IFP, France http://www.ifp.fr/IFP/en/ project/at.htm#kim/
10. erven V, Molotkov I A and Peník I 1977 Ray Method in Seismology (Praha: Univerzita Karlova)
11. erven V 2001 Seismic Ray Theory (Cambridge: Cambridge University Press)
12. Chapman C H 2004 Fundamentals of Seismic Wave Propagation (Cambridge: Cambridge University Press)
13. Chiu S K L and Stewart R R 1987 Tomographic determination of three-dimensional seismic velocity structure using well logs, vertical seismic profiles, and surface seismic data Geophysics 52 1085-98
14. Claerbout J F 1971 Towards a unified theory of reflector mapping Geophysics 36 467-81
15. Delprat-Jannaud F and Lailly P 1991 What information on the Earth model do reflection travel times hold? J. Geophys. Res. 97 19827-44
16. Delprat-Jannaud F and Lailly P 1993 Ill-posed and well-posed formulations of the reflection travel time tomography problem J. Geophys. Res. 98 6589-605
17. Delprat-Jannaud F and Lailly P 1995 Reflection tomography: how to handle multiple arrivals? J. Geophys. Res. 100 703-15
18. Devaney A J 1984 Geophysical diffraction tomography IEEE Trans. Geosci. Remote Sens. GE22 3-13
19. Duffet C and Sinoquet D 2006 Quantifying uncertainties on the solution model of seismic tomography Inverse Problems 22 525-38
20. Farra V and Madariaga R 1987 Seismic waveform modeling in heterogeneous media by ray perturbation theory J. Geophys. Res. 92 2697-712
21. Farra V and Madariaga R 1988 Non-linear reflection tomography Geophys. J. R. Astron. Soc. 95 135-47
22. Farra V, Virieux J and Madariaga R 1989 Ray perturbation theory for interfaces Geophys. J. Int. 99 377-90
23. Gauthier O, Virieux J and Tarantola R 1986 Two-dimensional nonlinear inversion of seismic waveforms Geophysics 51 1387-403
24. Gockenback M S, Symes W W and Tapia R A 1995 The dual regularization approach to seismic velocity inversion Inverse Problems 11 501-31
25. Haas A and Viallix J R 1989 Stochastic inversion by ray continuation: application to seismic tomography Geophys. Prospect. 37 337-57
26. Hale D, Hill N R and Stefani J 1992 Imaging salt with turning seismic waves Geophysics 57 1453-62
27. Hawkins K 1994 The challenge presented by North Sea Central Graben salt domes to all DMO algorithms First Break 12 327-43
28. Iyer H M and Hirahara K 1993 Seismic Tomography: Theory and Practice (London: Chapman and Hall)
29. Keller H B 1968 Numerical Methods for Two-Point Boundary-Value Problems (Waltham, MA: Blaisdell)
30. Kolb P, Collino F and Lailly P 1986 Pre-stack inversion of a 1D medium Proc. IEEE 74 498-508
31. Lailly P 1984 The seismic inverse problem as a sequence of before stack migrations Proc. SIAM Conf. on Inverse Scattering: Theory and Applications pp 206-20
32. Lailly P 1984 Migration methods: partial but efficient solutions to the seismic inverse problem Proc. SIAM Conf. on Inverse Problems of Acoustic and Elastic Waves pp 182-214
33. Lailly P and Sinoquet D 1996 Smooth velocity models in reflection tomography for imaging complex geological structures Geophys. J. Int. 124 349-62
34. Miller D, Oristaglio M and Beylkin G 1987 A new slant on seismic imaging: migration and integral geometry Geophysics 52 943-64
35. Nercessian A, Hirn A and Tarantola A 1984 Three dimensional seismic transmission prospecting of the Mont Dore volcano Geophys. J. R. Astron. Soc. 307-16
36. Nocedal J and Wright S J 1999 Numerical Optimization (Berlin: Springer)
37. Operto S, Ravaud C, Improta L, Virieux J, Herrero A and Dell'Aversane P 2004 Quantitative imaging of complex structures from dense wide-aperture seismic data by multiscale traveltime and waveform inversions Geophys. Prospect. 52 625-51
38. Pratt R G and Chapman C H 1992 Traveltime tomography in anisotropic media: II. Application Geophys. J. Int. 109 20-37
39. Pratt R G, Shin C and Hicks G J 1998 Gauss-Newton and full Newton methods in frequency-space seismic inversion Geophys. J. Int. 133 341-62
40. Santosa F and Symes W W 1989 An analysis of least-squares velocity inversion Monograph Soc. Expl. Geoph. vol 4
41. Sinoquet D 1995 Utilisation de modèles lisses pour línversion tomographique de données sismiques PhD Thesis Université Paris XIII, France (in English)
42. Stolk C C and Symes W W 2003 Smooth objective functionals for seismic velocity inversion Inverse Problems 19 73-89
43. Stork C 1992 Reflection tomography in the postmigrated domain Geophysics 57 680-92
44. Sword C 1987 Tomographic determination of interval velocities from reflection seismic data: the method of controlled directional reception PhD Thesis Stanford University
45. Versteeg R J 1991 Analyse du problème de la détermination du modèle de vitesse pour límagerie sismique PhD Thesis Université Paris VII, France
46. Virieux J and Farra V 1991 Ray tracing in 3-D complex isotropic media: an analysis of the problem Geophysics 56 2057-69
47. Xu S, Chauris H, Lambaré G and Noble M 2001 Common angle migration: a strategy for imaging complex media Geophysics 66 1877-94