| 1. | Euler ' s equation in the wavenumber domain
频率域中的欧拉方程 |
| 2. | Euler ' s equation in wavenumber domain has been derived based on its spatial expression and tested by gravity and magnetic anomalies of sphere model respectively
摘要基于空间域中的欧拉方程，推导出频率域中的欧拉方程。 |
| 3. | Chapter 4 discusses how to process live data by adopting wavenumber domain ( w _ k ) algorithm and its simplified algorithm , and achieves satisfying results
第四章采用波数域及其简化算法分别对星载旁视sar和机载前斜视sar真实数据进行处理，取得了预期的结果。 |
| 4. | Chapter 3 analyzes the principle of wavenumber domain ( w _ k ) algorithm and simplified wavenumber domain algorithm in detail . with the realization of emulation , performance of these two methods is compared
第三章详细分析了波数域成像算法及其简化算法的原理，采用上述两种方法进行了仿真，并对两者的性能作比较。 |
| 5. | Range - doppler algorithm is a one dimensional algorithm . wavenumber domain algorithm and chirp scaling algorithm are two dimensional algorithms . this paper discusses their theory and processing flow
Range - doppler算法是一种一维处理算法，波数域算法和chirpscaling算法是二维联合处理算法，本文讨论了它们的原理及流程。 |
| 6. | This paper discusses several questions about imaging algorithms of sar . mainly it discusses three imaging algorithms - range - doppler algorithm , wavenumber domain algorithm and chirp scaling algorithm . still it discusses the assistant processing algorithms of imaging algorithms - doppler centroid estimation algorithms and autofocus algorithms
本文论述了合成孔径雷达( sar )成像算法方面的一些问题，主要讨论了三种成像算法? ? - range - doppler算法，波数域算法及chirpscaling算法，并讨论了成像算法的辅助处理算法? ?中心频率估计算法及自聚焦算法。 |
| 7. | In term of analyzing and summarizing the existing achievement , propose an advanced and practical wavefield extrapolation operator and arithmetic of forward modeling and migration , which obtain numerical simulation and analysis completely and systemically and exploited new field of fractured reservoir seismic wavefield numerical simulation and applicationin in frequency - wavenumber domain
在总结、分析前人研究成果的基础上，提出了具有前瞻性和实用性的波场延拓算子与正演、偏移算法，较系统全面地进行了数值计算与分析，开辟了频率?波数域缝洞储层地震波场数值模拟与应用的新领域。 |
| 8. | The paper concentrates on seismic wave - field forward modeling and migration for the fractured reservoir . it researches the wavefield extrapolation operator for lateral variation of velocity , design four theoretical models and seven practical models with fracture and cavity . base on the progenitor , in the frequency - wavenumber domain with the pspi wavefield extrapolation operator and arithmetic of forward modeling and migration that applied lateral variation of velocity which is strong , the paper obtains the result of numerical simulation and the wavefield characteristic by the way of the forward modeling and depth migration of poststack seismic wavefield
本文围绕缝洞储层地震波场正演与偏移问题，研究了适用于横向变速波场延拓算子，建立了四个理论的缝洞模型和七个实际的缝洞模型，在总结、分析前人的研究成果的基础上，利用适合横向速度剧烈变化的相移加插值的波场延拓算子，在频率?波数域对上述的地质模型进行正演、偏移处理，最后得到了缝洞储层地震波场的一些特征。 |
| 9. | Author , starts from the one - way wave equation of wavefield extrapolation , research the relationship and transform condition of wavefield extrapolation operators , and propose the steady variational reference slowness rytov approximation general screen wavefield extrapolation operator ( vrselrf ) which can adapt severe lateral velocity variations , in frequency - wavenumber domain , and the improved wavefield extrapolation scheme , also give the method to improve the computation efficiency . the achievement establishes the theoretic basis of the whole research
首先，从波场延拓的单程波方程出发，系统地研究了频率波数域的波场延拓算子之间的相互关系和转换条件并在此基础上提出了能适应剧烈横向变速的频率波数域稳定的变参考慢度rytov近似广义屏波场延拓算子( vrselrf )和部分波场延拓改进方案及提高运算效率的措施，为整个研究打下理论基础。 |
| 10. | Author , secondly , starts from the approximate expandness of square root operator , perform mathematical calculations for finite difference operator in frequency - space domain , fourier finite difference operator in mixing domain ( frequency - space and frequency - wavenumber domain ) and general screen operator in mixing domain , compare and discuss their precision of their wavefield , adaptability for lateral velocity variations , computation efficiency and stability . thirdly , author , applies the steady variational reference slowness rytov approximation general screen wavefield extrapolation operator ( vrselrf ) in frequency - wavenumber domain , to the prestack and poststack forward modeling and depth migration
第二，从平方根算子的近似展开出发对频率?空间域的有限差分算子、混合域(频率?空间域；频率?波数域)的fourier有限差分算子、混合域的广义屏算子进行了推导并对其波场描述精度、对横向变速的适应性、计算效率和稳定性进行了比较与评述。 |
