基于压缩感知和稀疏表示的地震数据重建与去噪
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摘要
随着油气勘探的不断深入,勘探目标区构造和环境越来越复杂,加剧了地震勘探数据的不规则和不完整情况,影响对资料的处理和解释,并最终影响油气判断。但是,受Nyquist采样定理限制,传统的重建方法对采样率要求较高,采集和采样也不能灵活适应实际环境,勘探成本较大。本文基于新发展的压缩感知理论,将地震勘探采集阶段的资料测量和处理阶段的数据重建有机结合起来,充分利用地震资料在字典变换域的稀疏化特征,发展了更加灵活的采样和去噪策略,在大幅降低采样率和节约成本的同时,获得了理想的处理效果。
根据近几年在信号处理领域得到完善并快速发展的压缩感知理论,远低于传统Nyquist采样率的不完整数据也能够得到理想重建。基于此理论框架,本文主要研究了地震数据压缩重建中的稀疏表示和采样格式两个关键问题。在稀疏表示方面,首先研究了常用的傅里叶基函数方法,并针对目前该类技术中完全随机采样的不足,发展了泊松碟采样格式,以控制采样间隔。接下来,采用能够更优表示地震数据的曲波变换,构建了基于曲波变换稀疏促进策略的地震数据重建技术,极大地提高了重建质量,也降低了对采样率的要求。在采样格式方面,本文在该领域首次引入具有蓝色噪声频谱特征的采样方法,对包括Jitter采样、泊松碟采样和最远点采样在内的该类方法进行了分析和研究,验证了此类方法的有效性,对地震资料采集和不完整数据重建都有重要指导意义。
在上述数据规则化过程中,不可避免地会引入人为噪声,同时,实际地震资料也常受噪声干扰,严重影响包括数据重建在内的处理和解释工作。传统的去噪方法(如变换域阈值法),会在地震波前附近导致不光滑畸变现象,影响地震资料的质量。本文将全变差最小化技术和曲波阈值方法相结合,在去除地震噪声的同时,压制了不光滑干扰现象。此外,为了改善当前变换基函数不能根据目标地震数据特征自适应调整的状况,本文引入了具有学习能力的超完备冗余字典思想,将字典的构造和地震数据去噪过程有机结合起来,在完成稀疏表示的同时,去除了地震噪声,取得了较好效果。
Along with the further exploration of oil and gas, the potential fields and conditions for exploration are becoming more complex, which often increasingly distorts the acquired seismic data sets to be incomplete and irregular. It will affect the following data processing and interpretation, and then the identification of oil and gas. However, due to the limit of Nyquist sampling theory, most traditional reconstruction techniques require high-rate samples, and the way of survey and sampling cannot be adjusted to the practical conditions properly, which will increase the exploration costs. Based on a newly developed theory named compressive sensing and sparse representations for seismic records, this thesis presents a compressed reconstruction technique with more effective sampling schemes and denoising strategies for seismic data processing, by combining the two steps of seismic exploration with data recording and recovery. Both sampling rate and cost can be reduced by this technique, as well as the data quality being improved.
According to the well-developed compressive sensing theory from signal processing field, it is even possible to recover extraordinarily incomplete data under its corresponding Nyquist rate. Based on this frame, firstly, this thesis studies two of the principal issues for compressed seismic data reconstruction, i.e., sparse representations and sampling schemes. As to the first issue, starting with Fourier basis, we use Poisson Disc sampling to control gaps between samples, which compensates drawbacks of the currently used random sampling. Further more, we employ curvelet transform, which is regarded to be the optimally sparse representation for seismic data, developing a curvelet-based recovery strategy by sparsity-promoting inversion, which requires much less samples as well as achieving higher-quality reconstruction. As to the second issue, this thesis introduces sampling schemes with blue noise spectrum into this field, including Jitter sampling, Poisson Disc sampling and Farthest Point sampling. We analyze their advantages and show the effectiveness through numerical experiments. These researches have great significances for seismic data acquisition and reconstruction.
During the process of data regularization mentioned above, some artificial noise is probably involved. In addition, the practical seismic profiles acquired are also often interfered by real noise. Both would affect seismic processing and interpretation, including data reconstruction. The traditional transform-based methods, e.g., thresholding in transformed domain, usually cause non-smooth distortions in the vicinity of discontinuities like wavefronts, which would confuse the expected seismic features. In this thesis, total variation minimization strategy is employed, combining with curvelet threshoding method, in order to suppress this phenomenon, and the involved noise is eliminated as well. Further more, in order to improve the current sparse representations which cannot be adjusted to the targeted seismic data adaptively, this thesis introduces the idea of learning overcomplete redundant dictionary to deal with seismic noise, which is shrunk during the training and constructing process of the dictionary.
