First-arrival traveltime tomography using second generation wavelets

Geophysical Prospecting

Volumn 56, Issue 4, 2008, Pages 505-526

  Delost, Matthieu ^a   Virieux, Jean ^a   Operto, Stéphane ^a  

^a UNIVERSITÉ DE NICE SOPHIA ANTIPOLIS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ARCHITECTURAL DESIGN; COMPUTER NETWORKS; DIAGNOSTIC RADIOGRAPHY; IMAGING TECHNIQUES; LINEARIZATION; MATHEMATICAL OPERATORS; MATHEMATICAL TRANSFORMATIONS; MEDICAL IMAGING; MESH GENERATION; MODAL ANALYSIS; POWER GENERATION; RAY TRACING; REPAIR; RESTORATION; SCALES (WEIGHING INSTRUMENTS); SEISMOLOGY; SURFACES; THERMOGRAPHY (TEMPERATURE MEASUREMENT); TOMOGRAPHY; WAVELET TRANSFORMS;

(1 1 0) SURFACE; (U ,V) OPERATOR; ARRIVAL TIME; CROSS-HOLE TOMOGRAPHY; DIFFERENT SCALES; EUROPEAN; FAST WAVELET TRANSFORM (FWT); GEOSCIENTISTS; HAAR WAVELETS; INVERSION PROCEDURES; LINEARIZED SYSTEMS; MESH STRUCTURES; MULTI SCALING; MULTISCALE RECONSTRUCTION; POWER-OF-TWO; RESOLUTION ANALYSIS; SECOND GENERATION WAVELETS; SPECIFIC AREAS; TOMOGRAPHIC; TRAVEL-TIME TOMOGRAPHY; WAVELET COEFFICIENTS;

WAVELET DECOMPOSITION;

ARRIVAL TIME; DATA INVERSION; DECOMPOSITION ANALYSIS; LINEARITY; NUMERICAL MODEL; RAY TRACING; RECONSTRUCTION; SEISMIC TOMOGRAPHY; WAVELET ANALYSIS;

EID: 45349103603     PISSN: 00168025     EISSN: 13652478     Source Type: Journal    
DOI: 10.1111/j.1365-2478.2008.00710.x     Document Type: Article

References (57)

