The optimal fractional S transform of seismic signal based on the normalized second-order central moment

Abstract As the extension of time-bandwidth product (TBP) in the fractional domain, the generalized time-bandwidth product (GTBP) provides a rotation-independent measure of compactness. A new fractional S transform (FrST) is proposed to avoid missing the physical meaning of the fractional time–frequency plane. FrST is based on the GTBP criterion and the time–frequency rotation property of fractional Fourier transform (FrFT). In addition, we introduce the normalized second-order central moment (NSOCM) calculation method to determine the optimal order. The optimal order searching process can be converted into the NSOCM calculation. Compared with TBP search algorithms, the NSOCM approach has higher computational efficiency. The qualitative advantage of the NSOCM approach in the optimal order selection is demonstrated by a series of model tests. The optimal FrST based on NSOCM (OFrST) can produce more compact time–frequency support than the S transform. The real seismic data spectral decomposition results show that the proposed algorithm can obtain single-frequency visualization with better time-frequency concentration, thereby enhancing the precision of reservoir prediction.

[1]  Ran Tao,et al.  Spectral Analysis and Reconstruction for Periodic Nonuniformly Sampled Signals in Fractional Fourier Domain , 2007, IEEE Transactions on Signal Processing.

[2]  R. P. Lowe,et al.  Local S-spectrum analysis of 1-D and 2-D data , 1997 .

[3]  De-Ping Xu,et al.  Fractional S transform — Part 1: Theory , 2012, Applied Geophysics.

[4]  K. K. Sharma,et al.  Generalized fractional S-transform and its application to discriminate environmental background acoustic noise signals , 2014 .

[5]  Orhan Arikan,et al.  Short-time Fourier transform: two fundamental properties and an optimal implementation , 2003, IEEE Trans. Signal Process..

[6]  Jin Jiang,et al.  Frequency-based window width optimization for S-transform , 2008 .

[7]  Zhenhua He,et al.  The optimal fractional Gabor transform based on the adaptive window function and its application , 2013, Applied Geophysics.

[8]  Lalu Mansinha,et al.  Localization of the complex spectrum: the S transform , 1996, IEEE Trans. Signal Process..

[9]  Douglas L. Jones,et al.  A high resolution data-adaptive time-frequency representation , 1990, IEEE Trans. Acoust. Speech Signal Process..

[10]  LJubisa Stankovic,et al.  Time-frequency signal analysis based on the windowed fractional Fourier transform , 2003, Signal Process..

[11]  Luís B. Almeida,et al.  The fractional Fourier transform and time-frequency representations , 1994, IEEE Trans. Signal Process..

[12]  Jin Jiang,et al.  A Window Width Optimized S-Transform , 2008, EURASIP J. Adv. Signal Process..

[13]  Liying Zheng,et al.  Review of Computing Algorithms for Discrete Fractional Fourier Transform , 2013 .

[14]  Ran Tao,et al.  Short-Time Fractional Fourier Transform and Its Applications , 2010, IEEE Transactions on Signal Processing.

[15]  Aydin Akan,et al.  A fractional Gabor expansion , 2003, J. Frankl. Inst..

[16]  S. Roopa,et al.  S-transform based on analytic discrete cosine transform for time-frequency analysis , 2014, Signal Process..

[18]  Orhan Arikan,et al.  Generalized time-bandwidth product optimal short-time fourier transformation , 2002, 2002 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[19]  Chandra Sekhar Seelamantula,et al.  Fractional Hilbert transform extensions and associated analytic signal construction , 2014, Signal Process..

[20]  Robert Glenn Stockwell,et al.  A basis for efficient representation of the S-transform , 2007, Digit. Signal Process..

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

[22]  Zhenming Peng,et al.  Determining the optimal order of fractional Gabor transform based on kurtosis maximization and its application , 2014 .

[23]  Martin J. Bastiaans,et al.  On fractional Fourier transform moments , 2000, IEEE Signal Processing Letters.