Study of efficiency of seismic time-frequency spectral decomposition by matching pursuit for detecting thin layers

Most geologic changes have a seismic response but sometimes this is expressed only in certain spectral ranges hidden within the broadband data. Spectral decomposition is one of the methods which can be utilized to help interpreting such cases. There are several time-frequency methods including: short-time Fourier transform (STFT), continuous wavelet transform (CWT), Wigner-Ville distribution (WVD), S-transform, and matching pursuit decomposition (MPD). In this paper, we use the MPD method. This method is newer than the other time-frequency methods used in exploration seismology. Mallat and Zhang (1993) have improved time and frequency resolution simultaneously by using MPD method. In this method, a signal is decomposed into constructive wavelets. Time and frequency properties of wavelets are used locally for spectral decomposition. Pursuits are the algorithms which search the best time-frequency matching between the signal and a linear combination of selected wavelets from wavelet dictionary. Matching pursuit which is an iterative procedure optimizes signal estimation by each new wavelet chosen from a dictionary. These wavelets combined linearly to obtain the best match with the signal. A signal should expand to waveforms which their time-frequency properties could be matched to local structures. Such waveforms are called time-frequency atoms. There are many approaches to match wavelets of dictionary to a seismic signal and to obtain time-frequency spectrum in matching pursuit decomposition. The base of all approaches is the Mallat and Zhang’s algorithm. However, computing time of the original algorithm is very high due to many iterations and that is why particular conditions have been applied in different researches to limit the matching pursuit algorithm for obtaining the lower performing time. In this work, particular conditions are rather similar to Wang’s (2007) method.
On seismic data, layer thickness is described on the basis of the seismic travel time. When a layer with different properties has a thickness by one-fourth wavelength, top and base reflections will interfere constructively. For thin layers less than tuning thickness, combined seismic amplitude decreases with thickness (when reflection coefficients of the top and of the base are opposite). Generally, spectral decomposition has many applications in interpretation of seismic sections and so there will be extra needs to study and develop them. Thin layers and many stratigraphic hydrocarbon reservoirs are beneath the threshold of the vertical seismic resolution (tuning thickness) and because of their low thicknesses, they are not resolvable. For this reason, mapping the small-scale geological structures is one of the important interpretational cases. When the thickness of a thin layer decreases pick frequency slightly increases. In this work, this issue has been used to detect thin layers by time-frequency spectrum and by single-frequency sections obtained from MPD.
In this paper, we investigated the performance of the matching pursuit decomposition for time-frequency analysis of seismic sections to delineate and detect thin layers on synthetic data (including simple thin layer model and also wedge model) and real data. It is observed that the interpretation of thin layers is simpler by single-frequency sections. It is shown that for a simple thin layer if considerable frequency in single-frequency sections increases, ability in resolving layer interfaces would be increased. In the wedge model, as the frequency increases resolution threshold of layer interfaces moves to a lower thickness and therefore it would be possible to detect lower thickness layers. The tuning thickness has been decreased from 19 meters in original seismic section to 12 meters in 80 Hz frequency section. In the real data, it is shown that when a thin layer is not resolvable in a seismic section it might be detected using the MPD method. In this case, by providing 20, 40, 60, 80 and 100 Hz single-frequency sections when high frequency sections are studied, interfaces of thin layer are appeared gradually. It is concluded that time-frequency sections are useful instruments to detect and delineate thin layers.