Recent results in curvelet-based primary-multiple separation: application to real data

Transcription

1 Recent results in curvelet-based primary-multiple separation: application to real data Deli Wang 1,2, Rayan Saab 3, Ozgur Yilmaz 4, Felix J. Herrmann 2 1.College of Geoexploration Science and Technology, Jilin University,Changchun,China 2.Seismic Laboratory for Imaging and Modeling Department of Earth & Ocean Sciences The University of British Columbia at Vancouver 3.The Department of Electrical and Computer Engineering,The University of British Columbia 4.Department of Mathematics,The University of British Columbia

2 Contents Introduction Curvelet-based primary-multiple separation Examples Discussion and conclusion Acknowledgments

3 Introduction Problems with WE-based multiple elimination imperfect multiple predictions failure of direct subtraction after matched filtering Exploit the ability of curvelets to sparsify the to-be-separated signal components separation based on the curvelet parameterization location dip scale

4 Introduction n/2 slope α l -n/2 -n/2 n/2 (a) Discrete frequency tiling One curvelet Ying et al,2005

5 Contents Introduction Curvelet-based rimary-multiple separation Examples Discussion and Conclusion Acknowledgments

6 Curvelet-based separation Forward model s = s 1 + s 2 + n Soft thresholding s 1 = C T S w (Cs) where S w (x) := sgn(x) max(0, x w) and w := C s 2 predictions may contain moderate amplitude, phase and sign errors Herrmann et al,2006

7 Curvelet-based separation Nonlinear optimization from a Bayesian perspective Forward model s = s 1 + s 2 + n s 2 = A 2 x 2 + n 2 s 1 = A 1 x 1 + n n 2 (total data) (multiples) (primaries) where x 1 x 2 A 1,2 curvelet coefficients primaries curvelet coefficients multiples inverse curvelet transforms

8 Curvelet-based separation Separate by solving the nonlinear problem x = arg minx λ 1 x 1 1,w 1 + λ 2 x 2 1,w 2 + P w : s 2 A 2 x µ s 1 + s 2 A 1 x 1 A 2 x s 1 = A 1 x 1 and s 2 = A 2 x 2. where s 1,2 predicted primaries (1) and multiples (2) A 1,2 inverse discrete curvelet transforms λ 1,2 and µ are control parameters Can be solved by iterative soft thresholding. (For a detailed description please refer to Rayan Saab et al.,2007 and his later presentation this section)

9 Contents Introduction Curvelet-based primary-multiple separation Examples Discussion and conclusion Acknowledgments

10 Examples Example 1 Saga data: 128 shots 128 traces/shot 1024 samples/trace The original data contains many strong surface-related multiples

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32 Examples Example 2 Gulf of Suez data: 340 shots 95 traces/shot 626 samples/trace The original data contains many short period multiples and surface-related multiples

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60 Contents Introduction Curvelet-based primary-multiple separation Examples Discussion and conclusion Acknowledgments

61 Discussion and conclusions Curvelets represent the ideal domain for primary-multiple separation Curvelet construction allows for a separation based on differences in curvelet attributes and allows for a sparsity promoting formulation of the primary- multiple separation problem. The curvelet s multi-angular parameterization helps the separation, even for erroneous predictions. The nonlinear optimization algorithm shows a clear improvement in the primary-multiple separation. Results application to real data are encouraging improved velocity panel improved resolution

62 Contents Introduction Curvelet-based primary-multiple separation Examples Discussion and conclusion Acknowledgments

63 Acknowledgments Eric Verschuur, input in primary-multiple separation The authors of CurveLab, making their codes available. Sergey Fomel, developed Madagascar SLIM team:gilles Hennenfent,Sean Ross Ross,Cody Brown,Henryk Modzelewski et al. This work was in part financially supported by the NSERC Discovery (22R81254) and CRD Grants DNOISE ( ) of F.J.H. and was carried out as part of the SINBAD project with support, secured through ITF, from BG Group, BP, Chevron, ExxonMobil and Shell.