1. Aki K. and Lee W. 1976. Determination of three-dimentional velocity anomalies under a seismic array using first P-arrival times from local earthquakes. Journal of Geophysical Research 81, 4381-4399.
2. Benz H.M., Chouet S.A., Dawson P.B., Lahr J.C., Page R.A. and Hole J.A. 1996. Three-dimentional P and S wave velocity structure of Redoubt Volcano, Alaska. Journal of Geophysical Research 101, 8111-8128.
3. Böhm G. and Vesnaver A. 1999. In quest of the grid. Geophysics 64, 1116-1125.
4. Böhm G., Galuppo P. and Vesnaver A. 2000. 3D adaptative tomography using delauney triangles and voronoi polygons. Geophysical Prospecting 48, 723-744.
5. Bourgeois A., Bourget M., Lailly P., Poulet M., Ricarte P. and Versteeg R. 1991a. Marmousi, model and data. Proceedings of the EAEG Workshop on Practical Aspects of Seismic Data Inversion, pp. 5-16. EAEG.
6. Bourgeois A., Bourget M., Lailly P., Poulet M., Ricarte P. and Versteeg R. 1991b. Marmousi, model and data marmousi, model and data, the marmousi experience. Proceedings of the EAEG Workshop on Practical Aspects of Seismic Data Inversion. EAEG.
7. Chiao L.-Y. and Kuo B.-Y. 2001a. Multiscale seismic tomography. Geophysical Journal International 145, 517-527.
8. Chiao L.-Y. and Kuo B.-Y. 2001b. Multiscale seismic tomography. Geophysical Journal International 145, 517-527.
9. Chiao L.-Y. and Liang W.-T. 2003. Multiresolution parametrization for geophysical inverse problems. Geophysics 68, 199-209.
10. Cohen A., Daubechies I. and Feauveau J. 1992. Biorthogonal basis of compactly supported wavelets. Communications on Pure and Applied Mathematics 45, 485-560.
11. Dahlen F.A. 2004. Resolution limit of traveltime tomography. Geophysical Journal International 157, 315-331.
12. Daubechies I. 1988. Orthonormal bases of compactly supported wavelets. Communications on Pure and Applied Mathematics 41, 909-996.
13. Daubechies I., Grossmann A. and Meyer Y. 1986. Painless nonorthogonal expansions. Journal of Mathematical Physics 27, 1271-1283.
14. Delprat-Jannaud F. and Lailly P. 1993. Ill posed and well posed formulation of the reflection traveltime tomography problem. Journal of Geophysical Research 98, 6589-6605.
15. Farra V. and Madariaga R. 1988. Non-linear reflection tomography. Geophysical Journal 95, 135-147.
16. Grossmann A. and Morlet J. 1984. Decomposition of hardy functions into square integrable wavelets of constant shape. SIAM Journal on Mathematical Analysis 15, 723-736.
17. Hole J. A. 1992. Nonlinear high-resolution three-dimentional seismic travel time tomography. Journal of Geophysical Research 97, 6553-6562.
18. Kissling E., Ellsworth W.L., Eberhart-Phillips D. and Kradolfer U. 1994. Initial reference models in local earthquake tomography. Journal of Geophysical Research 99, 19635-19646.
19. Latorre D., Virieux J., Monfret T., Monteiller V., Vanorio T., Got J.L., and Lyon-Caen H. 2004. A new seismic tomography of Aigion area (Gulf of Corinth, Greece) from the 1991 data set. Geophysical Journal International 159, 1013-1031.
20. Madych W.R. 1999. Tomography, approximate reconstruction, and continuous wavelet transforms. Applied and Computational Harmonic Analysis 7, 54-100.
21. Mallat S. 1989a. Multifrequency approximations and wavelet orthonormal bases of l 2 (r). Transactions of the American Mathematical Society 315, 69-87.
22. Mallat S. 1989b. Multifrequency channel decompositions of images and wavelet models. IEEE Transactions on Acoustics, Speech, and Signal Processing 37, 2091-2110.
23. Mallat S. 1999. A Wavelet Tour of Signal Processing. Academic Press.
24. Menke W. 1984. Geophysical Data Analysis: Discrete Inverse Theory. Academic Press.
25. Meyer Y. 1999. Ondelettes et opérateurs, i:oNdelettes, ii:oPérateurs de calderon-zygmWnd, iii:(with r. coifman), opérateurs multilinéaires. Academic Press.
26. Michelini A. 1995. An adaptative-grid formalism for traveltime tomography. Geophysical Journal International 121, 489-510.
27. Mintzer F. 1985. Filter for distorsion-free multirate filter banks. IEEE Transactions on Acoustics, Speech, and Signal Processing 33, 626-630.
28. Monteiller V., Got J.-L., Virieux J. and Okubo P. 2005. An efficient algorithm for double-difference tomography and location in heterogeneous media, with an application to kilauea volcano. Journal of Geophysical Research 110, B12306.
