In this paper, the authors made Ricker wavelet-based adaptive matching pursuit decomposition of seismic signals and discussed the method of time-frequency representation by matching wavelets. Since the time-frequency information of matching wavelet's Wigner-Ville distribution is limited, this paper proposes a time-frequency representation based on adjustable window Short Time Fourier Transform. Furthermore, by using the complex spectrum of matching wavelets, this paper introduces a new time-frequency representation, which not only has the same resolution and energy concentration properties as Wigner-Ville method, but also retains the most basic time-frequency characteristics of the original signal without cross term and window truncation effects. Compared with time-frequency characteristics of Short Time Fourier transform and S-transform, the matching pursuit time-frequency representation and instantaneous spectral parameters have higher resolution. Real data application also shows that the matching pursuit time-frequency analysis is very suitable for seismic signal with non-stationary characteristics.
[1] Charles I P, Shenghong T, John P C, et al.Comparison of frequency attributes from CWT and MPD spectral decompositions of a complex turbidite channel model//Expanded Abstracts of 78th SEG Annual International Meeting,2008:394-397.
[2] Mallat S, Zhang Z. Matching pursuit with time-frequency dictionaries. IEEE transactions on signal processing,1993,41(12):3397-3415.
[3] Liu J, Wu Y, Han D, et al.Time-frequency decomposition based on Ricker wavelet//Expanded Abstracts of 74th SEG Annual International Meeting,2004,1937-1940.
[4] Liu J,and Marfurt K J. Matching pursuit decomposition using Morlet wavelets//Expanded Abstracts of 75th SEG Annual International Meeting, 2005,786-789.
[5] Wang Y.Seismic time-frequency spectral decomposition by matching pursuit [J].Geophysics,2007,72(1):13-20.