根据近几年在信号处理领域得到完善并快速发展的压缩感知理论,远低于传统Nyquist采样率的不完整数据也能够得到理想重建。基于此理论框架,本文主要研究了地震数据压缩重建中的稀疏表示和采样格式两个关键问题。在稀疏表示方面,首先研究了常用的傅里叶基函数方法,并针对目前该类技术中完全随机采样的不足,发展了泊松碟采样格式,以控制采样间隔。接下来,采用能够更优表示地震数据的曲波变换,构建了基于曲波变换稀疏促进策略的地震数据重建技术,极大地提高了重建质量,也降低了对采样率的要求。在采样格式方面,本文在该领域首次引入具有蓝色噪声频谱特征的采样方法,对包括Jitter采样、泊松碟采样和最远点采样在内的该类方法进行了分析和研究,验证了此类方法的有效性,对地震资料采集和不完整数据重建都有重要指导意义。
在上述数据规则化过程中,不可避免地会引入人为噪声,同时,实际地震资料也常受噪声干扰,严重影响包括数据重建在内的处理和解释工作。传统的去噪方法(如变换域阈值法),会在地震波前附近导致不光滑畸变现象,影响地震资料的质量。本文将全变差最小化技术和曲波阈值方法相结合,在去除地震噪声的同时,压制了不光滑干扰现象。此外,为了改善当前变换基函数不能根据目标地震数据特征自适应调整的状况,本文引入了具有学习能力的超完备冗余字典思想,将字典的构造和地震数据去噪过程有机结合起来,在完成稀疏表示的同时,去除了地震噪声,取得了较好效果。
Along with the further exploration of oil and gas, the potential fields and conditions for exploration are becoming more complex, which often increasingly distorts the acquired seismic data sets to be incomplete and irregular. It will affect the following data processing and interpretation, and then the identification of oil and gas. However, due to the limit of Nyquist sampling theory, most traditional reconstruction techniques require high-rate samples, and the way of survey and sampling cannot be adjusted to the practical conditions properly, which will increase the exploration costs. Based on a newly developed theory named compressive sensing and sparse representations for seismic records, this thesis presents a compressed reconstruction technique with more effective sampling schemes and denoising strategies for seismic data processing, by combining the two steps of seismic exploration with data recording and recovery. Both sampling rate and cost can be reduced by this technique, as well as the data quality being improved.
According to the well-developed compressive sensing theory from signal processing field, it is even possible to recover extraordinarily incomplete data under its corresponding Nyquist rate. Based on this frame, firstly, this thesis studies two of the principal issues for compressed seismic data reconstruction, i.e., sparse representations and sampling schemes. As to the first issue, starting with Fourier basis, we use Poisson Disc sampling to control gaps between samples, which compensates drawbacks of the currently used random sampling. Further more, we employ curvelet transform, which is regarded to be the optimally sparse representation for seismic data, developing a curvelet-based recovery strategy by sparsity-promoting inversion, which requires much less samples as well as achieving higher-quality reconstruction. As to the second issue, this thesis introduces sampling schemes with blue noise spectrum into this field, including Jitter sampling, Poisson Disc sampling and Farthest Point sampling. We analyze their advantages and show the effectiveness through numerical experiments. These researches have great significances for seismic data acquisition and reconstruction.
During the process of data regularization mentioned above, some artificial noise is probably involved. In addition, the practical seismic profiles acquired are also often interfered by real noise. Both would affect seismic processing and interpretation, including data reconstruction. The traditional transform-based methods, e.g., thresholding in transformed domain, usually cause non-smooth distortions in the vicinity of discontinuities like wavefronts, which would confuse the expected seismic features. In this thesis, total variation minimization strategy is employed, combining with curvelet threshoding method, in order to suppress this phenomenon, and the involved noise is eliminated as well. Further more, in order to improve the current sparse representations which cannot be adjusted to the targeted seismic data adaptively, this thesis introduces the idea of learning overcomplete redundant dictionary to deal with seismic noise, which is shrunk during the training and constructing process of the dictionary.
引文
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