Compressed wavefield extrapolation

Geophysics

Volumn 72, Issue 5, 2007, Pages

  Lin, Tim T Y ^a   Herrmann, Felix J ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; ELECTROMAGNETIC WAVE PROPAGATION; EXTRAPOLATION; INFORMATION THEORY; MATHEMATICAL OPERATORS; SIGNAL PROCESSING; THREE DIMENSIONAL; TWO DIMENSIONAL; WAVEFORM ANALYSIS;

HELMHOLTZ OPERATOR; SEISMIC WAVEFIELDS; WAVEFIELD EXTRAPOLATION;

SEISMIC WAVES;

ALGORITHM; HELMHOLTZ EQUATION; SEISMIC WAVE; SIGNAL PROCESSING; WAVE FIELD; WAVE PROPAGATION;

EID: 34548525109     PISSN: 00168033     EISSN: None     Source Type: Journal    
DOI: 10.1190/1.2750716     Document Type: Article

References (50)

1. Bednar, J. B., C. J. Bednar, and C. Shin, 2006, Two-way versus one-way: A case study style comparison: 76th Annual International Meeting, SEG, Expanded Abstracts, 2343-2347.
2. Berkhout, A. J., 1982, Seismic migration. Imaging of acoustic energy by wave field extrapolation: Elsevier.
3. Candès, E., 2007, Compressive sensing: Presented at the Institute of Applied Mathematics Seminars, University of British Columbia.
4. Candès, E. J., and L. Demanet, 2005, The curvelet representation of wave propagators is optimally sparse: Communications on Pure and Applied Mathematics, 58, 1472-1528. cpa CPMAMV 0010-3640 10.1002/ cpa.20078
5. Candès, E., L. Demanet, D. Donoho, and L. Ying, 2006a, Fast discrete curvelet transforms: SIAM Multiscale Modeling and Simulation, 5, 861-899.
6. Candès, E. J., and D. L. Donoho, 2000a, Curvelets - A surprisingly effective nonadaptive representation for objects with edges: In L. L. Schumaker, eds., Curves and surfaces: Vanderbilt University Press.
7. 2000b, Recovering edges in ill-posed problems: Optimality of curvelet frames: Annals of Statistics, 30, 784-842. 9j7 ASTSC7 0090-5364
8. 2004, New tight frames of curvelets and optimal representations of objects with piecewise C 2 singularities: Communications On Pure and Applied Mathematics, 57, 219-266. cpa CPMAMV 0010-3640 10.1002/cpa.10116
9. Candès, E. J., D. L. Donoho, L. Demanet, and L. Ying, 2005, Fast discrete curvelet transform: http://www.curvelet.org/papers/FDCT.pdf.
10. Candès, E. J., and J. Romberg, 2005, l 1 - magic. Software: http://www.acm.caltech.edu/limagic/.
11. Candès, E., J. Romberg, and T. Tao, 2006b, Stable signal recovery from incomplete and inaccurate measurements: Communications On Pure and Applied Mathematics, 59, 1207-1223. cpa CPMAMV 0010-3640
12. Chauris, H., 2006, Seismic imaging in the curvelet domain and its implications for the curvelet design: 76th Annual International Meeting, SEG, Expanded Abstracts, 2406-2410.
13. Chen, S. S., D. L. Donoho, and M. A. Saunders, 2001, Atomic decomposition by basis pursuit: SIAM Journal on Scientific Computing, 43, 129-159. 8sm SJOCE3 1064-8275
14. Claerbout, J. F., 1971, Toward a unified theory of reflector mapping: Geophysics, 36, 467-481. gpy GPYSA7 0016-8033 10.1190/1.1440185
15. Claerbout, J., and F. Muir, 1973, Robust modeling with erratic data: Geophysics, 38, 826-844. gpy GPYSA7 0016-8033 10.1190/1.1440378
16. Collino, F., and P. Joly, 1995, Splitting of operators, alternate directions, and paraxial approximations for the three-dimensional wave equation: SIAM Journal on Scientific Computing, 16, 1019-1048. jzc JSCOEB 0885-7474
17. Daubechies, I., M. Defrise, and C. de Mol, 2005, An iterative thresholding algorithm for linear inverse problems with a sparsity constrains: Communications On Pure and Applied Mathematics, 58, 1413-1457. cpa CPMAMV 0010-3640
18. de Hoop, M., J. L. Rousseau, and R.-S. Wu, 2000, Generalization of the phase-screen approximation for the scattering of acoustic waves: Wave Motion, 31, 43-70. wvm WAMOD9 0165-2125 10.1016/S0165-2125(99)00026-8
19. Dessing, F. J., 1997, A wavelet transform approach to seismic processing: Ph.D. thesis, Delft University of Technology.
20. Donoho, D. L., 2006, Compressed sensing: IEEE Transactions on Information Theory, 52, 1289-1306. iet IETTAW 0018-9448
21. Donoho, D. L., I. Drori, V. Stodden, and Y. Tsaig, 2005, SparseLab, Software: http://sparselab.stanford.edu/.
22. Douma, H., and M. de Hoop, 2006, Leading-order seismic imaging using curvelets: 76th Annual International Meeting, SEG, Expanded Abstracts, 2411-2415.
23. Elad, M., J. Starck, P. Querre, and D. Donoho, 2005, Simultaneous cartoon and texture image inpainting using morphological component analysis (MCA): Applied and Computational Harmonic Analysis, 19, 340-358. 6gx ZZZZZZ 0029-9006
24. Figueiredo, M., and R. Nowak, 2003, An EM algorithm for wavelet-based image restoration: IEEE Transactions on Image Processing, 12, 906-916. iei IIPRE4 1057-7149 10.1109/TIP.2003.814255
