【作者】 吉宏泰；

【导师】 孙建国；

【作者基本信息】 吉林大学 ， 地球探测与信息技术， 2010， 硕士

【摘要】 本文的研究工作主要有两个方面:分析了传统单程波动方程偏移中,采用不同方法近似相移算子进行偏移,其偏移像场能量变化的特点;在Kirchhoff真振幅理论的基础上,总结性的介绍了真振幅单程波动方程偏移方法,以克服传统单程波动方程偏移成像缺乏波场振幅信息的缺点。在研究传统单程波动方程偏移算法时,通过对比分析不同近似相移算子相位特点,叠后偏移单位脉冲响应、子波拉伸以及频谱等相关动力学特性。得出由不同近似相移算子计算后的偏移像场能量变化特点。通过在均匀介质条件下的研究,可为生产实践提供方法选择的依据。在总结学习前人提出的Kirchhoff真振幅理论的基础上,由拟微分算子的象征意义、定理以及单程波动方程组的耦合性,在二维条件下推导出真振幅条件下的上下行波方程组。并总结性的说明了其与全程波动方程具有相同的程函方程和运输方程。说明改造后的单程波动方程组具有保幅特性是真振幅偏移,能够提供更加可靠的地震成像信息。根据二维情况下真振幅单程波动方程组的特点,对传统单程波动方程偏移中的傅立叶有限差分法(FFD)进行改进。更多还原

【Abstract】 One-way wave equation migration is an extremely effective seismic migration imaging algorithm, with the method of classic Kirchhoff integral migration, it avoid the hypothesis of the asymptotic wave equation. Compared with reverse-time migration, one-way wave equation is efficient, and saves the computer memory space. One-way wave equation migration is mainly about the equation of square root operator (i.e. phase-shift operator), use different methods of singularities, fit differential phase shift operators are approaching, in order to improve the calculation precision of one-way wave equation, and enhance the ability to complex geological conditions. This article is mainly aimed at the method of different transmission shift operator and impulse responses of one-way equation, and analysis a series of related dynamic properties of migration imaging. According to the phase shift operator of one-way wave equation methods, we can divide it into three different methods: the frequency domain (ω-kdomain), time - space domains (t-xdomain) and mixed domains (ω-xdomain). The algorithm ofω-kdomain is simpler, we can directly recursive calculation according to the extrapolating. Extrapolating of t-xdomain algorithm contains 2D convolution computation, we can use FFT to manage in theω-xdomain, only use one convolution. Nowωplays a part of parameter. In theω-xdomain we also use FFT conversion,ω-x domain and t-x domain method is a relatively simple extrapolation, only consider for smooth surface that it is independent on time. Whenω-xfield changes toω-kdomain, although simplified calculation, but lost flexibility, and lateral velocity variation cannot handle. The biggest advantage in theω-xdomain is aimed at that different frequency components can use different effective, in addition, the wavelet is calculated, has a good flexibility and adaptability.Under the condition of uneven medium, impulse response analysis method, different direction due to the t-xdomain of wave propagation, its velocity different wave field rays not perpendicular to face, including from Persia array of semicircle arc shape closed curve which areas for development, this area was invalid part. Disperse phenomenon is in phase shift operator due to the t-xdomain of solving the approximate expansion. Considering the resolution of the wavelet controlled by three factors, through the comparison between the mixed domain and t-xdomain finite difference method,ω-kdomain has a high resolution of wavelet, but t-xdomain finite difference method of oscillation amplitudes tail in the initial sampling points bigger error, so the mixed domain has an advantage in improving the resolution of wavelet. Through the spectrum analysis, it shows that the one-way wave operators applicationω-kdomain to earthquake has advantages of lighting, but because of the calculation principle , its speed limit is only in the case without change of lateral velocity. Mixed domain operator can reserve energy though relatively weak, but its complex geological conditions for earthquake lighting has good effect. t-xdomain can complex medium environment, and maintain relatively mixed domain method more energy, but this kind of method is limited, only can use in some of the application of geological model said illumination analysis.By understanding the different algorithms of adaptive, can provide a reference basis for practical production, also provide information for further improved algorithm. Due to the accuracy of the migration imaging decision in actual geological conditions and taking the compensation method is also selected processing method. Under the principle of classical significance on the migration technology can simply to spread effect is relatively wave propagation lag compensation, accurately reflect the phase information, but did not consider wave field amplitude adjustment problems. Aim at one-way wave, geophysicists raise that we can use the theory of true amplitude improving traditional one-way equation method. This paper introduces the theory of one-way wave equation under the algorithms and process improvements based on true amplitude. It sufficiently shows that, true amplitude one-way equation is exact, rotate, and enough to provide more accurate and more meaningful data for seismic exploration.更多还原