عنوان مقاله [English]
نویسندگان [English]چکیده [English]
Because of the non-stationary property of seismic signals, time-frequency transforms have widely used in seismic data processing and interpretations. Spectral decomposition can reveal the characteristics that are not easily observed in the time representation or the frequency representation alone. Conventional spectral decompositions such as short-time Fourier transform (STFT) and Wigner–Ville distribution (WVD) have some restrictions, such as Heisenberg uncertainty principle and cross terms. In this paper, we used the deconvolution of a short-time Fourier transform spectrogram to overcome the mentioned restrictions.
The resolution of a time–frequency representation using STFT is strongly dependent on the length of the window function. A short window length will result in a good time resolution but a poor frequency resolution; a long window length will result in a poor time resolution but a good frequency resolution.
No window function is used to calculate the WVD of signals. Therefore, WVD has a high resolution in time and frequency simultaneously. However, the existence of the cross–terms has limited the application of this distribution (Boashash, 2003). Auger et al. (1996) introduced the smoothed pseudo WVD (SPWVD) to eliminate these cross-terms. Smoothing the WVD leads to a tradeoff between the time–frequency resolution and cross-term elimination.
When the smoothing function is the WVD of the window function used in STFT, the SPWVD will become the STFT spectrogram (Qiang and Wen-kai, 2010). There are no cross-terms in the STFT spectrogram, and yet it has a low resolution both in time and frequency. Therefore, a 2D deconvolution operator can be used to generate a high time-frequency representation of the signal with no cross-terms. To perform the 2D deconvolution, we used the iterative Lucy–Richardson algorithm. The resulted spectrogram after 2D deconvolution is nominated as deconvolutive STFT or DSTFT.
The efficiency of this method is evaluated by applying on both synthetic and real seismic data. The results of synthetic example show that the deconvolutive short-time Fourier transform spectrogram (DSTFT) has the fine resolution as the Wigner–Ville distribution (WVD) has but with no cross-terms.
Castagna et al. (2003) used the spectral decomposition to detect the low-frequency shadows associated with hydrocarbons. In fact, these shadows are often related to an additional energy occurring at low frequencies, rather than the preferential attenuation of higher frequencies. One possible explanation is that these are locally converted shear waves that have traveled mostly as P-waves and thus arrive slightly after the true primary event.
We used a deconvolutive short-time Fourier transform spectrogram to illuminate the low-frequency shadow corresponding to a gas reservoir at one of the gas fields in the South West of Iran. The results of the real data example show that the DSTFT analysis has a much better resolution than the conventional spectral decomposition and can potentially be used to detect hydrocarbons from a gas reservoir directly using low-frequency shadows.