Multiresolution parameterization for geophysical inverse problems

Geophysics

Volumn 68, Issue 1, 2003, Pages 199-209

  Chiao, Ling Yun ^a   Liang, Wen Tzong ^b  

^a NATIONAL TAIWAN UNIVERSITY   (Taiwan)

^b INSTITUTE OF EARTH SCIENCES   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

INVERSE PROBLEMS; MATRIX ALGEBRA; SEISMIC PROSPECTING; TOMOGRAPHY; WAVELET TRANSFORMS; DAMPING; DIFFERENTIAL EQUATIONS; DISCRETE WAVELET TRANSFORMS; GEOPHYSICS; PARAMETERIZATION; PIXELS; SEISMOLOGY;

MULTIRESOLUTION PARAMETRIZATION; ARBITRARY CORRELATION; DAMPED LEAST SQUARES; DISCRETE TRANSFORMS; GEOPHYSICAL INVERSE PROBLEMS; MODEL PARAMETERIZATION; MULTIRESOLUTION WAVELETS; SAMPLING METHOD; WAVELET REPRESENTATION;

GEOPHYSICS; INVERSE PROBLEMS;

DATA INVERSION; INVERSE PROBLEM; PARAMETERIZATION; WAVELET ANALYSIS;

EID: 0037219763     PISSN: 00168033     EISSN: None     Source Type: Journal    
DOI: 10.1190/1.1543207     Document Type: Article

References (47)

