Detection of buried channel using the deconvolutive short time Fourier transform

Time representation was the first way to describe a signal, and later on the frequency representation was introduced as another important way to describe a signal for its physical significance. Due to the non-stationary property of seismic data, time-frequency transform has to be used to analyze it. During the last decade, spectral decomposition techniques have proven to be an excellent tool to describe thin beds associated with channel sands, alluvial fans, and the like. However, with the traditional spectral decomposition method based on the short time Fourier Transform, it is difficult to acquire the accurate time-frequency spectrum for non-stationary seismic signals. Recently, the emergence of seismic attribute co-rendering, principal component analysis, cluster analysis, and neural networks has partially solved the problem, but the extraction of spectral attributes from spectral-decomposition tightly linked to the geology has more advantages over other approaches. Popular time–frequency methods have some disadvantages. A good time resolution requires a short window and a good frequency resolution require a narrow-band filter, i.e. a long window, but unfortunately, these two cannot be simultaneously realized. The Wigner-Ville Distribution (WVD) of a signal is the Fourier Transform of the signal’s time-dependent auto-correlation function, a quadratic expression which is bilinear in the signal. As a result, the cross-terms appear in the locations of the resulting time-frequency spectra that either interfere with the interpretation of auto-terms or for which we can provide no physical interpretation. Due to the existence of cross-terms, WVD is not often used. Reduction of the cross-terms is achieved by manipulating the ambiguity function as a mask that reduces the cross-terms while preserving the time and frequency resolution of WVD. The short-time Fourier Transform (STFT) spectrogram, which is the squared modulus of the STFT, is a smoothed version of WVD. An STFT spectrogram is a 2-D convolution of the signal WVD and the utilized window function. In this paper, we introduce a Deconvolutive Short-Time Fourier Transform (DSTFT) spectrogram method, which improves the time-frequency resolution and reduces the cross-terms simultaneously by applying a 2-D deconvolution operation on the STFT spectrogram. Compared to the STFT spectrogram, the spectrogram obtained by this method shows a significant improvement in the time-frequency resolution. In this study, we extract two attributes namely the peak frequency and the peak amplitude, based on the Deconvolutive Short- Time Fourier Transform. The maximum frequency attribute is directly related to the thickness of the thin-bed, like channel, and the maximum amplitude attribute also responds to the thin-bed. We use instantaneous seismic attributes: maximum instantaneous frequencies and their associated amplitudes, as a tool to detect seismic geomorphologic bodies and to identify thin layers. Then we use attributes extracted by Deconvolutive Short Time Fourier Transform to detect the burial channel in both synthetic and real 3D seismic data. Usually, the center of the channel is recognized by the lower maximum frequency and when the thickness of the channel gets thinner away from the center of the channel, the maximum frequency increases correspondingly. Therefore, this attribute could clearly describe the distribution of channel both vertically and horizontally. Results of this study on the synthetic and real seismic data examples illustrate the good performance of the DSTFT spectrogram compared with other traditional time-frequency representations.