Seismic data decomposition and reconstruction with sparse Gaussian beams and sparse optimisation method

References

• Alkhalifah T. 1995 Gaussian beam depth migration for anisotropic media: Geophysics 60 1474 1484 10.1190/1.1443881
   Web of Science ®Google Scholar
• Babich V. M. Popov M. M. 1989 Gaussian summation method: Radiophysics and Quantum Electronics 32 1063 1081 10.1007/BF01038632
   Google Scholar
• Cao J. J. Wang Y. F. Zhao J. T. Yang C. C. 2011 A review on restoration of seismic wavefields based on regularization and compressive sensing: Inverse Problems in Science and Engineering 19 679 704 10.1080/17415977.2011.576342
   Web of Science ®Google Scholar
• Cao J. J. Wang Y. F. Yang C. C. 2012 Seismic data restoration based on compressive sensing using the regularization and zero-norm sparse optimization: Chinese Journal of Geophysics 55 239 251 10.1002/cjg2.1718
   Web of Science ®Google Scholar
• Červený V. Pšenčík I. 1983 Gaussian beams in two-dimensional elastic inhomogeneous media: Geophysical Journal of the Royal Astronomical Society 72 417 433 10.1111/j.1365-246X.1983.tb03793.x
   Web of Science ®Google Scholar
• Chartrand R. Staneva V. 2008 Restricted isometry properties and nonconvex compressive sensing: Inverse Problems 24 035020 10.1088/0266-5611/24/3/035020
   Web of Science ®Google Scholar
• Costa, C. A., Raz, S., and Kosloff, D., 1989, Gaussian beam migration: 59th Annual International Meeting, SEG, Expanded Abstracts, 1169–1171.
   Google Scholar
• Geng Y. Wu R. S. Gao J. H. 2014 Gabor-frame-based Gaussian packet migration: Geophysical Prospecting 62 1432 1452 10.1111/1365-2478.12152
   Web of Science ®Google Scholar
• Gray S. H. 2005 Gaussian beam migration of common-shot records: Geophysics 70 S71 S77 10.1190/1.1988186
   Web of Science ®Google Scholar
• Gray S. H. Bleistein N. 2009 True-amplitude Gaussian-beam migration: Geophysics 74 S11 S23 10.1190/1.3052116
   Web of Science ®Google Scholar
• Herrmann F. J. Hennenfent G. 2008 Non-parametric seismic data recovery with curvelet frames: Geophysical Journal International 173 233 248 10.1111/j.1365-246X.2007.03698.x
   Web of Science ®Google Scholar
• Hill N. R. 1990 Gaussian beam migration: Geophysics 55 1416 1428 10.1190/1.1442788
   Web of Science ®Google Scholar
• Hill N. R. 2001 Prestack Gaussian-beam depth migration: Geophysics 66 1240 1250 10.1190/1.1487071
   Web of Science ®Google Scholar
• Klimeš L. 1989 Optimization of the shape of Gaussian beams of a fixed length: Studia Geophysica et Geodaetica 33 146 163 10.1007/BF01646581
   Web of Science ®Google Scholar
• Li H. Wang H. Z. Feng B. Hu Y. Zhang C. 2014 Efficient pre-stack depth migration method using characteristic Gaussian packets: Chinese Journal of Geophysics 57 2258 2268 [in Chinese]
   Web of Science ®Google Scholar
• Ma J. Plonka G. Chauris H. 2010 A new sparse representation of seismic data using adaptive easy-path wavelet transform: IEEE Geoscience and Remote Sensing Letters 7 540 544 10.1109/LGRS.2010.2041185
   Web of Science ®Google Scholar
• Marfurt K. J. Kirlin R. L. Farmer S. L. Bahorich M. S. 1998 3-D seismic attributes using a semblance-based coherency algorithm: Geophysics 63 1150 1165 10.1190/1.1444415
   Web of Science ®Google Scholar
• Meinshausen N. Yu B. 2009 Lasso-type recovery of sparse representations for high-dimensional data: Annals of Statistics 37 246 270 10.1214/07-AOS582
   Web of Science ®Google Scholar
• Nowack R. Aki K. 1984 The two-dimensional Gaussian beam synthetic method: testing and application: Journal of Geophysical Research 89 7797 7819 10.1029/JB089iB09p07797
   Web of Science ®Google Scholar
• Popov M. M. 1982 A new method of computation of wave fields using Gaussian beams: Wave Motion 4 85 97 10.1016/0165-2125(82)90016-6
   Web of Science ®Google Scholar
• Raz S. 1987 Beam stacking: a generalized preprocessing technique: Geophysics 52 1199 1210 10.1190/1.1442383
   Web of Science ®Google Scholar
• Sacchi M. D. Ulrych T. J. Walker C. J. 1998 Interpolation and extrapolation using a high-resolution discrete Fourier transform: IEEE Transactions on Signal Processing 46 31 38 10.1109/78.651165
   Web of Science ®Google Scholar
• Tanushev, N. M., Tsai, R., Fomel, S., and Engquist, B., 2011, Gaussian beam decomposition for seismic migration: SEG Technical Program, Expanded Abstracts, 30, 3356–3361.
