S-transform with maximum energy concentration and its application to detect gas bearing zones and low-frequency shadows

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Abstract

Seismic attribute is a quantitative measure of an interested seismic characteristic. There are several seismic attributes. In recent years, time-frequency (TF) attributes have been developed which to reach them, TF analyzing of seismic data is required. A high resolution TF representation (TFR) can yield more accurate TF attributes. There are several TFR methods including short-time Fourier transform, wavelet transforms, S-transform, Wigner-Ville distribution, Hilbert-Huang transform and etc. In this paper, the S-transform is considered and an algorithm is proposed to improve its resolution. In the Fourier-based TFR methods, the width of the utilized window is the main factor affecting the resolution. The standard S-transform (SST) employs a Gaussian window which its standard deviation, controller the window width, changes inversely with frequency (Stockwell et al., 1996). It was an idea to use a frequency dependent window for TF decomposition. However, the TF resolution of SST is far from ideal; it demonstrates weak temporal resolution at low frequencies and weak spectral resolution at high frequency components. Later on, the generalized S-transform was proposed using an arbitrary window function whose shape is controlled by several free parameters (McFadden et a., 1999; Pinnegar and Mansinha, 2003). Another approach to improve the resolution of a TFR is based on energy concentration concept (Gholami, 2013; Djurovic et al., 2008). According this approach, in this paper, an algorithm is proposed to find the optimum windows for S-transform to get a TFR with maximum energy concentration. To reach this aim, an optimization problem is defined where an energy concentration measure (ECM) is employed to condition the windows so as the TFR would have the maximum energy concentration. Here, we utilize a Gaussian as the window function. Then different windows are constructed by a range of different values of standard deviations in a non-parametric form. Different TFRs are constructed by different windows. The optimum TFR is one with maximum energy concentration. The optimization is performed for each frequency component, individually, and hence, there would be an optimum window width for each frequency component. There are several ECMs which they are used in different applications (Hurley and Rickard, 2009). In this paper, we employ Modified Shannon Entropy as the ECM. As one knows, SST algorithm needs to be implemented in frequency domain (Stockwell et al., 1996). It is due to the dependency of the standard deviation of Gaussian window on the frequency. However, the proposed method of our paper can also be implemented in time domain where the optimum windows would be found, adaptively, for each time sample of the signal. We apply the proposed method to a synthetic signal to compare its performance with some other TF analysis methods in providing a well-concentrated TF map. The comparison of the results shows the superiority of the proposed method rather than STFT and SST. We also perform a quantitative experiment to evaluate the performance of the TFRs. The results confirm the best performance by the proposed method compared with STFT and SST. Then the proposed method is employed to detect gas bearing zones and low-frequency shadows on a seismic data set related to a gas reservoir of Iran. For this aim, some TF seismic attributes are extracted. The attributes include instantaneous amplitude, dominant instantaneous frequency, sweetness factor, single-frequency section and cumulative relative amplitude percentile (C80). The attributes are also extracted by SST to compare with those of the proposed method. The results show that the attributes obtained by the proposed method have more resolution; so that gas bearing zones and low-frequency shadows are better localized on the attribute sections obtained by the proposed method.

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References

Boashash, B., 1991, Time-frequency signal analysis in advances in spectrum analysis and array processing, Prentice Hall, Englewood Cliffs, NJ.
 
Castagna, J. P., Sun, S. and Seigfried, R. W., 2003, Instantaneous spectral analysis: Detection of low-frequency shadows associated with hydrocarbons, The Leading Edge, 22, 120–127.
 
Chopra, S. and Marfurt, K. J., 2005, Seismic attributes-A historical perspectives, Geophysics, 70, 3SO-28SO.
 
Djurovic, I., Sejdic, E. and Jiang, J., 2008, Frequency-based window width optimization for S-transform, Int. J. Elect. Commun., 62, 245–250.
 
Gabor, D., 1946, Theory of communication: J. Inst. Elect. Eng., 93, 429–457.
 
