Bayesian wavefield separation by transform-domain sparsity promotion

Successful removal of coherent-noise sources greatly determines seismic imaging quality. Major advances have been made in this direction, e.g., surface-related multiple elimination (SRME) and interferometric ground-roll removal. Still, moderate phase, timing, amplitude errors, and clutter in predicted signal components can be detrimental. Adopting a Bayesian approach, along with assuming approximate curvelet-domain independence of the to-be-separated signal components, we construct an iterative algorithm that takes predictions produced by, for example, SRME as input and separates these components in a robust manner. In addition, the proposed algorithm controls the energy mismatch between separated and predicted components. Such a control, lacking in earlier curvelet-domain formulations, improves results for primary-multiple separation on synthetic and real data.

[1]  Gerard T. Schuster,et al.  Interferometric Predcition and Least Squares Subtraction of Surface Waves , 2006 .

[2]  Ray Abma,et al.  Comparisons of adaptive subtraction methods for multiple attenuation , 2005 .

[3]  Robert G. Fuller,et al.  Numerical Computations in US Undergraduate Physics Courses , 2006, Computing in Science & Engineering.

[4]  William H. Dragoset,et al.  Some remarks on surface multiple attenuation , 1998 .

[5]  E. J. Van Dedem.  3D surface-related multiple prediction , 2002 .

[6]  Warren S. Ross,et al.  Traveltime prediction and suppression of 3-D multiples , 1999 .

[7]  Yuanqing Li,et al.  Analysis of Sparse Representation and Blind Source Separation , 2004, Neural Computation.

[8]  D. Lin,et al.  3D SRME Application in the Gulf of Mexico , 2004, 66th EAGE Conference & Exhibition.

[9]  Jing Chen,et al.  Surface Related Multiple Attenuation on Sigsbee2B Dataset , 2004 .

[10]  Felix J. Herrmann,et al.  Seismic denoising with nonuniformly sampled curvelets , 2006, Computing in Science & Engineering.

[11]  Laurent Demanet,et al.  Fast Discrete Curvelet Transforms , 2006, Multiscale Model. Simul..

[12]  D. J. Verschuur,et al.  3D surface-related multiple prediction: A sparse inversion approach , 2005 .

[13]  D. J. Verschuur,et al.  Adaptive surface-related multiple elimination , 1992 .

[14]  I. Daubechies,et al.  An iterative thresholding algorithm for linear inverse problems with a sparsity constraint , 2003, math/0307152.

[15]  T. Ulrych,et al.  Analytic minimum entropy deconvolution , 1982 .

[16]  Arthur B. Weglein,et al.  Source signature estimation based on the removal of first-order multiples , 1997 .

[17]  Bill Dragoset,et al.  Practical, 3D Surface-related Multiple Prediction (SMP) , 2004 .

[18]  H. L. Taylor,et al.  Deconvolution with the l 1 norm , 1979 .

[19]  Ray Abma,et al.  Weighted subtraction for diffracted multiple attenuation , 2003 .

[20]  Arthur B. Weglein,et al.  An inverse-scattering series method for attenuating multiples in seismic reflection data , 1997 .

[21]  Barak A. Pearlmutter,et al.  Blind Source Separation by Sparse Decomposition in a Signal Dictionary , 2001, Neural Computation.

[22]  D. J. Verschuur,et al.  Estimation of multiple scattering by iterative inversion, Part I: Theoretical considerations , 1997 .

[23]  Douglas W. Oldenburg,et al.  Wavelet estimation and deconvolution , 1981 .

[24]  Roald van Borselen,et al.  3D SRME: Acquisition & Processing Solutions , 2004 .

[25]  D. J. Verschuur,et al.  Adaptive curvelet-domain primary-multiple separation , 2008 .

[26]  Felix J. Herrmann,et al.  Curvelet-based seismic data processing : A multiscale and nonlinear approach , 2008 .

[27]  F. Herrmann,et al.  Non-linear primary-multiple separation with directional curvelet frames , 2007 .

[28]  P. M. van den Berg,et al.  Seismic applications of acoustic reciprocity , 1993 .