本文關(guān)鍵詞： 稀疏時頻分解 譜分解 過完備時頻字典 正交匹配追蹤 高分辨率　出處：《吉林大學》2016年博士論文　論文類型：學位論文

【摘要】：隨著我國油氣資源勘探開發(fā)程度的深入,勘探目標漸漸由常規(guī)的構(gòu)造油氣藏向非常規(guī)、隱蔽、地層和巖性等復雜油氣藏等過渡。這既是挑戰(zhàn),也是我們發(fā)展新的方法和技術(shù)以進一步完善對地下油氣儲層的認識和適應新勘探要求的契機。在這種前提下,地震勘探作為油氣資源勘探的重要手段之一,其原有的采集、處理和解釋技術(shù)都需要向提供更準確、更豐富和更高分辨率地下信息的方向發(fā)展。隨著勘探區(qū)域的地下介質(zhì)情況較以往更加復雜,地震信號的非平穩(wěn)性往往也愈加明顯。傳統(tǒng)的譜分解技術(shù)是描述和分析地震數(shù)據(jù)非平穩(wěn)性的常規(guī)工具,但已逐漸不能滿足人們對新勘探環(huán)境下分辨率和精度的要求。傳統(tǒng)的譜分解技術(shù)實際上可以視為基于一組具有時頻局部性的基對地震信號進行分解,但由于基的選擇及分解方式的選取等原因,其分解結(jié)果往往不夠稀疏,這也是限制傳統(tǒng)譜分解技術(shù)分辨率一個重要因素。本文認為如果能夠選擇與地震信號固有的時頻屬性更加吻合的基信號,并選取更加稀疏的分解方式,則地震信號可以被更加稀疏的分解為若干子成分信號,基于分解結(jié)果再計算時頻分布能夠一定程度上提高時頻分布的分辨率。此外,本文所討論稀疏時頻分解不僅僅限于提高時頻譜的分辨率,而是更關(guān)注如何從分解出的子成分信號中提取更多信息,獲得更豐富的地下介質(zhì)信息,增加解釋能力,為生產(chǎn)和開發(fā)提供進一步的技術(shù)支持。本文首先回顧了經(jīng)典的傅里葉變換和譜分解技術(shù),并由此引出了地震信號稀疏時頻分解方法。一組基信號(非正交基)的數(shù)目遠多于信號維數(shù),且具有時頻局部屬性的基信號的集合被稱為過完備時頻字典。本文列舉了多種基本的過完備時頻字典,并著重討論了其中三種過完備時頻字典,及相應的稀疏時頻分解方法。因為這三種字典都比較復雜,且過于冗余,本文主要選擇基于貪婪算法的稀疏時頻分解方法。這三種過完備時頻字典分別為傳統(tǒng)的Morlet小波字典,本文新構(gòu)造的衰減Ricker子波字典,以及由數(shù)學領(lǐng)域引入的EMD字典。上述三種過完備時頻字典,由于其中原子性質(zhì)的不同,各自描述地震信號的角度也不同。對于其中的每一種過完備時頻字典,按照從認識到改進再到應用的順序,本文會先從字典中原子信號的性質(zhì)以及相應過完備時頻字典的構(gòu)造開始介紹,然后討論適合該過完備時頻字典的具體稀疏時頻分解方法(本文中主要指基于貪婪算法的稀疏時頻分解,下同),最后討論其在地震數(shù)據(jù)處理和解釋中的應用。本文討論的第一種過完備時頻字典為傳統(tǒng)的Morlet小波字典。因為Morlet小波原子能夠較好的表征地震子波在地下介質(zhì)中傳播時所發(fā)生的吸收衰減和頻散現(xiàn)象,所以常被用于匹配追蹤等常規(guī)的地震數(shù)據(jù)稀疏時頻分解算法中。本文在現(xiàn)有的基于Morlet小波字典的單地震道匹配追蹤算法和多地震道匹配追蹤算法中引入了基于最小二乘問題描述的正交匹配追蹤的思想,衍生出兩種新的基于貪婪算法的稀疏時頻分解方法,本文稱為單地震道正交匹配追蹤算法和多地震道正交匹配追蹤算法,并指出前者為后者一個特例。結(jié)合合成地震記錄和實際數(shù)據(jù),驗證了上述兩種新算法能夠更加稀疏地對地震數(shù)據(jù)進行時頻分解。最后通過時頻譜和頻率切片等應用驗證了基于Morlet小波字典的稀疏時頻分解較傳統(tǒng)譜分解方法能夠一定程度上提高分辨率。本文討論的第二種過完備時頻字典為衰減Ricker子波字典。該字典中的原子是本文新提出的一種時頻原子,通過在經(jīng)典的Ricker子波的基礎上加入了描述地震波吸收衰減的品質(zhì)因子Q,從而使該時頻原子能夠表征傳播過程中的時變地震子波�；谒pRicker子波字典,采用單地震道正交匹配追蹤和多地震道正交匹配追蹤的分解方式同樣可以稀疏地分解地震數(shù)據(jù)。由于該原子的時頻聚焦性不如Morlet小波,本文不推薦采用其描述地震信號的時頻分布,而是利用基于該字典分解出的各個子成分信號所對應的參數(shù)Q,通過插值對地下介質(zhì)中地震波的吸收衰減進行描述。與譜比法求取Q值等傳統(tǒng)方法相比,這樣估計Q值的方式不再需要假設地下介質(zhì)為均勻吸收模型,且具有一定的自適應性。此外,應用基于衰減Ricker子波字典的稀疏時頻分解方法對地震信號進行分解時,能夠通過反推衰減前的Ricker子波的方法對地震波吸收衰減進行補償,簡便有效。本文討論的第三種過完備時頻字典為EMD字典。經(jīng)驗模態(tài)分解近年來被引入并廣泛地應用于非平穩(wěn)地震信號的描述中,但其分解方式仍是基于經(jīng)驗,缺乏有力的數(shù)學證明。實際上該方法也可視為一種基于極其冗余的過完備時頻字典的稀疏時頻分解。本文從數(shù)學領(lǐng)域引入了EMD字典,該字典從理論上指明了一直以來缺少數(shù)學依據(jù)的經(jīng)驗模態(tài)分解算法所對應的過完備時頻字典�；谠撟值涞拿枋�,本文另外從生物信號領(lǐng)域引入了一種新的稀疏時頻分解方法——局部均值分解,并通過合成地震記錄及實際地震信號進行測試,從分解方式和分解結(jié)果上比較了其與經(jīng)驗模態(tài)分解的異同,同時討論上了述兩種基于EMD字典的稀疏時頻分解方法在計算時頻分布和提取地震分量剖面等方面中的應用�；谏鲜龅娜N過完備時頻字典,針對不同的研究目標和需求,選取不同的字典及配套的地震數(shù)據(jù)稀疏時頻分解方法,即構(gòu)成了本次博士論文中基于貪婪算法的地震數(shù)據(jù)稀疏時頻分解方法的研究框架。
[Abstract]:As China's oil and gas exploration and development of deep exploration target, gradually constructed by conventional oil gas reservoir to unconventional, hidden, stratigraphic and lithologic reservoirs and other complex transition. This is a challenge, and we develop new methods and technologies to further improve the understanding of the underground oil reservoir and adaptation new exploration opportunities. In this context, as an important means of seismic exploration of oil and gas exploration, the acquisition, processing and interpretation techniques are needed to provide more accurate, more and more high resolution direction. With the information of underground underground media exploration area is more complex, non stability of seismic signal is more obvious. The traditional spectral decomposition technique is to describe and analyze the seismic data of unconventional tools of stationarity, but has not been able to meet the people on the new exploration environment resolution The requirements of precision and. Spectral decomposition technique can actually