Gholami, A., 2013, Sparse time-frequency decomposition and some applications, IEEE Transactions on Geoscience and Remote Sensing, 51, 3598–3604.
 
Hart, B. S., 2008, Channel detection in 3-D seismic data using sweetness, AAPG Bulletin, 92, 733-742.
 
Herrera, R. H., Han, J. and van der Baan, M., 2014, Applications of the synchrosqueezing transform in seismic time-frequency analysis, Geophysics, 79, V55–V64.
 
Hurley, N. and Rickard, S., 2009, Comparing measures of sparsity, IEEE Transactions on Information Theory, 55, 4723–4741.
 
Jones, D. and Baraniuk, G., 1994, A simple scheme for adapting time-frequency representation, IEEE Transactions on Signal Processing, 42, 3530–3535.
 
Jones, D. and Parks, T., 1990, A high resolution data-adaptive time-frequency representation: IEEE Transactions on Acoustics, Speech and Signal Processing, 38, 2127–2135.
 
Liu, G., Fomel, S. and Chen, X., 2011, Time-frequency analysis of seismic data using local attributes, Geophysics, 76, P23–P34.
 
Mallat, S., 1999, A wavelet tour of signal processing, 2 ed., Academic Press, San Diego, California.
 
Marfurt, K. J. and Kirlin, R. L., 2001, Narrow-band spectral analysis and thin-bed tuning, Geophysics 66, 1274–1283.
 
McFadden, P. D., Cook, J. G. and Forster, L. M., 1999, Decomposition of gear vibration signals by the generalized S-transform, Mechanical Systems and Signal Processing, 13, 691–707.
 
Perz, M., 2001, Coals and their confounding effects, CSEG Recorder, 26, 34–53.
 
Pinnegar, R. C. and Mansinha, L., 2003, The S-transform with windows of arbitrary and varying shape, Geophysics, 68, 381–385.
 
Rankine, L., Stevenson, N., Mesbah, M. and Boashash, B., 2005, A quantitative comparison of non-parametric time-frequency representations, 13th European Signal Processing Conference (EUSIPCO2005), Antalya, Turkey.
 
Riedel, M., Collett, T. S., Kumar, P., Sathe, A. V. and Cook, A., 2010, Seismic imaging of a fractured gas hydrate system in the Krishnae-Godavari Basin offshore India, Marine and Petroleum Geology, 27, 1476-1493.
 
Rutherford, S. R. and Williams, R. H., 1989, Amplitude-versus-offset variations in gas sands, Geophysics, 54, 680–688.
 
Sahu, S. S., Panda, G. and George, N. V., 2009, An Improved S-Transform for Time-Frequency Analysis, IEEE International Advance Computing Conference, Patiala, India.
Sinha, S., Routh, P. S., Anno, P. D. and Castagna, J. P., 2005, Spectral decomposition of seismic data with continuous-wavelet transform, Geophysics, 70, P19–P25.
 
Stockwell, R. G., Mansinha, L. and Lowe, R., 1996, Localization of the complex spectrum: The S-transform, IEEE Transactions on Signal Processing, 44, 998–1001.
 
Stockwell, R. G., 2007, Why use the S-Transform?, AMS Pseudo differential operators: partial differential equations and time-frequency analysis, 52, 279-309.
 
Stankovic, L., 2001. A measure of some time-frequency distributions concentration, Signal Processing, 81, 212–223.
 
Van der Baan, M., Fomel, S. and Perz, M., 2010, Non-stationary phase estimation: A tool for seismic interpretation?, The Leading Edge, 29, 1020–1026.
 
Wu, X. and Liu, T., 2009, Spectral decomposition of seismic data with reassigned smoothed pseudo Wigner-Ville distribution, Journal of Applied Geophysics, 68, 386–393.
 
Xue, Y. J., Cao, J. X. and Tian, R. F., 2013, A comparative study on hydrocarbon detection using three EMD-based time-frequency analysis methods, Journal of Applied Geophysics, 89, 0926–9851.
Journal of the Earth and Space Physics
Volume 41, Issue 3 - Serial Number 3
October 2015
Pages 403-412

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