Adaptive multiple subtraction with wavelet-based complex unary Wiener filters

ABSTRACTAdaptive subtraction is a key element in predictive multiple-suppression methods. It minimizes misalignments and amplitude differences between modeled and actual multiples, and thus reduces multiple contamination in the data set after subtraction. Due to the high crosscorrelation between their waveforms, the main challenge resides in attenuating multiples without distorting primaries. As they overlap on a wide frequency range, we split this wide-band problem into a set of more tractable narrow-band filter designs, using a 1D complex wavelet frame. This decomposition enables a single-pass adaptive subtraction via complex, single-sample (unary) Wiener filters, consistently estimated on overlapping windows in a complex wavelet transformed domain. Each unary filter compensates for amplitude differences within its frequency support, and can correct small and large misalignment errors through phase and integer delay corrections. This approach greatly simplifies the matching filter estimation and, despit...

[1]  Mauricio D. Sacchi,et al.  Latest views of the sparse Radon transform , 2003 .

[2]  Simon Spitz,et al.  Pattern recognition, spatial predictability, and subtraction of multiple events , 1999 .

[3]  A. Guitton.  A pattern‐based approach for multiple removal applied to a 3D Gulf of Mexico data set , 2006 .

[4]  M. Taner,et al.  SEMBLANCE AND OTHER COHERENCY MEASURES FOR MULTICHANNEL DATA , 1971 .

[5]  Palle E. T. Jorgensen,et al.  Comparison of Discrete and Continuous Wavelet Transforms , 2007, Encyclopedia of Complexity and Systems Science.

[6]  M. Turhan Taner,et al.  Long period multiple suppression by predictive deconvolution in the x–t domainl1 , 1995 .

[7]  M. T. Taner,et al.  LONG PERIOD SEA-FLOOR MULTIPLES AND THEIR SUPPRESSION* , 1980 .

[8]  F. Herrmann,et al.  Robust Curvelet-Domain Primary-Multiple Separation with Sparseness Constraints , 2005 .

[9]  Luc T. Ikelle,et al.  Multidimensional signature deconvolution and free-surface multiple elimination of marine multicomponent ocean-bottom seismic data , 2001 .

[10]  Philippe Herrmann,et al.  De-aliased, High-Resolution Radon Transforms , 2000 .

[11]  A. Pica,et al.  Simultaneous Source Separation Using Wave Field Modeling and PEF Adaptive Subtraction , 2009 .

[12]  Philippe Herrmann,et al.  3D surface-related multiple modeling , 2005 .

[13]  S. Ventosa,et al.  Window length selection for optimum slowness resolution of the local-slant-stack transform , 2012 .

[14]  Yong Ma,et al.  Adaptive multiple subtraction using a constrained L1-norm method with lateral continuity , 2009 .

[15]  S. M. Doherty,et al.  Seismic Data Analysis: Processing, Inversion, and Interpretation of Seismic Data , 2000 .

[16]  Martin Schimmel,et al.  Noise reduction and detection of weak, coherent signals through phase-weighted stacks , 1997 .

[17]  Laurent Jacques,et al.  A panorama on multiscale geometric representations, intertwining spatial, directional and frequency selectivity , 2011, Signal Process..

[18]  Ramesh Neelamani,et al.  Adaptive subtraction using complex-valued curvelet transforms , 2010 .

[19]  J. MonkDavid.  Wave‐equation multiple suppression using constrained cross‐equalization , 1991 .

[20]  Imtiaz Ahmed.  2D Wavelet Transform Domain Adaptive Subtraction For Enhancing 3D SRME , 2007 .

[21]  Kristopher A. Innanen,et al.  Adaptive separation of free-surface multiples through independent component analysis , 2008 .

[22]  Sergey Fomel.  Adaptive Multiple Subtraction Using Regularized Nonstationary Regression , 2008 .

[23]  Sergey Fomel,et al.  Adaptive multiple subtraction using regularized nonstationary regression , 2008 .

[24]  M. Taner,et al.  Complex seismic trace analysis , 1979 .

[25]  D. Ristow,et al.  Time-Varying Prediction Filtering by Means of UPDATING* , 1979 .

[26]  T. Quarta,et al.  Improvement in GPR coherent noise attenuation using τ-p and wavelet transforms , 2004 .

[27]  Martin Vetterli,et al.  Adaptive filtering in subbands with critical sampling: analysis, experiments, and application to acoustic echo cancellation , 1992, IEEE Trans. Signal Process..

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

[29]  M. Imhof,et al.  Amplitude preservation of Radon-based multiple-removal filters , 2006 .

[30]  Yanghua Wang,et al.  Multiple subtraction using an expanded multichannel matching filter , 2003 .

[31]  D. J. Verschuur,et al.  Estimation of multiple scattering by iterative inversion; Part II, Practical aspects and examples , 1997 .

[32]  Daniela Donno,et al.  Improving multiple removal using least-squares dip filters and independent component analysis , 2011 .

[33]  D. J. Verschuur,et al.  Estimation of primaries and near-offset reconstruction by sparse inversion: Marine data applications , 2009 .

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

[35]  Felix J. Herrmann,et al.  Curvelet imaging and processing : adaptive multiple elimination , 2004 .

[36]  Mark Noble,et al.  Curvelet-based multiple prediction , 2010 .

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

[38]  Complex Wavelet Adaptive Multiple Subtraction with Unary Filters , 2011 .

[39]  L. Lines.  SUPPRESSION OF SHORT-PERIOD MULTIPLES-DECONVOLUTION OR MODEL-BASED INVERSION? , 2004 .

[40]  B. Buttkus.  HOMOMORPHIC FILTERING — THEORY AND PRACTICE* , 1975 .

[41]  Dan Hampson,et al.  Inverse Velocity Stacking For Multiple Elimination , 1986 .

[42]  Caroline Chaux,et al.  Noise Covariance Properties in Dual-Tree Wavelet Decompositions , 2007, IEEE Transactions on Information Theory.

[43]  Bill Dragoset,et al.  A perspective on 3D surface-related multiple elimination , 2010 .

[44]  Bill Dragoset,et al.  An introduction to this special section—Multiple attenuation , 2005 .

[45]  D. Leporini,et al.  A new wavelet estimator for image denoising , 1997 .

[46]  Fast Radon Transform for Multiple Attenuation , 1998 .

[47]  E. Robinson,et al.  PRINCIPLES OF DIGITAL WIENER FILTERING , 1967 .

[48]  Maarten V. de Hoop,et al.  Seismic imaging with the generalized Radon transform: a curvelet transform perspective , 2009 .

[49]  P. Anno,et al.  Spectral decomposition of seismic data with continuous-wavelet transform , 2005 .

[50]  Mei Wu,et al.  A case study of f-k demultiple on 2D offshore seismic data , 2011 .

[51]  Yanghua Wang,et al.  Improving adaptive subtraction in seismic multiple attenuation , 2009 .

[52]  A. Guitton,et al.  Adaptive subtraction of multiples using the L1‐norm , 2004 .

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

[54]  J. MonkDavid.  WAVE‐EQUATION MULTIPLE SUPPRESSION USING CONSTRAINED GROSS‐EQUALIZATION1 , 1993 .

[55]  R. Wombell,et al.  Attenuation of Residual Multiples and Coherent Noise in the Wavelet Transform Domain , 2004, 66th EAGE Conference & Exhibition.

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

[57]  Jelena Kovacevic,et al.  Wavelets and Subband Coding , 2013, Prentice Hall Signal Processing Series.

[58]  D. J. Verschuur,et al.  Focal transformation, an imaging concept for signal restoration and noise removal , 2006 .