多分辨分析理论与深度成像和地震数据处理
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摘要
地震数据处理,特别是对波动方程地震偏移成像方法的研究是二十世纪后期研究的主要方向,建立在波场反向外推基础上的波动方程地震偏移成像方法取得了很大的成功,但随着地球物理勘探的深入发展,这些方法还不能满足地球物理勘探的要求。另一方面,随着勘探技术的提高,使得要保存和处理的地震数据量不断膨胀,如何节省存贮地震数据所需空间(物理空间和计算空间),已成为地震勘探工作中一个非常关心的问题。本研究涉及到地球物理科学、理论数学、计算数学、信号处理、计算机技术等多门学科,并仍然是今后需要深入研究的重要课题,研究有较好的理论与实际价值。
随着小波分析的发展,近年来发展起来的Ridgelet变换是定义在Radon域上的一维小波变换,它是基于现代调和分析的理论和方法,利用一系列高维“脊函数”迭加的实现了对高维(大于0维)奇性有效描述。由于Ridgelet变换同时具有小波具有良好的局部性与Radon变换的直线(或平面)奇性分析能力,而反映地质构造的地震观测数据具有的沿直线(或平面)的奇性特征,使得Ridgelet变换成为地震数据有效的描述和分析工具。
论文提出了更能表征地球物理结构特征的多分辨地震偏移成像外推计算方法,建立了基于Ridgelet变换的多分辨地震偏移成像外推计算方法,论文理论及实验结果表明方法能有效地应用于地震成像,能较好、较精确地解决或反映地球复杂结构的局部特征,能有效
Seismic data processing methods, especially the seismic migration imaging methods for wave equation, are the main research directions in late 20th century. The seismic migration imaging methods, based on the inverse wave field extrapolation for the wave equation, had made a great success. As the development of geophysics, these imaging methods were not satisfied the needs of seismic exploration. Many new methods are put forward and applied to seismic exploration. Another side, with the progress of seismic exploration technologies, a huge amount of data need to store and process. How to save the spaces (physical spaces and computing spaces) is becoming more and more concerned in seismic exploration works. To resolve those problems a lot of knowledge, such as geophysics, pure mathematics, computing mathematics, signal processing, computer technology, et. al, were embroiled. They will be significant topics for future researches. So the research has its values of theory and practice.The ridgelet transform which was developed from wavelet analysis, was defined as one dimensional wavelet transform on the Radon domain. Based on the theories and methods of recent harmonic analysis, combined with a serial of high dimension ridge functions iterative approach, it can represent the singularities (more than zero dimension singularities) of higher space. Because ridgelet transform has not only good local properties of wavelet, but also line (or plane) singularities analysis abilities of Radon transform, and the observing seismic data just has this properties along line (or plane) singularities. Therefore, ridgelet transform can be as a good representation tool of seismic data.The multi-scale seismic migration inverse extrapolation imaging method, applied ridgelet transform, was proposed in this thesis. This
method can describe the structure of the wave field more efficiently. The theoretical analysis and experimental results were showed that this method was more powerful to represent these complex local singularities and more accurate to describe the local characters of the physical geography structure. It is a development of using wavelet analysis in seismic imaging, which often failed when it is used to represent the higher singularities, such as linear (or curvilinear), plane (or curved surface) singularities.Using wavelet non-uniform sampling, a new high multiresolution imaging method, which based on the integral solution of wave equation, was introduced. Appling the multi-resolution analysis theory, the multi-resolution wavelet representation for the second partial differential operator was deduced, and was applied to wave equation imaging treatment. The 2D/3D wavelet domain - frequency domain - depth imaging method (WFD) has been established. By applying this method to synthetic models and practical seismic data imaging, good results were obtained.The Local Orthonormal Finite Ridgelet Transform (LFRIT) was studied. Applied LFRIT or combined wavelet with LFRIT, some new seismic data (or image) de-nosing and compression methods were proposed in this thesis. The approaches can not only deal with line (or plane) singularities, but also deal with curve (or curved surface) singularities. Experimental results showed that it could achieve a higher compression ratio and good reconstructed image than Wavelet.
随着小波分析的发展,近年来发展起来的Ridgelet变换是定义在Radon域上的一维小波变换,它是基于现代调和分析的理论和方法,利用一系列高维“脊函数”迭加的实现了对高维(大于0维)奇性有效描述。由于Ridgelet变换同时具有小波具有良好的局部性与Radon变换的直线(或平面)奇性分析能力,而反映地质构造的地震观测数据具有的沿直线(或平面)的奇性特征,使得Ridgelet变换成为地震数据有效的描述和分析工具。
论文提出了更能表征地球物理结构特征的多分辨地震偏移成像外推计算方法,建立了基于Ridgelet变换的多分辨地震偏移成像外推计算方法,论文理论及实验结果表明方法能有效地应用于地震成像,能较好、较精确地解决或反映地球复杂结构的局部特征,能有效
Seismic data processing methods, especially the seismic migration imaging methods for wave equation, are the main research directions in late 20th century. The seismic migration imaging methods, based on the inverse wave field extrapolation for the wave equation, had made a great success. As the development of geophysics, these imaging methods were not satisfied the needs of seismic exploration. Many new methods are put forward and applied to seismic exploration. Another side, with the progress of seismic exploration technologies, a huge amount of data need to store and process. How to save the spaces (physical spaces and computing spaces) is becoming more and more concerned in seismic exploration works. To resolve those problems a lot of knowledge, such as geophysics, pure mathematics, computing mathematics, signal processing, computer technology, et. al, were embroiled. They will be significant topics for future researches. So the research has its values of theory and practice.The ridgelet transform which was developed from wavelet analysis, was defined as one dimensional wavelet transform on the Radon domain. Based on the theories and methods of recent harmonic analysis, combined with a serial of high dimension ridge functions iterative approach, it can represent the singularities (more than zero dimension singularities) of higher space. Because ridgelet transform has not only good local properties of wavelet, but also line (or plane) singularities analysis abilities of Radon transform, and the observing seismic data just has this properties along line (or plane) singularities. Therefore, ridgelet transform can be as a good representation tool of seismic data.The multi-scale seismic migration inverse extrapolation imaging method, applied ridgelet transform, was proposed in this thesis. This
method can describe the structure of the wave field more efficiently. The theoretical analysis and experimental results were showed that this method was more powerful to represent these complex local singularities and more accurate to describe the local characters of the physical geography structure. It is a development of using wavelet analysis in seismic imaging, which often failed when it is used to represent the higher singularities, such as linear (or curvilinear), plane (or curved surface) singularities.Using wavelet non-uniform sampling, a new high multiresolution imaging method, which based on the integral solution of wave equation, was introduced. Appling the multi-resolution analysis theory, the multi-resolution wavelet representation for the second partial differential operator was deduced, and was applied to wave equation imaging treatment. The 2D/3D wavelet domain - frequency domain - depth imaging method (WFD) has been established. By applying this method to synthetic models and practical seismic data imaging, good results were obtained.The Local Orthonormal Finite Ridgelet Transform (LFRIT) was studied. Applied LFRIT or combined wavelet with LFRIT, some new seismic data (or image) de-nosing and compression methods were proposed in this thesis. The approaches can not only deal with line (or plane) singularities, but also deal with curve (or curved surface) singularities. Experimental results showed that it could achieve a higher compression ratio and good reconstructed image than Wavelet.
引文
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