Curvelet domain adaptive least-squares subtraction of internal multiples

Yuan, Y., Wang, Y., Liu, Y. and Chang, X., 2011. Curvelet domain adaptive least-squares subtraction of internal multiples. Journal of Seismic Exploration, 20: 273-288. The elimination of internal multiples has always been a challenge in seismic processing. Compared to surface-related multiples, the amplitudes of internal multiples are more complicated and have a wider range due to different geological interfaces, and these complexities make the conventional prediction-subtraction algorithm not easy to be implemented. In this paper, a new method has been proposed to reduce the negative influence of energy diversity in internal multiples subtraction based on curvelet transform. First, we apply multi-resolution and multi-directional analysis to the seismic record with internal multiples, to map seismic events with different spectral and directional features into different curvelet domains. Then, internal multiples can be estimated by minimizing the misfit between the curvelet coefficients of the real seismic data and components of the predicted multiples under least-squares sense in curvelet sub-domains. A simple experimental data with three crossed events and a synthetic seismic record with complex internal multiples are used to validate the effectiveness of the proposed method. Results indicate that our approach is effective in suppressing internal multiples, preserving geological signals and avoiding distortion of primary events even when intersection or coincidence occurs.
- Candés, E.J. and Donoho, D.L., 1999. Curvelets: A Surprisingly Effective Nonadaptive
- Representation of Objects with Edges. Vanderbilt University Press, New York.
- Candés, E.J. and Donoho, D.L., 2002a. Continuous Curvelet Transform: I. Resolution of the
- Wavefront Set. Manuscript, Department of Statistics, Stanford University, Stanford.
- Candés, E.J. and Donoho, D.L., 2002b. Continuous Curvelet Transform: II. Discretization into
- Frames. Manuscript, Department of Statistics, Stanford University, Stanford.
- Candés, E.J. and Donoho, D.L., 2004. New tight frames of curvelets and optimal representations
- of objects with piecewise C? singularities. Communic. Pure Appl. Mathemat., 57: 219-266.
- Candés, E.J. and Donoho, D.L., 2006. Fast discrete curvelet transforms. Multiscale Model.
- Simulat., 5: 861-899.
- Dragoset, W.H., 1999. A practical approach to surface multiple attenuation. The Leading Edge, 18:
- 104-108.
- Fletcher, R.P., Fowler, P.J. and Kitchenside, P., 2005. Suppressing artifacts in prestack reverse
- time migration. Expanded Abstr., 75th Ann. Internat. SEG Mtg., Houston: 2049-2051.
- Fomel, S., 2009. Adaptive multiple subtraction using regularized nonstationary regression.
- Geophysics, 74: V25.
- Guitton, A. and Verschuur, D.J., 2004. Adaptive subtraction of multiples using L,-norm. Geophys.
- Prosp., 52: 27-38.
- Herrmann, F.J. and Verschuur, D.J., 2004. Curvelet-domain multiple elimination with sparseness
- constraints. Expanded Abstr., 74th Ann. Internat. SEG Mtg., Denver: 1333-1336.
- Levinson, N., 1947. The Wiener rms (root mean square) error criterion in filter design and
- prediction. J. Mathemat. Phys., 25: 261-278.
- Jin, D., Chang, X. and Liu, Y., 2008. Algorithm improvement and strategy of internal multiples
- prediction based on inverse scattering series method. Chin. J. Geophys., 51: 171-185.
- Li, X., Liu, Y., Chang, X. and Li, P., 2010. The adaptive subtraction of multiple using the
- equipoise multichannel L,-norm matching. Chin. J. Geophys., 53: 963-973.
- Lin, D., Young, J. and Huang, Y., 2004. 3-D SRME application in the Gulf of Mexico. Expanded
- Abstr., 74th Ann. Internat. SEG Mtg., Denver: 1257-1260.
- Liu, Y., Jin, D., Chang, X., Li, P. Sun, H. and Luo, Y., 2010. Multiple subtraction using
- statistically estimated inverse wavelets. Geophysics, 75: WB247.
- Liu, Y., Sun, H. and Chang, X., 2005. Least-squares wave-path migration. Geophys. Prosp., 53:
- 811-816.
- Robinson, E.A. and Treitel, S., 1980. Geophysical Signal Analysis. Prentice Hall Inc., Englewood
- Cliffs, New Jersey.
- Verschuur, D.J., Berkhout, A.J. and Wapenaar, C.P.A., 1992. Adaptive surface-related multiple
- elimination. Geophysics, 57: 1166-1177.
- Verschuur, D.J. and Kelamis P.G., 1997. Surface-related multiple elimination on 3-D land data.
- Expanded Abstr., 67th Ann. Internat. SEG Mtg., Dallas: 1383-1386.
- Verschuur, D.J. and Prein, R.J., 1999. Multiple removal results from Delft University. The Leading
- Edge, 18: 86-91.
- Verschuur, D.J., Berkhout, A.J., 2005. Removal of internal multiples with the common-focus-point
- (CFP) approach: Part 2 - Application strategies and data examples. Geophysics, 70: V61-
- V72.
- Wang, Y., Dong, S. and Xue, Y., 2009. Surface waves suppression using interferometric prediction
- and curvelet domain hybrid L,/L, norm subtraction. Expanded Abstr., 79th Ann. Internat.
- SEG Mtg., Houston: 3292.
- Weglein, A.B., Carvalho, F.A. and Stolt, R.H., 1997. An inverse scattering series method for
- attenuating multiples in seismic reflection data. Geophysics, 62: 1975-1989.
- Widrow, B. and Sterns, $.D., 1985. Adaptive Signal Processing. Prentice-Hall, New York.
- Wiener, N., 1949. Exploration, Interpolation, and Smoothing of Stationary Time Series. J. Wiley,
- New York.