be viewed as a group of time-frequency localization based on seismic signal decomposition based on the traditional, but due to the selection of the base and the decomposition mode selection, the decomposition results are not sparse, this is also the limit of traditional spectrum is an important factor in solution resolution. This paper argues that if can signal time-frequency attribute selection and seismic signal inherent more consistent, and select more sparse decomposition, the seismic signal can be more sparse decomposition into several sub components of the signal, then calculate the decomposition results of time-frequency distribution can be improved to a certain extent, the resolution of time-frequency distribution based on this paper. In addition, the sparse time-frequency decomposition not only improve the resolution of spectrum, but pay more attention to how to extract more information from the decomposition of sub components in the signal, get rich The underground media information, increase the ability to explain, provide technical support for the production and development. This paper firstly reviews the classical Fourier transform and spectral decomposition technology, and thus leads to the seismic signal sparse time-frequency decomposition method. A set of base signal (non orthogonal basis) the number of far more than the dimension of signal collection, and has a base signal the local time-frequency property called overcomplete time-frequency dictionary. The paper enumerates several basic overcomplete time-frequency dictionary, and mainly discusses the three overcomplete time-frequency dictionary, and the corresponding sparse frequency decomposition method. Because these three dictionaries are more complex, and too redundant, this paper select the sparse frequency decomposition based on greedy algorithm methods. These three kinds of overcomplete time-frequency dictionaries were Morlet wavelet dictionary tradition, the newly proposed Ricker wavelet attenuation dictionary, and by the field of mathematics into the word EMD Three. The code over complete time-frequency dictionary, because the atoms of different nature, their description of seismic signal angle is also different. For each kind of overcomplete time-frequency dictionary which, according to the application from understanding to improve the order, this paper will start from the dictionary of atoms in the nature of the signal and the corresponding overcomplete when the structure frequency dictionary began, and then discuss the specific for overcomplete sparse Frequency Dictionary of time-frequency decomposition method (this paper mainly refers to the sparse greedy algorithm based on time-frequency decomposition, the same below), and discuss its application in seismic data processing and interpretation. This paper discusses in the first over complete time-frequency dictionary as the traditional Morlet wavelet dictionary. Absorption attenuation and dispersion phenomena for characterization of seismic wavelet Morlet wavelet atom can spread in the underground media occurs, is often used for matching tracking routine Seismic data sparse time-frequency decomposition algorithm. Based on the single Morlet seismic wavelet dictionary matching pursuit algorithm and multi seismic matching pursuit algorithm introduced the orthogonal least squares problem description matching pursuit based on the idea of based on existing, derived from the two frequency decomposition method of sparse greedy algorithm based on the new. As a single seismic channel orthogonal matching pursuit algorithm and multi seismic orthogonal matching pursuit algorithm, and points out