29. Montelli R., Nolet G., Dahlen F.A., Masters G., Engdahl E.R. and Hung S. H. 2004. Finite-frequency tomography reveals a variety of plumes in the mantle. Science 303, 338-343.
30. Nguyen T.Q. and Vaidyannathan P.P. 1989. Two-channnel perfect reconstruction fir qmf structures which yield linear phase analysis ans synthesis filters. IEEE Transcations on Acoustics, Speech, and Signal Processing 37, 676-690.
31. Nolet G., Montelli R. and Vireux J. 1999. Explicit, approximate expressions for the resolution and a posteriori covariance of massive tomographic systems. Geophysical Journal International 138, 36-44.
32. Operto S., Ravaut C., Improta L., Virieux J., Herrero A. and Dell'Aversana P. 2004. Quantitative imaging of complex structures from multi-fold wide aperture seismic data. Geophysical Prospecting 52, 625-651.
33. Paige C.C. and Saunders M.A. 1982. ALGORITHM 583 LSQR: Sparse linear equations and least squares problems. ACM Transactions on Mathematical Software 8, 195-209.
34. Podvin P. and Lecomte I. 1991. Finite difference computation of traveltimes in very contrasted velocity model: A massively parallel approach and its associated tools. Geophysical Journal International 105, 271-284.
35. Pratt R.G., Shin C. and Hicks G.J. 1998. Gauss-newton and full newton methods in frequency-space seismic waveform inversion. Geophysical Journal International 133, 341-362.
36. Spakman W. and Bijwaard H. 1998. Irregular cell parametrization of tomographic problems. Annales Geophysicae 16, 28.
37. Spakman W. and Nolet G. 1988. Imaging algorithms, accuracy and resolution. In: Mathematical Geophysics (ed. N. Vlaar), pp. 155-187. D Reidel, Dordrecht.
38. Spakman W., Bijwaard H. and Engdahl E.R. 1998. Closing the gap between regional and global travel time tomography. Journal of Geophysical Research 103, 30055-30078.
39. Sweldens W. 1994. The lifting scheme, a custom design construction of biorthogonal wavelets. Technical Report 1994:7, University of South Carolina.
40. Sweldens W. 1997. The lifting scheme, a construction of second generation wavelets. SIAM Journal on Mathematical Analysis 29, 511-546.
41. Sweldens W. and Schroder P. 1995. Buidling your own wavelets at home. Technical Report 1995:5, University of South Carolina.
42. Tarantola A. 1987. Inverse Problem Theory: Methods for Data Fitting and Model Parameter Estimation. Elsevier.
43. Tarantola A. and Valette B. 1982. Generalized nonlinear inverse problems solved using the least square criterion. Reviews of Geophysics and Space Physics 20, 219-232.
44. Tikhonov A. and Arsenin V. 1977. Solution of Ill-posed Problems. Winston, Washington DC.
45. Trinks I., Singh S.C., Chapman C.H., Barton P.J., Bosch M. and Cherrett A. 2005. Adaptative traveltime tomography of densely sampled seismic data. Geophysical Journal International 160, 925-938.
46. Vaidyannathan P.P. 1993. Theory an design of m-channel maximally decimated quadrature mirror filters with arbitrary m, having perfect reconstruction property. SIAM Journal on Mathematical Analysis 30, 141-162.
47. Versteeg R. 1994. The marmousi experience: Velocity model determination on a synthetic complex data set. The Leading Edge 13, 927-936.
48. Vesnaver A. 1994. Towards the uniqueness of tomographic inversion solutions. Journal of Seismic Exploration 3, 323-334.
49. Vesnaver A. 1996. Irregular grids in seismic tomography and minimum time ray tracing. Geophysical Journal International 125, 147-165.
50. Vetterli M. 1986. Filter banks allowing prefect reconstruction. Signal Processing 10, 219-244.
51. Vetterli M. and Herley C. 1989. Wavelet and filter banks: Theory and design. IEEE Transactions on Acoustics, Speech, and Signal Processing 37, 1057-1071.
52. Wesseling P. 2002. An Introduction to Multigrid Methods. John Wiley.
53. Woods J.W. and O'neil S.D. 1986. Subband coding of images. IEEE Transactions on Acoustics, Speech, and Signal Processing 34, 1278-1288.
54. Zelt C. and Smith R. B. 1992. Seismic traveltime inversion for 2-D crustal velocity structure. Geophysical Journal International 108, 16-34.
55. Zhang H. and Thurber C. 2005. Adaptative mesh seismic tomography based on tetrahedral and voronoi diagrams: Application to parkfield, california. Journal of Geophysical Research 110, B04303.
56. Zhang J., ten Brink U.S. and Toksöz M.N. 1998. Nonlinear refraction and reflection travel time tomography. Journal of Geophysical Research 103, 29743-29757.
57. Zhou H. 2003. Multiscale traveltime tomography. Geophysics 68, 1639-1649.