1. Andrew, B., and Gao, H. -Y., 1996, Applied wavelet analysis with S-PLUS: Springer-Verlag.
2. Bergeron, S. T., Vincent, A. P., Yuen, D. A., Tranchant, B. J. S. and Tchong, C., 1999, Viewing seismic velocity anomalies with 3-D continuous Gaussian wavelets: Geophys. Res. Lett., 26, 2311-2314.
3. Bijwaard, H., Spakman, W., and Engdahl, E. R., 1998, Closing the gap between regional and global travel time tomography: J. Geophys. Res., 103, 30 055-30 078.
4. Boschi, L., and Dziewonski, A. M., 1999, High- and low-resolution images of the Earth's mantle: Implications of different approaches to tomographic modeling: J. Geophys. Res., 104, 25 567-25 594.
5. Brandt, A., 1973, Multi-level adaptive technique (MLAT) for fast numerical solution to boundary value problems, in Cabannes, H., and Temam, R., Eds., Proc. 3rd Internat. conf. on numerical methods in fluid mechanics: Springer-Verlag. 1, 82-89.
6. Brandt, A., 1977, Multi-level adaptive solutions to boundary value problems: Math. Comput., 31, 333-390.
7. Brandt, A., 1982, Guide to multigrid development, in Hackbusch, W., and Trottenberg, U., Eds., Multigrid methods: Springer-Verlag, 220-312.
8. Briggs, I. C., 1974, Machine contouring using minimum curvature: Geophysics, 39, 39-48.
9. Caress, D., and Parker, R. L., 1989, Spectral interpolation and downward continuation of marine magnetic anomaly data: J. Geophys. Res., 94, 17 397-17 407.
10. Chiao, L. -Y., and Kuo, B. -Y., 2001, Multiscale seismic tomography: Geophys. J. Internat., 145, 517-527.
11. Chou, C. W., and Booker, J. R., 1979, A Backus-Gilbert approach to inversion of travel-time data for three-dimensional velocity structure: Geophys. J. Roy. Astr. Soc., 59, 325-344.
12. Clapp, R. G., Biondi, B. L., Fomel, S., and Claerbout, J. F., 1998, Regularizing velocity estimation using geologic dip information: 68th Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts. 1850-1853.
13. Cohen A., Daubechies I., and Feauveau J.-C., 1992, Biorthogonal bases of compactly supported wavelets: Comm. Pure Appl. Math., 45, 485-560.
14. Cohen, L., 1995, Time-Frequency analysis: Prentice-Hall Inc.
15. Delprat-Jannaud, F., and Lailly, P., 1993, III-posed and well-posed formulations of the reflection travel time tomography problem: J. Geophys. Res., 98, 6589-6605.
16. Gouvcia, W. P., and Scales, J. A., 1997, Resolution of seismic waveform inversion: Bayes versus Occam: Inverse Problems. 13, 323-349.
17. Goswami, J. C., and Chan, A. K., 1999, Fundamentals of wavelets: Theory, algorithms, and applications: John Wiley & Sons Inc.
18. Grossmann, A., and Morlet, J., 1984, Decomposition of Hardy functions into square integrable wavelets of constant shape: SIAM J. Math. Anal., 15, 723-736.
19. Gualtiero, B., and Vesnaver, A. L., 1999, In quest of the grid: Geophysics, 64, 1116-1125.
20. Herzfeld, U. C., 1992, Least-squares collocation, geophysical inverse theory and geostatistics: A bird's eye view: Geophys. J. Internat., 111, 237-249.
21. Journel, A. G., and Huijbregts, C., 1989, Mining geostatistics: Academic Press.
22. Lines, L. R., and Treitel, S., 1983, Tutorial: A review of least-squares inversion and its application to geophysical problems: Geophys. Prosp., 32, 159-186.
23. 2(R): Trans. Am. Math. Soc., 315, 69-88.
24. Mallat, S., 1989b, A theory of multiresolution signal decomposition: the wavelet representation: IEEE Trans. Pattern Analysis and Machine Intelligence, 11, 674-693.
25. Mallat, S., 1998, A wavelet tour of signal processing. Academic Press, San Diego, 577 pp.
26. Menke, W., 1984, Geophysical data analysis: Discrete inverse theory: Academic Press.
27. Meyerholtz, K. A., Pavlis, G. L., and Szpakowski, S. A., 1989, Convolutional quelling in seismic tomography: Geophysics, 54, 570-580.
28. Michelena, R. J., and Harris, J. M., 1991, Tomographic travetime inversion using natural pixels: Geophysics, 56, 635-644.
29. Moritz, H., 1984, Least squares collocation, in Grafarend, E. W., and Rapp, R. H., Eds., Advances in geodesy: Am. Geophys. Union, 27-36.
30. Ory, J., and Pratt, R. G., 1995, Are our parameter estimators biased? The significance of finite-difference regularization operators: Inverse Problems, 11, 397-424.
31. Paige, C. C., and Saunders, M. A., 1982, LSQR: An algorithm for sparse linear equations and sparse least squares: Trans. Mart. Software, 8. 43-71.
32. Parker, R. L., 1994, Geophysical inverse theory: Princeton Univ. Press.
33. Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P., 1992, Numerical recipes in Fortran: The art of scientific computing, 2nd ed.: Cambridge Univ. Press.
34. Sandwell, D. T., 1987, Biharmonic spline interpolation of GEOS-3 and SEASAT altimeter data: Geophys. Res. Lett., 14, 139-142.
35. Scales, J. A., Docherty, P., and Gersztenkorn, A., 1990, Regularization of nonlinear inverse problems: imaging the near-surface weathering layer: Inverse Problems, 6, 115-131.
36. Shannon, C. E., 1948, The mathematical theory of communications: University of Illinois Press.
37. Smith, W. H. F., and Wessel, P., 1990, Gridding with continuous curvature splines in tension: Geophysics, 55, 293-305.
38. Starck, J. L., Murtagh, F., and Bijaoui, A., 1998, Image processing and data analysis: The multiscale approach: Cambridge University Press.
39. Sweldens, W., 1996, The lifting scheme: Accustom-design construction of biorthogonal wavelets: Appl. Comput. Harmon, Anal., 3, 186-200.
40. Tarantola, A., 1987, Inverse problem theory: Methods for data fitting and model parameter estimation: Elsevier.
41. Tarantola, A., and Nercessian, A., 1984, Three-dimensional inversion without blocks: Geophys. J. Roy. Astr. Soc., 76, 299-306.
42. Trampert, J., and Snieder, R., 1996, Model estimations biased by truncated expansions. Possible artifacts in seismic tomography: Science, 271, 1257-1260.
43. Thurber, C., and Eberhart-Phillips, D., 1999, Local earthquake tomography with flexible gridding: Comput. and Geosci., 25, 809-818.
44. Van Decar, J. C., and Snieder, R., 1994, Obtaining smooth solutions to large, linear, inverse problems: Geophysics, 59, 818-829.
45. Wessel, J. K., and Smith, H. F., 1991, Free software helps map and display data: EOS. 72, 441, 445-446.
46. Wesseling, P., 1991, An introduction to multigrid methods: John Wiley & Sons.
47. Zhou, H.-W., 1996, A high-resolution P wave model for the top 1200km of the mantle: J. Geophys. Res., 101, 27 791-27 810.