Sparsity-promoting migration with multiples

Transcription

1 Sparsity-promoting migration with multiples Tim Lin, Ning Tu and Felix Herrmann SLIM Seismic Laboratory for Imaging and Modeling the University of British Columbia

2 Courtesy of Verschuur, 29 SLIM Motivation Depth Lateral distance(m) a migrated section from data with multiples

3 Motivation 2 4 Depth Lateral distance(m) a migrated section from multiple free data

4 SLIM Motivation = Time(s) Time(s) Time(s) So Lateral Distance(m) 2 4 Lateral Distance(m) 2 4 Lateral Distance(m)

5 SLIM Motivation = Time(s) Time(s) Time(s) So Lateral Distance(m) 2 4 Lateral Distance(m) 2 4 Lateral Distance(m)

6 Rethink multiples But wait a minute, are they really garbage? receiver coordinate source coordinate amplitude spectrum:

7 Rethink multiples receiver coordinate source coordinate amplitude spectrum:

8 Rethink multiples Surface-related multiples: provide wider illumination angles contain more higher spatial wave number contents more sensitive to velocity changes

9 Rethink multiples They may help to deduce subsurface structure...but how?

10 van Groenestijn and Verschuur, 29 SLIM Motivation EPSI (Estimation of Primaries via Sparse Inversion) exploits the sparsity of the up-going Green s function EPSI tries to derive the up-going Green s function velocity model is a lot sparser than Green s function

11 Motivation There seems to be some interaction between EPSI and imaging...what about let them get married, and how?

12 Reiter, 1991 SLIM Multiples in imaging Introduce free surface to the smooth background velocity model violates the Born approximation assumptions more requirements on the exactness of the velocity model

13 Tarantola, 1984 SLIM Multiples in imaging Full-waveform inversion de-multiple before inversion consists of several migration based updates

14 Berkhout and Verschuur, 23 SLIM Multiples in imaging Focal transform first multiples mapped to primaries needs the estimate of the primaries as the operator de-multiple followed by migration

15 Our approach We combine EPSI with migration EPSI models primaries as well as multiples combine EPSI with sparsity promoting migration

16 Verschuur, 1992 Lin and Herrmann, 21 Herrmann, 28 SLIM EPSI Formulation EPSI reveals the relationship: ˆP = Ĝ( ˆQ ˆP) Formulating the EPSI operator: F t BlockDiag f [( ˆQ ˆP) I]F t M g = p

17 van Groenestijn and Verschuur, 29 SLIM EPSI Formulation g = argmin g p Mg 2 s.t. g kτ g p : estimate of the up-going Green s function : the up-going wavefield

18 Lin and Herrmann, 21 SLIM Robust EPSI Replace the computationally prohibitive l norm with l 1 norm. Robust EPSI: g = argmin g g 1 s.t. p Mg 2 σ

19 Nemeth, 1999 Wang and Sacchi, 27 SLIM Regularized least-squares migration Regularized least-squares migration: δ m = argmin δm 1 2 g Kδm λ δm 2 2

20 Herrmann and Li, 21 SLIM Sparsity promoting migration Sparsity-promoting migration: δ m = S argmin δx δx 1 s.t. g KS δx 2 σ

21 Combine EPSI with migration We formulate this linearized inversion process as δ m = S argmin δx δx 1 s.t. p MKS δx 2 σ

22 Numerical experiments Make linearized data: multiple-free data p 1 = Kδm data with multiples p 2 = MKδm

23 Data preview: multiple free,,./,. )*'$&#(,.1, / !+,,,!-,,, -,, +,,,!""#$%&'( total shots: 128, shot number: 65

24 Image preview: multiple free 2 4 Depth Lateral distance(m) migrated section: time-weighted

25 Data preview: with multiples,,./,. )*'$&#(,.1, / !+,,,!-,,, -,, +,,,!""#$%&'( total shots: 128, shot number: 65

26 Image preview: with multiples 2 4 Depth Lateral distance(m) migrated section: time weighted

27 Three scenarios: mig-multiple free Migration from multiple free data: δ m = S argmin δx δx 1 s.t. p 1 KS δx 2 σ

28 Three scenarios: mig-with multiples Migration from data with multiples: δ m = S argmin δx δx 1 s.t. p 2 KS δx 2 σ

29 van der Berg and Friedlander, 28 SLIM Three scenarios: mig/epsi-with multiples Migration combined with EPSI from data with multiples: δ m = S argmin δx δx 1 s.t. p 2 MKS δx 2 σ Solver: spgl1

