| 1. | High frequency approximate solution of wave equation of bit vibration source in seismic while drilling
随钻地震钻头震源波动方程的高频近似解法 |
| 2. | ( 2 ) the symplectic integrator method is applied to the high frequency asymptotic evolution of the wave equation based on maslov symplectic geometrical theory
( 2 )将辛算法运用到基于masiov ?辛几何理论的求解波动方程的高频近似方法中。 |
| 3. | Furthermore , there are complex structures such as the engine fans at the end of the inlets . it ' s hard to deal with such problems if we use high frequency method or low frequency numerical value method only
对于厘米波段雷达而言，进气道属于电大尺寸目标，其终端有涡轮叶片之类的复杂结构，单用高频近似法或低频数值法都难以解决。 |
| 4. | Such limit is not due to the method itself , but is due to the limits of the speed and memory of computers . at present , we mainly use the high - frequency approximate method to analyze the electrical - large size target whose shape is relatively regular
矩量法不适于分析电大尺寸的物体，这种限制不是由于方法本身，而是硕士学位论文凡1入ster ’ 5th卜515由于计算机速度与存储能力的限制。目前主要采用高频近似方法来研究电尺寸较大而形状相对规则的目标。 |
| 5. | But using the high - frequency approximate method to deal with the coupling of parts of electrical - large size target is troublesome as well as not accurate . combining the moment method and the high - frequency approximate method is a development trend and study way in the future
但高频近似方法对于电尺寸大而形状很复杂的散射体各部件之间的相对祸合处理起来有些麻烦且不很精确。将高频近似方法和数值方法(如矩量法)相结合，是以后的发展趋势和研究方向。 |
| 6. | The important parts of this work consist of : 1 . the high frequency asymptotic evaluation of wave equations in nonhomogeneous medium by maslov ' s method is systematically studied , and formulations of the high frequency asymptotic evaluation in nonhomogeneous medium which varying only in one direction are constructed
本论文的工作作为国家自然科学基金地震波传播与成像项目( no . 40174032 )的一部分，得到如下结果： (一)论文分析了利用maslov方法求解非均匀介质中波动方程高频近似解的基本原理和求解过程，构造了介质系数只在一个方向变化时波动方程高频近似解的通用计算公式。 |
| 7. | At the same time , as more and more radio sources have been set up , electromagnetic pollution in urban area becomes more serious , which is harmful to people ' s healthy and communication system so it is necessary to simulate the electromagnetic propagation in urban area by computer being an approximate hf method in evaluating em scattering ， the complex ray method （ crm ） is valuable in actual applications ， mainly benefited from its simple physical model ， convenient mathematical formulation and computational efficiency , especially with the scenes of scattering from complex objects based on the condition mentioned above , a hybrid ray model of the urban area electromagnetic wave propagation prediction was established with the foundation of ray tracing theory and complex ray theory
复射线技术作为一种求解波场问题的高频近似方法，由于其具有物理模型简单、数学处理方便、计算效率高等优点，在复杂的目标散射特性分析等应用领域中有着重要的应用价值。基于以上的情况，本文在射线追踪理论和复射线理论的基础上，为城区环境建立了混合射线预测模型。本文采用椭圆模型对已有的射线追踪方法进行加速，并将复射线理论应用到城区环境电波传播预测中，提出新的预测方法混合射线方法。 |
| 8. | Since the cause of caustics phenomena is that the tangent plane of lagrange submanifold in caustic fields is perpendicular to the original physical space , we solve the high frequency asymptotic problem in a new mixed space by changing the projecting direction , then we get the high frequency asymptotic solutions of wave equations efficiently near and on the caustics
由于出现焦散现象的原因在于lagrange子流形在该处的切平面与物理空间垂直，通过转换适当的投影方向，然后将这个投影方向上得到的高频近似解再变换回到原来的物理空间中，得到了在焦散附近适用的高频近似解。 |
| 9. | This thesis discusses maslov ' s method , wavelet transform and their applications to asymptotic evaluation of wave equations in high frequency fields . the method of solving wave equations in caustic domain by symplectic geometrical theory , and the method of simplifying two - dimension wave equations in slowly varying nonhomogeneous medium by wavelet - transform theory are proposed . the caustics phenomena of electromagnetic wave propagation in concave reflector , the singularities of caustics , and the method of computing wave fields in and far away from the caustics in concave reflector are also discussed
本论文探讨了maslov方法在波动方程高频近似中的应用及焦散区的具体求解方法；讨论了用小波变换化简二维非均匀缓变介质条件下的波动方程；本文还讨论了凹面反射的焦散现象、凹面反射焦散区的奇性种类，讨论了二、三维凹面反射波动场非焦散区、焦散区的计算方法。 |
| 10. | From 1920s up to now , various techniques and methods for wave field decomposition , propagation and migration / imaging have been well developed , such as the kirchhoff asymptotic method , frequency - wavenumber domain phase - shift and phase - shift - plus - interpolation methods , and the one - way wave equation based phase - screen and generalized screen methods , etc . wave field extrapolation in these methods is implemented based on the expansion of the wave field by sets of basic functions like spatial fourier harmonies , modes , and green ' s functions
自上个世纪二十年代至今，波场分解、传播与偏移成像技术经历了将近一个世纪的发展，形成了多种不同的方法，如kirchhoff波动方程高频近似解方法，频率-波数域的相移( phase - shift )方法和相移-内插( pspi )方法，以及在混合域中基于单向波动方程的相位屏、广义屏方法等。 |