   Google Scholar
• Wang, Y. F., 2007, Computational methods for inverse problems and their applications: Higher Education Press (Beijing).
   Google Scholar
• Wang W. H. Pei J. Y. Zhang J. F. 2007 Prestack seismic data reconstruction using weighted parabolic Radon transform: Chinese Journal of Geophysics 50 737 746 10.1002/cjg2.1088
   Web of Science ®Google Scholar
• Wang Y. F. Cao J. J. Yang C. C. 2011 a Recovery of seismic wavefields based on compressive sensing by an l 1-norm constrained trust region method and the piecewise random sub-sampling: Geophysical Journal International 187 199 213 10.1111/j.1365-246X.2011.05130.x
   Web of Science ®Google Scholar
• Wang, Y. F., Stepanova, I. E., Strakhov, V. N., and Yagola, A. G., 2011b, Inverse problems in geophysics and solution methods: Higher Education Press (Beijing).
   Google Scholar
• Wang Y. F. Yang C. C. Cao J. J. 2012 On Tikhonov regularization and compressive sensing for seismic signal processing: Mathematical Models and Methods in Applied Sciences 22 1150008 10.1142/S0218202511500084
   Web of Science ®Google Scholar
• Wang Y. F. Liu P. Li Z. H. Sun T. Yang C. C. Zheng Q. S. 2013 Data regularization using Gaussian beams decomposition and sparse norms: Journal of Inverse and Ill-posed Problems 21 1 23 10.1515/jip-2012-0030
   Web of Science ®Google Scholar
• Weber M. 1988 Computation of body-wave seismograms in absorbing 2-D media using the Gaussian beam method: comparison with exact methods: Geophysical Journal International 92 9 24 10.1111/j.1365-246X.1988.tb01116.x
   Web of Science ®Google Scholar
• White B. S. Norris A. Bayliss A. Burridge R. 1987 Some remarks on the Gaussian beam summation method: Geophysical Journal International 89 579 636 10.1111/j.1365-246X.1987.tb05184.x
   Web of Science ®Google Scholar
• Yuan, Y. X., 1993, Numerical methods for nonlinear programming: Shanghai Science and Technology Publication.
   Google Scholar
• Žáček K. 2006 Decomposition of the wave field into optimized Gaussian packets: Studia Geophysica et Geodaetica 50 367 380 10.1007/s11200-006-0023-y
   Web of Science ®Google Scholar
• Zhu T. Gray S. H. Wang D. 2007 Prestack Gaussian-beam depth migration in anisotropic media: Geophysics 72 S133 S138 10.1190/1.2711423
   Web of Science ®Google Scholar
• Zou H. 2006 The adaptive lasso and its oracle properties: Journal of the American Statistical Association 101 1418 1429 10.1198/016214506000735
   Web of Science ®Google Scholar