that the former is the one exception. Combined with the actual data and the synthetic seismic records, verification of the two new algorithms can be more sparse for seismic data time-frequency decomposition. Finally verify the sparse wavelet dictionary based on Morlet compared with the traditional frequency decomposition spectral decomposition method can to some extent improve the resolution by spectrum and frequency. This paper discusses the application of section second overcomplete time-frequency dictionary for failure By Ricker wavelet dictionary. The dictionary of atoms is a new time-frequency atom in this paper, based on the classical Ricker wavelet to describe seismic wave absorption and attenuation quality factor Q, so that the time-frequency atom can characterize the propagation process of time-varying seismic wavelet Ricker wavelet dictionary based on attenuation. Using single seismic channel, orthogonal matching pursuit and orthogonal matching decomposition of seismic trace can also be sparse decomposition of seismic data. The time-frequency focus than Morlet wavelet of the atom, it is not recommended to use the description of the time-frequency distribution of seismic signal, but the use of Q parameters corresponding to different components of the signal decomposition dictionary based on the, based on seismic wave attenuation in underground medium interpolation description. Compared with the spectral ratio method to calculate the Q value of the traditional method, so the estimation of Q no longer need fake Set the underground medium for uniform absorption model, and has certain adaptability. In addition, the application of sparse dictionary based on attenuation of Ricker wavelet time-frequency decomposition method to decompose the seismic signal, by backstepping before decaying Ricker wavelet to seismic wave absorption and attenuation in compensation, simple and effective. This paper discusses the third kinds of complete time-frequency dictionary EMD dictionary. EMD in recent years is introduced and applied to non-stationary seismic signal description, but its decomposition is still based on experience, lack of proof of strong mathematics. In fact this method can be regarded as a kind of extremely redundant overcomplete sparse frequency decomposition based on time-frequency dictionary. This paper introduces the EMD dictionary from the field of mathematics, the dictionary has been pointed out the lack of empirical mode decomposition algorithm for the mathematical basis of the corresponding overcomplete time-frequency dictionary from the theory base. In the dictionary described in this paper from the biological signal field by introducing a new sparse frequency decomposition method, local mean decomposition, and tested by synthetic seismogram and actual seismic signals from the decomposition and the decomposition results were compared with the empirical mode decomposition and discuss the similarities and differences of the two a sparse EMD dictionary based on time-frequency decomposition method in the calculation of time-frequency distribution and extraction of components and other aspects in the application of seismic profile. Three kinds of overcomplete time-frequency dictionary based on the above, according to the research objectives and requirements of different frequency decomposition methods, seismic data sparse dictionary and matching different, which constitute the research the framework of this doctoral thesis in seismic data sparse greedy algorithm based on time-frequency decomposition method.

【學位授予單位】：吉林大學
【學位級別】：博士
【學位授予年份】：2016
【分類號】：P631.4

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