Most geologic changes have a seismic response but sometimes this is expressed only in certain spectral ranges, buried within the broadband data. Spectral decomposition can be utilized to help interpretations for such cases. Compared with several different spectral decomposition technologies, the generalized S transform is believed to be efficient and provides good temporal and spectral resolution. It has been used for heavy oil recovery and 4D SAGD monitoring cases and proved to be successful. The results correlate very well with well logs and provide useful information for seismic interpretations.
Spectral decomposition is a novel technology developed in recent years. It has proved to be very useful for seismic data interpretation, because decomposing data into its spectral components reveals stratigraphic and structural details that are often obscured in the broadband data. In a geologically complex area, a target event''s variations in amplitude as a function of frequency can be traced more clearly when viewed in terms of a frequency band. And lithology and fluid driven spectral variations, such as peak frequency shifting due to attenuation and absorption, can be better delineated. Thus, spectral decomposition provides a technique to help seismic interpretations. Popularly used spectral decomposition methods include Short windowed Fourier transform (SWFT) (Partyka, 1999), Morlet wavelet based wavelet transform (MWT) (X. Miao & W. Moon, 1994, Castagna, 2003), and Matching Pursuit Decomposition (MPD) (X. Miao & S. Cheadle 1998). SWFT involves explicit use of windows, which affects temporal and spectral resolution. Wave-packagelike spectral decomposition - even though it provides better spectral resolution - reduces temporal resolution, which is undesirable for thin bed interpretation. In this paper, in addition to the previously discussed MWT and MPD methods, we investigate a generalized S transform (ST) based spectral decomposition method. We explore the merits and disadvantages of the methods, and apply them to the seismic data to show the interpretive benefits of spectral decomposition.
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The Morlet wavelet is a modulated Gaussian function, which is a non-orthogonal compactly supported complex wavelet, although it has side lobes. The decomposition of the MWT is represented in the scale (or voice) and time domain (X. Miao & W. Moon, 1994). Since scale is related to frequency, we can convert the MWT representation into the frequency-time domain and use it for spectral decomposition. The wavelet transform based spectral decomposition has an implicitly defined analysis window, thus without the tapering effects inherent to the more commonly used short window Fourier method.
The S transform is proposed by Stockwell et. al. (1996) as an extension to the Morlet wavelet transform. The mother wavelet for the S transform is also a modulated Gaussian function, but it keeps the modulation part with no scaling and no shifting. the S transform becomes the generalized S transform Here A, a and b are constants introduced to add a variety of forms in the mother wavelet so it can better correlate with signals. It directly decomposes signals into the frequency and time domains.