25. Figueiredo, M., R. D. Nowak, and S. J. Wright, 2007, Gradient projection for sparse reconstruction, Software: http://www.lx.it.pt/~mtf/GPSR/.
26. Grimbergen, J., F. Dessing, and C. Wapenaar, 1998, Modal expansion of one-way operator on laterally varying media Geophysics, 63, 995-1005. gpy GPYSA7 0016-8033 10.1190/1.1444410
27. Guitton, A., and D. J. Verschuur, 2004, Adaptive subtraction of multiples using the l 1 -norm: Geophysical Prospecting, 52, 27-27. 8uc GPPRAR 0016-8025 10.1046/j.1365-2478.2004.00401.x
28. Hale, D., N. R. Hill, and J. Stefani, 1992, Imaging salt with turning seismic waves Geophysics, 57, 1453-1462. Discussion and reply by authors in GEO-58-8-1205-1206. gpy GPYSA7 0016-8033 10.1190/1.1443213
29. He, C., M. Lu, and C. Sun, 2004, Accelerating seismic migration using FPGA-based coprocessor platform: 12th Annual Symposium on Field-Programmable Custom Computing Machines, IEEE, 207-216.
30. Hennenfent, G., and F. J. Herrmann, 2006a, Application of stable signal recovery to seismic interpolation: 76th Annual International Meeting, SEG, Expanded Abstracts, 2797-2801.
31. 2006b, Seismic denoising with non-uniformly sampled curvelets Computing in Science and Engineering, 8, 16-25. 99u CSENFA 1521-9615 10.1109/ MCSE.2006.49
32. Herrmann, F. J., U. Boeniger, and D. J. Verschuur, 2007, Nonlinear primary-multiple separation with directional curvelet frames: Geophysical Journal International, 17, 781-799. gji GJINEA 0956-540X
33. Koh, K., S. J. Kim, and S. Boyd, 2007, Simple matlab solver for 11-regularized least squares problems, Software: http://www-stat.stanford.edu/~tibs/lasso.html.
34. Levy, S., D. Oldenburg, and J. Wang, 1988, Subsurface imaging using magnetotelluric data: Geophysics, 53, 104-117. gpy GPYSA7 0016-8033 10.1190/1.1442393
35. Mulder, W., and R. Plessix, 2004, How to choose a subset of frequencies in frequency-domain finite-difference migration: Geophysical Journal International, 158, 801-812. gji GJINEA 0956-540X 10.1111/ j.1365-246X.2004.02336.x
36. Oldenburg, D. W., S. Levy, and K. P. Whittall, 1981, Wavelet estimation and deconvolution: Geophysics, 46, 1528-1542. gpy GPYSA7 0016-8033 10.1190/1.1441159
37. Paige, C. C., and M. A. Saunders, 1982, LSQR: An algorithm for sparse linear equations and sparse least squares: Transactions on Mathematical Software, 8, 43-71. att ACMSCU 0098-3500 10.1145/355984.355989
38. Plessix, R., and W. Mulder, 2004, Frequency-domain finite difference amplitude-preserving migration: Geophysical Journal International, 157, 975-987. gji GJINEA 0956-540X 10.1111/j.1365-246X.2004.02282.x
39. Riyanti, C., Y. Eriangga, R. Plessix, W. Mulder, C. Vulk, and C. Oosterlee, 2006, A new iterative solver for the time-harmonic wave equation: Geophysics, 71, no. 5, E57-E63. gpy GPYSA7 0016-8033 10.1190/ 1.2231109
40. Sacchi, M. D., T. J. Ulrych, and C. Walker 1998, Interpolation and extrapolation using a high resolution discrete Fourier transform: IEEE Transactions on Signal Processing, 46, 31-38. itl ITPRED 105587X
41. Sacchi, M. D., D. R. Velis, and A. H. Cominguez, 1994, Minimum entropy deconvolution with frequency-domain constraints: Geophysics, 59, 938-945. gpy GPYSA7 0016-8033 10.1190/1.1443653
42. Santosa, F., and W. Symes, 1986, Linear inversion of band-limited reflection seismogram: SIAM Journal of Scientific Computing, 7. jzc JSCOEB 0885-7474
43. Smith, H., 1997, A hardy space for fourier integral operators: Journal of Geometric Analysis, 7. b7p JGANEG 1050-6926
44. Stoffa, P. L., J. T. Fokkema, R. M. de Luna Freire, and W. P. Kessinger, 1990, Split-step Fourier migration: Geophysics, 55, 410-421. gpy GPYSA7 0016-8033 10.1190/1.1442850
45. Taylor, H. L., S. Banks, and J. McCoy, 1979, Deconvolution with the l 1 norm: Geophysics, 44, 39. gpy GPYSA7 0016-8033 10.1190/1.1440921
46. Tibshirani, R., 1996, Least absolute shrinkage and selection operator, Software: http://www-stat.stanford.edu/~tibs/lasso.html.
47. Tsaig, Y., and D. Donoho, 2006, Extensions of compressed sensing: Signal Processing, 86, 549-571. spq SPRODR 0165-1684
48. Ulrych, T. J., and C. Walker, 1982, Analytic minimum entropy deconvolution: Geophysics, 47, 1295-1302. gpy GPYSA7 0016-8033 10.1190/ 1.1441389
49. Ying, L., L. Demanet, and E. Candès, 2005, 3D discrete curvelet transform: Wavelets XI, SPIE, Conference Proceedings, 591413.
50. Zwartjes, P., and A. Gisolf, 2006, Fourier reconstruction of marine-streamer data in four spatial coordinates: Geophysics, 71, no. 6, V171-V186. gpy GPYSA7 0016-8033 10.1190/1.2335419