30 Mig-multiple free 2 4 Depth Lateral distance(m)

31 Mig-with multiples 2 4 Depth Lateral distance(m)

32 Mig/EPSI-with multiples 2 4 Depth Lateral distance(m)

33 Mig/EPSI-with multiples 2 4 Depth Lateral distance(m)

34 Mig-multiple free 2 4 Depth Lateral distance(m)

35 Convergence rate with/ without EPSI 1.8 scenario 1 scenario 2 scenario 3 relative residual iterations

36 De-migrated section,,./,. )*'$&#(,.1, / !+,,,!-,,, -,, +,,,!""#$%&'( total shots: 128, shot number: 65, SNR: 23dB

37 Guitton, 22 SLIM Mig-multiples 2 4 Depth Lateral distance(m)

38 Mig/EPSI-multiples 2 4 Depth Lateral distance(m)

39 Conclusions By combing EPSI with migration: multiples are well handled multiples actually help imaging

40 Future plans Alternating optimization now EPSI operator is built using a precalculated wavelet wavelet will be estimated during the imaging process Incorporate into full-waveform inversion

41 References Berkhout, A. J., and D. J. Verschuur, 23, Transformation of multiples into primary reflections: SEG Technical Program Expanded Abstracts, 22, Guitton, A., 22, Shot-profile migration of multiple reflec- tions: SEG Technical Program Expanded Abstracts, 21, Herrmann, F. J., 28, Seismic wavefield inversion with curvelet-domain sparsity promotion, Presented at SEG. Herrmann, F. J. and X. Li, Randomized dimensionality reduction for fullwaveform inversion: Presented at the 72nd EAGE Conference & Exhibition. Lin, T., and F. J. Herrmann, 21, Stabilized estimation of primaries via sparse inversion: Presented at the 72nd EAGE Conference & Exhibition. Wang, J. and M. D. Sacchi, High-resolution wave-equation amplitude-variationwith-ray-parameter (AVP) imaging with sparseness constraints: Geophysics, 72, S11-S18

42 References Nemeth, T, C. Wu and G. T. Schuster, Least-squares migration of incomplete reflection data: Geophysics, 64, Reiter, E. C., M. N. Tokso z, T. H. Keho, and G. M. Purdy,1991, Imaging with deepwater multiples: Geophysics, 56, Tarantola, A., 1984, Inversion of seismic reflection data in the acoustic approximation: Geophysics, 49, van den Berg, E., and M. P. Friedlander, 28, Probing the pareto frontier for basis pursuit solutions: SIAM Journal on Scientific Computing, 31, van Groenestijn, G. J. A., and D. J. Verschuur, 29, Estimation of primaries and near-offset reconstruction by sparse inversion: Marine data applications: Geophysics, 74, R119 R128. Verschuur, D. J., 1992, Adaptive surface-related multiple elimination: Geophysics, 57,1166.

43 Acknowledgement This work was in part financially supported by the Natural Sciences and Engineering Research Council of Canada Discovery Grant (22R81254) and the Collaborative Research and Development Grant DNOISE II ( ). This research was carried out as part of the SINBAD II project with support from the following organizations: BG Group, BP, Chevron, ConocoPhillips, Petrobras, Total SA, and WesternGeco. E. J. Candès, L. Demanet, D. L. Donoho, and L. Ying for CurveLab ( E. van der Berg and M. Friedlander for SPGl1 ( spgl1/)

44 Thanks slim.eos.ubc.ca