Spectral decomposition and de‐noising via time‐frequency and space‐wavenumber reassignment

The reassignment method remaps the energy of each point in a time-frequency spectrum to a new coordinate that is closer to the actual time-frequency location. Two applications of the reassignment method are developed in this paper. We first describe time-frequency reassignment as a tool for spectral decomposition. The reassignment method helps to generate more clear frequency slices of layers and therefore, it facilitates the interpretation of thin layers. The second application is to seismic data de-noising. Through thresholding in the reassigned domain rather than in the Gabor domain, random noise is more easily attenuated since seismic events are more compactly represented with a relatively larger energy than the noise. A reconstruction process that permits the recovery of seismic data from a reassigned time-frequency spectrum is developed. Two approaches of the reassignment method are used in this paper, one of which is referred to as the trace by trace time reassignment that is mainly used for seismic spectral decomposition and another that is the f − x spatial reassignment that is mainly used for seismic de-noising. Synthetic examples and two field data examples are used to test the proposed method. For comparison, the Gabor transform method, inversion-based method and common f − x deconvolution method are also used in the examples.

[1]  K. Kodera,et al.  A new method for the numerical analysis of nonstationary signals , 1976 .

[2]  Kelly Fitz,et al.  Algorithms for computing the time-corrected instantaneous frequency (reassigned) spectrogram, with applications. , 2004, The Journal of the Acoustical Society of America.

[3]  M. Sacchi,et al.  Microseismic data denoising using a 3C group sparsity constrained time-frequency transform , 2012 .

[4]  Richard G. Baraniuk,et al.  Instantaneous Frequency Estimation Using the Reassignment Method , 1997 .

[5]  T. Claasen,et al.  THE WIGNER DISTRIBUTION - A TOOL FOR TIME-FREQUENCY SIGNAL ANALYSIS , 1980 .

[6]  David C. Henley,et al.  Gabor deconvolution: Estimating reflectivity by nonstationary deconvolution of seismic data , 2011 .

[7]  D. Gabor,et al.  Theory of communication. Part 1: The analysis of information , 1946 .

[8]  C. Robert Pinnegar,et al.  The S-transform with windows of arbitrary and varying shape , 2003 .

[9]  Marc Teboulle,et al.  A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems , 2009, SIAM J. Imaging Sci..

[10]  S. Chopra,et al.  Thin-bed reflectivity inversion , 2006 .

[11]  Yandong Li,et al.  High-frequency anomalies in carbonate reservoir characterization using spectral decomposition , 2011 .

[12]  M. Sacchi,et al.  fx Gabor Seismic Data Reconstruction , 2009 .

[13]  G. Partyka,et al.  Interpretational applications of spectral decomposition in reservoir characterization , 1999 .

[14]  Mirko van der Baan,et al.  Empirical mode decomposition for seismic time-frequency analysis , 2013 .

[15]  Fabrice Plante,et al.  Improvement of speech spectrogram accuracy by the method of reassignment , 1998, IEEE Trans. Speech Audio Process..

[16]  Thomas Elboth,et al.  Time‐frequency seismic data de‐noising , 2010 .

[17]  Sean A Fulop,et al.  Accuracy of formant measurement for synthesized vowels using the reassigned spectrogram and comparison with linear prediction. , 2010, The Journal of the Acoustical Society of America.

[18]  Mauricio D. Sacchi,et al.  Spectral decomposition with f−x−y preconditioning , 2013 .

[19]  Stéphane Mallat,et al.  Matching pursuits with time-frequency dictionaries , 1993, IEEE Trans. Signal Process..

[20]  Jerome Mars,et al.  Improving surface-wave group velocity measurements by energy reassignment , 2003 .

[21]  François Auger,et al.  Time-Frequency Reassignment: From Principles to Algorithms , 2018, Applications in Time-Frequency Signal Processing.

[22]  Yanghua Wang.  Multichannel matching pursuit for seismic trace decomposition , 2010 .

[23]  Mauricio D. Sacchi,et al.  High-resolution wave-equation amplitude-variation-with-ray-parameter (AVP) imaging with sparseness constraints , 2007 .

[24]  H. R. Siahkoohi,et al.  Random Noise Suppression from Seismic Data Using Time-frequency Peak Filtering , 2009 .

[25]  Alexander D. Poularikas,et al.  Transforms and Applications Handbook, Third Edition , 2010 .

[26]  K. Kodera,et al.  Analysis of time-varying signals with small BT values , 1978 .

[27]  Mauricio D. Sacchi,et al.  Complex spectral decomposition via inversion strategies , 2010 .

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

[29]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[30]  John P. Castagna,et al.  Constrained least-squares spectral analysis: Application to seismic data , 2012 .

[31]  John P. Castagna,et al.  Inverse Spectral Decomposition , 2004 .

[32]  Xiang Li,et al.  Efficient least‐squares imaging with sparsity promotion and compressive sensing , 2012 .

[33]  Dennis Gabor,et al.  Theory of communication , 1946 .

[34]  Gary F. Margrave,et al.  Seismic Depth Imaging with the Gabor Transform , 2008 .

[35]  L. Canales.  Random Noise Reduction , 1984 .

[36]  Patrick Flandrin,et al.  Improving the readability of time-frequency and time-scale representations by the reassignment method , 1995, IEEE Trans. Signal Process..

[37]  A. Barnes.  A tutorial on complex seismic trace analysis , 2007 .

[38]  A. Poularikas.  The transforms and applications handbook , 2000 .

[39]  Yanghua Wang,et al.  Seismic time-frequency spectral decomposition by matching pursuit , 2007 .

[40]  Kelly Fitz,et al.  Correction to: 'On the Use of Time/Frequency Reassignment in Additive Sound Modeling' , 2002 .