ABSTRACT
The Wigner-Ville distribution (WVD) is a high-resolution time-frequency spectral analysis method for nonstationary signals; yet, it suffers from cross-term interference among signal components. We proposed applying a masking filter directly to the WVD time-frequency spectrum to suppress the cross-term interference. Conventional methods for suppressing interference include the smoothed pseudo-WVD (SP-WVD) method, which incorporates smooth filtering in the time and frequency directions. We exploited the SP-WVD spectrum as a reference to design the masking filter; thus, the mask-filtered WVD (MF-WVD) procedure is data-adaptive. The MF-WVD method preserves the high-resolution energy concentration in the spectrum portrayed by the standard WVD, while suppressing the cross-term interference cleanly as in the SP-WVD method. Applying the MF-WVD method to field 3D seismic data generates high-resolution spectral cubes for various frequencies, and these spectral cubes may be used intuitively for detecting reservoir-related characteristics.
REFERENCES
- 1995, Improving the readability of time-frequency and time-scale representations by the reassignment method: IEEE Transactions on Signal Processing, 43,
1068–1089 , doi:10.1109/78.382394 .ITPRED 1053-587X , - 1988, Note on the use of the Wigner distribution for time–frequency signal analysis: IEEE Transactions on Acoustics, Speech, and Signal Processing, 36,
1518–1521 , doi:10.1109/29.90380 .IETABA 0096-3518 , - 1989, Improved time-frequency representations of multicomponent signals using exponential distribution: IEEE Transactions on Acoustic Speech and Signal Processing, 37,
862–871 , doi:10.1109/ASSP.1989.28057 . , - 1980a, The Wigner distribution — A tool for time-frequency signal analysis — Part 1: Continuous time signals: Philips Journal of Research, 35,
217–250 .PHJRD9 0165-5817 , - 1980b, The Wigner distribution — A tool for time-frequency signal analysis — Part 2: Discrete time signals: Philips Journal of Research, 35,
276–300 .PHJRD9 0165-5817 , - 1980c, The Wigner distribution — A tool for time-frequency signal analysis — Part 3: Relations with other time-frequency signal transformations: Philips Journal of Research, 35,
372–389 .PHJRD9 0165-5817 , - 1989, Time-frequency distributions — A review: Proceedings of the IEEE, 77,
941–981 , doi:10.1109/5.30749 . , - 1995, Time-frequency analysis, theory and applications: Prentice Hall. ,
- 2016, Sedimentary characterization of the Upper Paleozoic coal-bearing tight sand strata, Daniudi Gas Field, Ordos Basin, China: Journal of Earth Science, 27,
823–834 , doi:10.1007/s12583-016-0705-5 . , - 2010, Time-frequency energy distributions meet compressed sensing: IEEE Transactions on Signal Processing, 58,
2974–2982 , doi:10.1109/TSP.2010.2044839 . , - 1984,
A general class of estimators for the Wigner-Ville spectrum of non-stationary processes , in A. BensoussanJ. L. Lions, eds., Analysis and optimization of systems:Lecture Notes in Control and Information Sciences 62, Springer,15–31 , doi:10.1007/BFb0004941 . , - 1946, Theory of communication — Part 1: The analysis of information: Journal of the Institution of Electrical Engineers, 93,
429–441 , doi:10.1049/ji-1.1947.0015 . , - 1991, A class of fast Gaussian binomial filters for speech and image processing: IEEE Transactions on Signal Processing, 39,
723–727 , doi:10.1109/78.80892 .ITPRED 1053-587X , - 2020, Prediction of hydrocarbon reservoirs within coal-bearing formations: Journal of Geophysics and Engineering, 17,
