We present an efficient representation for spectral decomposition of seismic signals by using the deconvolutive short time Fourier transform (DSTFT) spectrogram. The DSTFT spectrogram improves the time and frequency resolution of the short time Fourier transform (STFT) spectrogram by applying a 2-D iterative deconvolution operation on the STFT spectrogram. Our research on synthetic and real seismic data example illustrates the good performance of the DSTFT spectrogram compared with other traditional time frequency representations.
Seismic signal is non-stationary since its frequency response varies with time. As a result, spectral decomposition can reveal the characteristics that are not easily observed in the time representation or the frequency representation alone. It has been applied in many fields of seismic signal analysis such as resolution enhancement, thickness estimation for thin beds, stratigraphic visualization, noise attenuation and direct hydrocarbon detection, which aims to characterize the time-dependent frequency response of subsurface rocks and reservoirs. There exist many spectral decomposition methods, among which the STFT spectrogram is widely applied. Besides the STFT spectrogram, Cohen’s class distribution (1989) is also another important spectral decomposition method. Wigner-Ville distribution (WVD) and smoothed pseudo Wigner-Ville distribution (SPWVD) are important members of Cohen’s class distribution. In fact, the STFT spectrogram can also be treated as a particular case of Cohen’s class distribution when the kernel function is the WVD of the time window function. There has been many successful seismic applications of spectral decomposition. Chakraborty et al. (1995) introduced the wavelet transform to the seismic interpretation. Wang (2006) applied the matching pursuit decomposition to detecting the gas reservoir. Li and Zheng (2008) applied the smoothed Wigner-Ville distribution to the characterization of carbonate reservoir. In this paper, we apply the DSTFT spectrogram in spectral decomposition of synthetic seismic data and real seismic data. The experimental results show that the DSTFT spectrogram has better time and frequency resolution than other traditional time frequency representations.
In our simulations, a synthetic seismic trace that contains seismic wavelet at different time locations with different center frequencies is applied to make comparisons with other time-frequency representations. The first seismic event (at 200ms) is superstition of two 10 Hz wavelets with a delay time 60ms. The third seismic event (at 800ms) is the superposition of the two 40 Hz wavelets with a delay time arrival 30ms. Figure 1 shows the synthetic seismic trace and the corresponding time-frequency representations of WVD, SPWVD, STFT spectrogram and DSTFT spectrogram, respectively. WVD has the best time-frequency resolution; however, the existence of the cross-term interferences makes the interpretation difficult. The resolution of STFT spectrogram timefrequency is also poor. Compared to the above distributions, DSTFT spectrogram is shown to be free of the cross-term interferences present in WVD, and displays finer resolution than STFT spectrogram and SPWVD.
Fiugre2 shows the results of the real seismic trace using the above time frequency representations. The sample frequency is 250 Hz and the time duration is 450ms. All the applied window is Gaussian function with a duration of 50ms.
