Curvelet-domain multiple matching method combined with cubic B-spline function

• Autorzy: Wang T. , Wang D. , Tian M. , Hu B. , Liu C.

Identyfikatory

DOI

10.1007/s11600-018-0155-9

• Języki publikacji: EN

Abstrakty

EN

Since the large amount of surface-related multiple existed in the marine data would influence the results of data processing and interpretation seriously, many researchers had attempted to develop effective methods to remove them. The most successful surface-related multiple elimination method was proposed based on data-driven theory. However, the elimination effect was unsatisfactory due to the existence of amplitude and phase errors. Although the subsequent curveletdomain multiple–primary separation method achieved better results, poor computational efficiency prevented its application. In this paper, we adopt the cubic B-spline function to improve the traditional curvelet multiple matching method. First, select a little number of unknowns as the basis points of the matching coefficient; second, apply the cubic B-spline function on these basis points to reconstruct the matching array; third, build constraint solving equation based on the relationships of predicted multiple, matching coefficients, and actual data; finally, use the BFGS algorithm to iterate and realize the fast-solving sparse constraint of multiple matching algorithm. Moreover, the soft-threshold method is used to make the method perform better. With the cubic B-spline function, the differences between predicted multiple and original data diminish, which results in less processing time to obtain optimal solutions and fewer iterative loops in the solving procedure based on the L1 norm constraint. The applications to synthetic and field-derived data both validate the practicability and validity of the method.

Słowa kluczowe

EN

soft threshold; multiple matching; multiple prediction; cubic B-spline function; curvelet-domain

PL

miękki próg; dopasowanie wielokrotne

• Wydawca: Instytut Geofizyki PAN ; Springer
• Czasopismo: Acta Geophysica
• Rocznik: 2018
• Tom: Vol. 66, no. 4
• Strony: 559--573
• Opis fizyczny: Bibliogr. 23 poz.

Twórcy

autor

Wang T.

• Institute of Geophysical and Geochemical Exploration (IGGE), Chinese Academy of Geological Sciences, Langfang 065000, China
• College of Geo-Exploration Science and Technology, Jilin University, Changchun 130026, China

autor

Wang D.

• College of Geo-Exploration Science and Technology, Jilin University, Changchun 130026, China

autor

Tian M.

• Institute of Geophysical and Geochemical Exploration (IGGE), Chinese Academy of Geological Sciences, Langfang 065000, China

autor

Hu B.

• College of Geo-Exploration Science and Technology, Jilin University, Changchun 130026, China

autor

Liu C.

• College of Geo-Exploration Science and Technology, Jilin University, Changchun 130026, China

Bibliografia

• 1. Berkhout AJ, Verschuur DJ (1997) Estimation of multiple scattering by iterative inversion, part I: theoretical considerations. Geophysics 62(5):1586–1595
• 2. Candes E, Demanet L, Donoho D et al (2006) Fast discrete curvelet transforms. Multiscale Model Simul 5(3):861–899
• 3. Dedem EJ, Verschuur DJ (2005) 3D surface-related multiple prediction: a sparse inversion approach. Geophysics 70(3):V31–V43
• 4. Dragoset WH, Jeričević Ž (1998) Some remarks on surface multiple attenuation. Geophysics 63(2):772–789
• 5. Gordon WJ, Riesenfeld RF (1974) B-spline curves and surfaces. Comput Aided Geom Des 167:95
• 6. Guitton A (2005) Multiple attenuation in complex geology with a pattern-based approach. Geophysics 70(4):V97–V107
• 7. Hennenfent G, Herrmann FJ (2006) Seismic denoising with nonuniformly sampled curvelets. Comput Sci Eng 8(3):16–25
• 8. Herrmann FJ, Verschuur E (2004) Curvelet-domain multiple elimination with sparseness constraints. in: SEG technical program expanded abstracts 2004. Society of Exploration Geophysicists, pp 1333–1336
• 9. Herrmann FJ, Böniger U, Verschuur DJE (2007a) Non-linear primary-multiple separation with directional curvelet frames. Geophys J Int 170(2):781–799
• 10. Herrmann FJ, Wang D, Hennenfent G et al (2007b) Curvelet-based seismic data processing: a multiscale and nonlinear approach. Geophysics 73(1):A1–A5
• 11. Herrmann FJ, Wang D, Verschuur DJ (2008) Adaptive curvelet-domain primary-multiple separation. Geophysics 73(3):A17–A21
• 12. Kaplan ST, Innanen KA (2008) Adaptive separation of free-surface multiples through independent component analysis. Geophysics 73(3):V29–V36
• 13. Liu J, Lu W (2015) Adaptive multiple subtraction based on multiband pattern coding. Geophysics 81(1):V69–V78
• 14. Lu W, Liu L (2008) Adaptive multiple subtraction based on constrained independent component analysis. Geophysics 74(1):V1–V7
• 15. Lu W, Mao F (2005) Adaptive multiple subtraction using independent component analysis. Lead Edge 24(3):282–284
• 16. Morales JL, Nocedal J (2011) Remark on “Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound constrained optimization”. ACM Trans Math Softw (TOMS) 38(1):7
• 17. Pan RJ, Yao ZQ (2005) Quadratic B-spline interpolation curves based on dynamic parametrization. Jisuanji Xuebao (Chin J Comput) 28(3):334–342
• 18. Verschuur DJ (2006) Seismic multiple removal techniques: past, present and future. EAGE Publications, Houten
• 19. Verschuur DJ, Berkhout AJ (1997) Estimation of multiple scattering by iterative inversion, part II: practical aspects and examples. Geophysics 62(5):1596–1611
• 20. Verschuur DJ, Berkhout AJ, Wapenaar CPA (1992) Adaptive surface-related multiple elimination. Geophysics 57(9):1166–1177
• 21. Wu X, Hung B (2015) High-fidelity adaptive curvelet domain primary-multiple separation. First Break 33(1):53–59
• 22. Xu X, Zhong T (2006) Construction and realization of cubic spline interpolation function. Autom Meas Control 25(2):76–78
• 23. Zhu C, Byrd RH, Lu P et al (1997) Algorithm 778: l-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization. ACM Trans Math Softw (TOMS) 23(4):550–560