نشانگر لرزه‌‌ای تک‌بسامد به‌‌دست آمده از روش‌‌های تبدیل موجک پیوسته و تعقیب تطابق

Seismic data, being non-stationary in nature, have varying frequency content across time. Time-frequency decomposition(also called spectral decomposition) of a seismic signal aims to characterize the time-dependent frequency response of subsurface rocks and reservoirs. Castagna et al. (2003) use matching-pursuit decomposition for instantaneous spectral analysis to detect low-frequency shadows beneath hydrocarbon reservoirs. A case history of using spectral decomposition and coherency to interpret incised valleys is shown by Peyton et al. (1998). Partyka et al. (1999) use windowed spectral analysis to produce discrete-frequency energy cubes for applications in reservoir characterization. Continuous wavelet transform (CWT) was introduced by Morlet et al. (1982). In CWT, time frequency atoms are chosen in such a way that their time support changes for different frequencies according to Heisenberg’s uncertainty principle (Mallat, 1999; Daubechies, 1992). This study used the Morlet wavelet, which provides an easy interpretation from scale to frequency.
Time-frequency CWT (TFCWT; Sinha, 2005) analysis provides high-frequencyresolution at low frequencies and high time resolution at high frequencies. This optimal time-frequency resolution property of the TFCWT makes it useful in seismic data analysis. Computing the TFCWT in the Fourier domain is a fast process. Furthermore, TFCWT is an invertible process such that the inverse Fourier transform of the time summation of the TFCWT reconstructs the original signal, provided the inverse wavelet transform exists. The purposes of this study require only the forward transform; reproducibility is not a strict requirement. Seismic data analysts sometimes observe low-frequency shadows in association with hydrocarbon reservoirs. The shadow is probably caused by attenuation of high-frequency energy in the reservoir itself.
Matching pursuit decomposition involves the cross-correlation of a wavelet dictionary against the seismic trace. The projection of the best correlating wavelet on the seismic trace is then subtracted from that trace. The wavelet dictionary is then cross-correlated against the residual, and again the best correlating wavelet projection is subtracted. The process is repeated iteratively until the energy remaining in the residual falls below some acceptable threshold. As long as the wavelet dictionary meets simple admissibility conditions, the process will converge. Most importantly, the wavelets need not be orthogonal. The output of the process is a list of wavelets with their respective arrival times and amplitudes for each seismic trace. The inverse transform is accomplished simply by summing the wavelet list and the residual, thus reconstructing the original trace. The wavelet list is readily converted to a time-frequency analysis by superposition of the wavelet frequency spectra.
The CWT dilates and compresses wavelets to provide a time-scale spectrum instead of a time-frequency spectrum. Converting a scalogram into a time-frequency spectrum using the center frequency of a scale gives an erroneous attenuation in the spectrum. The TFCWT overcomes this problem and gives a more robust technique of time-frequency localization. Since TFCWT is fundamentally derived from the continuous-wavelet transform, wavelet dilation and compression effectively provides the optimal window length, depending upon the frequency content of the signal. Thus, it eliminates the subjective choice of a window length and provides an optimal time-frequency spectrum with an absence of erroneous attenuation effect for a non-stationary signal. It has high-frequency resolution at low frequencies and high time resolution at high frequencies, whereas the spectrogram has fixed time-frequency resolution throughout. Matching Pursuit Decomposition (MPD) requires no windowing of the seismic data and thus has the best combination of temporal and spectral resolution in comparison to TFCWT and the continuous wavelet transform. Most hydrocarbon reservoirs have a seismic response, but sometimes this is expressed only in certain spectral ranges, hidden within the broadband data. Gas-bearing layers have been an interesting area of research for geophysicists, especially spectral decomposition researchers, since they have a very specific spectral attribute: low-frequency gas shadows.
This paper presents an investigation of the application and efficiency of Time-Frequency Continuous Wavelet Transform and Matching Pursuit method in time-frequency analysis of seismic sections to delineate and detect low-frequency gas shadows on real data from an Iranian gas reservoir. The results from the MPD are compared with those of the CWT and TFCWT applying single frequency seismic sections at frequencies of 15 Hz and 25 Hz with the expectation that low-frequency gas shadows will be observable in this range of frequencies.