Research Of The Methods For Seismic Data Sparse Time-Frequency Decomposition Based On The Greed Algorithm

As the in-depth exploration of China's oil and gas resources, the targets of exploration transit gradually from conventional reservoirs of oil and gas construction to the unconventional, subtle, stratigraphic and lithological reservoirs which are complex. This is not only a challenge, but also the opportunity of developing new methods and techniques to further improve the understanding of underground resources and adapt to the new exploration needs. In this context, as an important tools of oil and gas exploration, the techniques of acquisition, processing and interpretation for seismic data are needed to provide more accurate and richer and of higher resolution underground information. As the underground medium in the exploration area is more complex than before, the nonstationarity of seismic signal is as well as more obvious. The conventional tools for describing and analyzing the nonstationary seismic data, namely the spectral decomposition, is not able to satisfy the requirement of resolution and precision. The traditional spectral decomposition technique is able to represent the seismic signal as a joint-function of time and frequency, so as to describe the energy distribution of seismic wave in time-frequency domain. These spectral decomposition technologies actually can be regarded as decompositions based on a group of basis signal with time-frequency locality, but due to the selection of the basis and the decomposition mode, the decomposition results are always not sparse, resulting the limited resolution in time-frequency distribution. This thesis argues that if we can select the basis signals which match the time-frequency attribute of seismic data better, and select more sparse decomposition methods, then the resolution of time-frequency distribution can be improved to a certain extent, and more information of underground medium would be provided for further support to the seismic technics.Firstly in this thesis, the Fourier transform and the traditional spectral decomposition techniques were discussed in terms of basis functions and the relevant decomposition methods. And then I brought in the concept of sparse time-frequency decomposition for seismic signals. The collection of basic signals can be called as the time-frequency dictionary and a variety of time-frequency dictionaries are listed in this thesis. Especially, three time-frequency dictionaries as well as the corresponding sparse time-frequency decomposition methods were stressed. These time-frequency dictionaries mentioned above are the traditional Morlet wavelet dictionary, the attenuated-Ricker wavelet dictionary, and the EMD dictionary respectively. Flowing the line of cognition, improvement, and seismic application, each time-frequency dictionary was introduced from the properties of atoms to the construction procedure based on the atoms, and then I discussed the specific algorithm of sparse decomposition based on the dictionary, and finally I discussed its application in seismic data processing and interpretation.The time-frequency dictionary discussed firstly in this thesis was the traditional Morlet wavelet dictionary. Because the Morlet wavelet can represent the attenuation and dispersion, so it is often used in conventional seismic sparse time-frequency decomposition algorithm, e.g. the matching pursuit. By introducing the idea of the orthogonal matching pursuit into the existing single-channel matching pursuit and multi-channel matching pursuit based on the Morlet wavelet dictionary, we developed two new methods. I termed these new methods as single-channel orthogonal matching pursuit and multi-channel orthogonal matching pursuit. And I pointed out that the single-channel decomposition mode actually is a special case of multi-channel decomposition. And then I tested the decompositions with synthetic data and field data, and verify in the time-frequency spectrum and frequency slice applications with high time-frequency resolution.The second over-complete time-frequency dictionary discussed in this PHD thesis was the attenuated-Ricker wavelet dictionary. Based on the classical Ricker wavelet, the atoms in the attenuated-Ricker wavelet dictionary were constructed through the nonstationary convolution in the time-frequency domain by adding the quality factor Q. The attenuated-Ricker wavelet can represents the energy attenuation of seismic wave in the subsurface media. The decomposition based on the attenuated-Ricker wavelet dictionary also can generate the sparse decomposition. But because the time-frequency locality is worse than Morlet wavelet atom, it is not recommended to use when constructing time-frequency distribution, but it can be used describe the absorption property of underground medium to by interpolation of the parameter Q from the decomposed atoms. In addition, based on the decomposition results, the attenuation can be compensated by rebuilding the Ricker wavelet simply and effectively.Thirdly, this thesis discussed the EMD dictionary. The empirical mode decomposition can be used to describe the nonstationary seismic signal. In fact,the method can also be viewed as a based on an extremely redundant dictionary. The EMD dictionary theoretically points out the corresponding time-frequency Dictionary of the empirical mode decomposition algorithm which has always been the lack of mathematical basis. Based on the EMD dictionary, in this thesis I introduced a new time-frequency decomposition method from the field of biological signal processing, namely the local mean decomposition. And I applied this method to the seismic data, and compared with the empirical mode decomposition from the view of the decomposition methods and the decomposed components. And we test both the decomposition in the application of time-frequency distribution and constant frequency slice.Based on the three over-complete time-frequency dictionary mentioned above, as to different research targets and demands, we can select corresponding sparse decomposition methods. This is the main research line of the sparse time-frequency decomposition for seismic data demonstrated in this thesis.