基于贪婪算法的地震数据稀疏时频分解方法研究

发布时间：2018-01-25 20:30

本文关键词： 稀疏时频分解谱分解过完备时频字典正交匹配追踪高分辨率　出处：《吉林大学》2016年博士论文　论文类型：学位论文

【摘要】：随着我国油气资源勘探开发程度的深入,勘探目标渐渐由常规的构造油气藏向非常规、隐蔽、地层和岩性等复杂油气藏等过渡。这既是挑战,也是我们发展新的方法和技术以进一步完善对地下油气储层的认识和适应新勘探要求的契机。在这种前提下,地震勘探作为油气资源勘探的重要手段之一,其原有的采集、处理和解释技术都需要向提供更准确、更丰富和更高分辨率地下信息的方向发展。随着勘探区域的地下介质情况较以往更加复杂,地震信号的非平稳性往往也愈加明显。传统的谱分解技术是描述和分析地震数据非平稳性的常规工具,但已逐渐不能满足人们对新勘探环境下分辨率和精度的要求。传统的谱分解技术实际上可以视为基于一组具有时频局部性的基对地震信号进行分解,但由于基的选择及分解方式的选取等原因,其分解结果往往不够稀疏,这也是限制传统谱分解技术分辨率一个重要因素。本文认为如果能够选择与地震信号固有的时频属性更加吻合的基信号,并选取更加稀疏的分解方式,则地震信号可以被更加稀疏的分解为若干子成分信号,基于分解结果再计算时频分布能够一定程度上提高时频分布的分辨率。此外,本文所讨论稀疏时频分解不仅仅限于提高时频谱的分辨率,而是更关注如何从分解出的子成分信号中提取更多信息,获得更丰富的地下介质信息,增加解释能力,为生产和开发提供进一步的技术支持。本文首先回顾了经典的傅里叶变换和谱分解技术,并由此引出了地震信号稀疏时频分解方法。一组基信号(非正交基)的数目远多于信号维数,且具有时频局部属性的基信号的集合被称为过完备时频字典。本文列举了多种基本的过完备时频字典,并着重讨论了其中三种过完备时频字典,及相应的稀疏时频分解方法。因为这三种字典都比较复杂,且过于冗余,本文主要选择基于贪婪算法的稀疏时频分解方法。这三种过完备时频字典分别为传统的Morlet小波字典,本文新构造的衰减Ricker子波字典,以及由数学领域引入的EMD字典。上述三种过完备时频字典,由于其中原子性质的不同,各自描述地震信号的角度也不同。对于其中的每一种过完备时频字典,按照从认识到改进再到应用的顺序,本文会先从字典中原子信号的性质以及相应过完备时频字典的构造开始介绍,然后讨论适合该过完备时频字典的具体稀疏时频分解方法(本文中主要指基于贪婪算法的稀疏时频分解,下同),最后讨论其在地震数据处理和解释中的应用。本文讨论的第一种过完备时频字典为传统的Morlet小波字典。因为Morlet小波原子能够较好的表征地震子波在地下介质中传播时所发生的吸收衰减和频散现象,所以常被用于匹配追踪等常规的地震数据稀疏时频分解算法中。本文在现有的基于Morlet小波字典的单地震道匹配追踪算法和多地震道匹配追踪算法中引入了基于最小二乘问题描述的正交匹配追踪的思想,衍生出两种新的基于贪婪算法的稀疏时频分解方法,本文称为单地震道正交匹配追踪算法和多地震道正交匹配追踪算法,并指出前者为后者一个特例。结合合成地震记录和实际数据,验证了上述两种新算法能够更加稀疏地对地震数据进行时频分解。最后通过时频谱和频率切片等应用验证了基于Morlet小波字典的稀疏时频分解较传统谱分解方法能够一定程度上提高分辨率。本文讨论的第二种过完备时频字典为衰减Ricker子波字典。该字典中的原子是本文新提出的一种时频原子,通过在经典的Ricker子波的基础上加入了描述地震波吸收衰减的品质因子Q,从而使该时频原子能够表征传播过程中的时变地震子波。基于衰减Ricker子波字典,采用单地震道正交匹配追踪和多地震道正交匹配追踪的分解方式同样可以稀疏地分解地震数据。由于该原子的时频聚焦性不如Morlet小波,本文不推荐采用其描述地震信号的时频分布,而是利用基于该字典分解出的各个子成分信号所对应的参数Q,通过插值对地下介质中地震波的吸收衰减进行描述。与谱比法求取Q值等传统方法相比,这样估计Q值的方式不再需要假设地下介质为均匀吸收模型,且具有一定的自适应性。此外,应用基于衰减Ricker子波字典的稀疏时频分解方法对地震信号进行分解时,能够通过反推衰减前的Ricker子波的方法对地震波吸收衰减进行补偿,简便有效。本文讨论的第三种过完备时频字典为EMD字典。经验模态分解近年来被引入并广泛地应用于非平稳地震信号的描述中,但其分解方式仍是基于经验,缺乏有力的数学证明。实际上该方法也可视为一种基于极其冗余的过完备时频字典的稀疏时频分解。本文从数学领域引入了EMD字典,该字典从理论上指明了一直以来缺少数学依据的经验模态分解算法所对应的过完备时频字典。基于该字典的描述,本文另外从生物信号领域引入了一种新的稀疏时频分解方法——局部均值分解,并通过合成地震记录及实际地震信号进行测试,从分解方式和分解结果上比较了其与经验模态分解的异同,同时讨论上了述两种基于EMD字典的稀疏时频分解方法在计算时频分布和提取地震分量剖面等方面中的应用。基于上述的三种过完备时频字典,针对不同的研究目标和需求,选取不同的字典及配套的地震数据稀疏时频分解方法,即构成了本次博士论文中基于贪婪算法的地震数据稀疏时频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.

【学位授予单位】：吉林大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：P631.4

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