Improved inversion through use of the null space

Geophysics

Volumn 62, Issue 3, 1997, Pages 869-883

  Rowbotham, Peter S ^a,b   Pratt, R Gerhard ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

^b Elf Geoscience Research Centre   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ACOUSTIC WAVE TRANSMISSION; ANISOTROPY; CORE ANALYSIS; GEOLOGY; IMAGING TECHNIQUES; INTERFACES (MATERIALS); INVERSE PROBLEMS; VECTORS; WELL LOGGING;

LEAST SQUARES TRAVELTIME INVERSION TECHNIQUES; SEISMIC TRAVELTIME TOMOGRAPHY;

SEISMIC PROSPECTING;

DATA INVERSION; DATA PROCESSING; NULL SPACE; SEISMIC TOMOGRAPHY; TOMOGRAPHY; TRAVELTIME INVERSION;

EID: 0031141906     PISSN: 00168033     EISSN: None     Source Type: Journal    
DOI: 10.1190/1.1444195     Document Type: Article

References (36)

1. 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, 903-923.
2. Bregman, N. D., Bailey, R. C., and Chapman, C. H., 1989a, Ghosts in tomography: the effects of poor angular coverage in 2-D seismic traveltime inversion: Can. J. of Expl. Geophys., 25, 7-27.
3. _ 1989b, Crosshole seismic tomography: Geophysics, 54,200-215.
4. Carrion, P., 1991, Dual tomography for imaging complex structures: Geophysics, 56, 1395-1404.
5. Carrion, P., Costa, J., Pinheiro, J. E. F., and Schoenberg, M., 1992, Crossborehole tomography in anisotropic media: Geophysics, 57, 1194-1198.
6. Carrion, P., Jacovitti, G., and Neri, A., 1993, Gaussian and nonGaussian tomographic modelling via simulated annealing: J. Seis. Expl., 2, 189-204.
7. Chapman, C. H., and Pratt, R. G., 1992, Travellime tomography in anisotropic media-I: Theory: Geophys. J. Internat., 109, 1-19.
8. Chiu, S. K. L., and Stewart, R. R., 1987, Tomographic determination of 3-D seismic velocity structure using well logs, vertical seismic profiles, and surface seismic data: Geophysics, 52, 1085-1098.
9. Deal, M. M., and Nolet, G., 1993, Conservative filtering of tomographic images: Am. Geophys. Union Fall Meeting, 419.
10. _ 1996, Null space shuttles: Geophys. J. Internat., 124, 372-380.
11. Delprat-Jannaud, F., and Lailly, P., 1992, What information on the earth model do reflection travel times provide?: J. Geophys. Res., 97, 19827-19844.
12. Dines, K. A., and Lytle, R. J., 1979, Computerized geophysical tomography: Proc. Inst. Electr. Electron. Eng., 67, 1065-1073.
13. Ellis, R. G., and Oldenburg, D. W., 1994, Applied geophysical inversion: Geophys. J. Internat., 116, 5-11.
14. Gersztenkorn, A., and Scales, J. A., 1988, Smoothing seismic tomograms with alpha-trimmed means: Geophys. J. Internat., 92, 67-72.
15. Hyndman, D. W., Harris, J. M., and Gorelick, S. M., 1994, Coupled seismic and tracer test inversion for aquifer property characterization: Water Resources Research, 30, 1965-1977.
16. Iyer, H. M., and Hirahara, K., 1993, Seismic tomography: Theory and practice: Chapman and Hall.
17. Lanczos, C., 1961, Linear differential operators: Van Nostrand.
18. Lendzionowski, V., Walden, A. T., and White, R. E., 1990, Seismic character mapping over reservoir intervals: Geophys. Prosp., 38, 951-969.
19. McCann, C., Assefa, S., Sothcott, J., McCann, D. M., and Jackson, P. D., 1989, In-situ borehole measurements of compressional and shear wave attenuation in Oxford Clay: Scientific Drilling, 1, 11-20.
20. Menke, W., 1984, Geophysical data analysis: Discrete inverse theory: Academic Press Inc.
21. Michelena, R. J., 1992, Traveltime tomography in azimuthally anisotropic media: 62nd Ann. Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 757-761.
22. Michelena, R. J., Muir, F., and Harris, J. M., 1993, Anisotropic traveltime tomography: Geophys. Prosp., 41, 381-412.
23. Neri, A., Carrion, P., Jacovitti, G., and Vesnaver, A., 1993, Tomographic reconstruction from incomplete data set with deterministic and stochastic constraints: SPIE, 2033, 22-33.
24. Nolet, G., 1987, Seismic tomography with application to global seismology and exploration geophysics: D. Reidel Publ. Co.
25. Ory, J., and Pratt, R. G., 1995, Are our parameter estimators biased? The significance of finite-difference regularization operators: Inverse Problems, 11, 397-424.
26. Pratt, R. G., and Chapman, C. H., 1992, Traveltime tomography in anisotropic media-II. Application: Geophys. J. Internat., 109, 20-37.
27. Pratt, R. G., McGaughey, W. J., and Chapman, C. H., 1993, Anisotropic velocity tomography: A case study in a near surface rockmass: Geophysics, 58, 1748-1763.
28. Pratt, R. G., and Sams, M. S., 1996, Reconciliation of crosshole seismic velocities with well information in a layered sedimentary environment: Geophysics, 61, 549-560.
29. Scales, J. A., Docherty, P., and Gersztenkorn, A., 1990, Regularisation of nonlinear inverse problems: imaging the near-surface weathering layer: Inverse Problems, 6, 115-131.
30. Tarantola, A., and Nercessian, A., 1984, Three-dimensional inversion without blocks: Geophys. J. Roy. Astr. Soc., 76, 299-306.
31. Thomsen, L., 1986, Weak elastic anisotropy: Geophvsics, 51, 1954-1966.
32. Walden, A. T., and Hosken, J. W. J., 1986, The nature of the nonGaussianity of primary reflection coefficients and its significance for deconvolution: Geophys, Prosp., 34, 1038-1066.
33. Williamson, P. R., 1993, Anisotropic crosshole tomography in layered media. Part II: Applications, results and conclusions: J. Seis. Expl., 2, 223-238.
34. Worthington, M. H., 1984, An introduction to geophysical tomography: First Break, 2, No. 11, 20-26.
35. Zhang, J., and McMechan, G. A., 1995, Estimation of resolution and covariance for large matrix inversions: Geophys. J. Internat., 121, 409-426.
36. Zhang, Y. C., Shen, L. C., and Liu. C., 1994, Inversion of induction logs based on maximum flatness, maximum oil, and minimum oil algorithms: Geophysics, 59, 1320-1326.