484–492 , doi:10.1093/jge/gxaa007 . , - 1992, Alias-free generalized discrete-time time-frequency distributions: IEEE Transactions on Signal Processing, 40,
2757–2765 , doi:10.1109/78.165662 . , - 1995, An adaptive optimal-kernel time-frequency representation: IEEE Transactions on Signal Processing, 43,
2361–2371 , doi:10.1109/78.469854 .ITPRED 1053-587X , - 2008, Spectral decomposition using Wigner-Ville distribution with applications to carbonate reservoir characterization: The Leading Edge, 27,
1050–1057 , doi:10.1190/1.2967559 . , - 2017, High-resolution characterization of geologic structures using the synchrosqueezing transform: Interpretation, 5, no. 1,
T75–T85 , doi:10.1190/INT-2016-0006.1 . , - 2008, Feature extraction and image processing for computer vision: Academic Press. ,
- 2016, VSP wave separation by adaptive masking filters: Journal of Geophysics and Engineering, 13,
412–421 , doi:10.1088/1742-2132/13/3/412 . , - 1991, Wavelets and signal processing: IEEE Signal Processing Magazine, 8,
14–38 , doi:10.1109/79.91217 .ISPRE6 1053-5888 , - 2001, Computer vision, theory and applications: Prentice Hall. ,
- 2005, Spectral decomposition of seismic data with continuous-wavelet transform: Geophysics, 70, no. 6,
P19–P25 , doi:10.1190/1.2127113 .GPYSA7 0016-8033 , - 1998, On the realization of the polynomial Wigner-Ville distribution for multicomponent signals: IEEE Signal Processing Letters, 5,
157–159 , doi:10.1109/97.700915 . , - 2001, Seismic sequence analysis and attribute extraction using quadratic time-frequency representations: Geophysics, 66,
1947–1959 , doi:10.1190/1.1487136 .GPYSA7 0016-8033 , - 1948, Théorie et application de la notion de signal analytique: Câbles et transmissions, 2A,
61–74 . , - 2003, Multiple attenuation: Coping with the spatial truncation effect in the Radon transform domain: Geophysical Prospecting, 51,
75–87 , doi:10.1046/j.1365-2478.2003.00355.x .GPPRAR 0016-8025 , - 2007, Seismic time-frequency spectral decomposition by matching pursuit: Geophysics, 72, no. 1,
V13–V20 , doi:10.1190/1.2387109 .GPYSA7 0016-8033 , - 2010, Multichannel matching pursuit for seismic trace decomposition: Geophysics, 75, no. 4,
V61–V66 , doi:10.1190/1.3462015 .GPYSA7 0016-8033 , - 2012, Reservoir characterization based on seismic spectral variations: Geophysics, 77, no. 6,
M89–M95 , doi:10.1190/geo2011-0323.1 .GPYSA7 0016-8033 , - 2021, The W transform: Geophysics, 86, no. 1,
V31–V39 , doi:10.1190/geo2020-0316.1 .GPYSA7 0016-8033 , - 2005, Mesozoic lithospheric deformation in the North China block: Numerical simulation of evolution from orogenic belt to extensional basin system: Tectonophysics, 405,
47–63 , doi:10.1016/j.tecto.2005.05.012 .TCTOAM 0040-1951 , - 2020, Multichannel maximum-entropy method for the Wigner-Ville distribution: Geophysics, 85, no. 1,
V25–V31 , doi:10.1190/geo2019-0347.1 .GPYSA7 0016-8033 , - 1932, On the quantum correction for thermodynamic equilibrium: Physical Review, 40,
749–759 , doi:10.1103/PhysRev.40.749 .PHRVAO 0031-899X , - 1992,
Reduced interference time-frequency distributions , in B. Boashash, ed., Time-frequency signal analysis: Methods and applications: Longman Cheshire,74–98 , doi:10.2307/2532288 . , - 1996, Multiple suppression by 2D filtering in the parabolic τ-p domain: A wave-equation-based method: Geophysical Prospecting, 44,
375–401 , doi:10.1111/j.1365-2478.1996.tb00154.x .GPPRAR 0016-8025 ,