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41.
42.
The common-ray approximation eliminates problems with ray tracing through S-wave singularities and also considerably simplifies
the numerical algorithm of the coupling ray theory for S waves, but may introduce errors in travel times due to the perturbation
from the common reference ray. These travel-time errors can deteriorate the coupling-ray-theory solution at high frequencies.
It is thus of principal importance for numerical applications to estimate the errors due to the common-ray approximation applied.
The anisotropic-common-ray approximation of the coupling ray theory is more accurate than the isotropic-common-ray approximation.
We derive the equations for estimating the travel-time errors due to the anisotropic-common-ray (and also isotropic-common-ray)
approximation of the coupling ray theory. The errors of the common-ray approximations are calculated along the anisotropic
common rays in smooth velocity models without interfaces. The derivation is based on the general equations for the second-order
perturbations of travel time. 相似文献
43.
起伏地表条件下的声波散射数值模拟的积分方程法 总被引:2,自引:1,他引:2
从散射理论的角度来看,起伏地表可以看作是一种特殊的扰动介质,因此应用散射积分方程求解起伏地表条件下的散射场在理论上是可行的。从三维频率域声波方程出发,由格林函数定理,得出起伏地表条件下的散射积分方程。散射积分方程为关于起伏地表的面积分和与速度扰动体有关的体积分之和,同时给出了格林函数在奇异点的积分方法。由于数值离散求解积分方程存在着计算时间太长和存储内存不足的问题,采用电磁散射积分方程的拟解析近似的方法。在假设反射函数为缓变函数的基础上,最终得到其近似表达式,因此散射场的数值求解不必再借助于代数方程组,只要进行数值积分即可。这种方法避开了传统数值计算方法存在的问题,为地震散射波场快速正演模拟打下了基础。理论分析表明,这种方法适用于小扰动的问题。当扰动较大时,拟解析近似会产生较大的误差。 相似文献
44.
InSAR高程模型及其精度分析 总被引:3,自引:0,他引:3
提出了一种改进的InSAR高程模型,建立了高程和干涉相位的直接关系,并对公式推导中一般采用的平行射线近似处理方法所引入的高程误差进行了量化分析。结果表明,对于星载雷达而言,平行射线近似误差不能忽略。给出了近似误差与基线参数的确定性关系及相应的误差传播曲线,有助于误差纠正和重建高精度DEM。另外,基于改进的高程模型,推导出了高程测量误差传播公式,明确了基线长度和方向对测高精度的影响,对合理选择干涉像对具有指导意义。 相似文献
45.
基于k阶Voronoi多边形划分的k阶数据场拟合 总被引:2,自引:1,他引:2
讨论了k阶Voronoi图的离散点集的生成算法,挖掘了k阶Voronoi图的性质并加以证明;参照k阶Voronoi图的定义提出了k阶空间数据场的定义,并结合参考点利用其影响因子给出了低阶空间数据场的拟合函数通式;利用k阶Voronoi图对平面空间的平面区域最近邻近划分实现了对空间数据场的分割,从而将大量参考点集数据场化解为多个单元数据场的低阶拟舍,有效地降低了数据场拟舍的难度;提出了合并拟合和叠加拟合策略,实现了将单元数据场综合为完整的空间数据场。 相似文献
46.
An integrated wavelet concept of physical geodesy 总被引:4,自引:1,他引:3
For the determination of the earth's gravity field many types of observations are nowadays available, including terrestrial
gravimetry, airborne gravimetry, satellite-to-satellite tracking, satellite gradio-metry, etc. The mathematical connection
between these observables on the one hand and gravity field and shape of the earth on the other is called the integrated concept
of physical geodesy. In this paper harmonic wavelets are introduced by which the gravitational part of the gravity field can
be approximated progressively better and better, reflecting an increasing flow of observations. An integrated concept of physical
geodesy in terms of harmonic wavelets is presented. Essential tools for approximation are integration formulas relating an
integral over an internal sphere to suitable linear combinations of observation functionals, i.e. linear functionals representing
the geodetic observables. A scale discrete version of multiresolution is described for approximating the gravitational potential
outside and on the earth's surface. Furthermore, an exact fully discrete wavelet approximation is developed for the case of
band-limited wavelets. A method for combined global outer harmonic and local harmonic wavelet modelling is proposed corresponding
to realistic earth's models. As examples, the role of wavelets is discussed for the classical Stokes problem, the oblique
derivative problem, satellite-to-satellite tracking, satellite gravity gradiometry and combined satellite-to-satellite tracking
and gradiometry.
Received: 28 February 1997 / Accepted: 17 November 1997 相似文献
47.
研究了复平面上 ,广义 Hermite-Fejer插值多项式的收敛性。得到了其在空间 lp(| z| =1 ) (0
相似文献
48.
提出内蕴大地边值问题,使得有可能利用重力场边界观测研究地球重力场的内蕴结构。文中构造了椭球问题的迭代逼近求解程式,并给出了具体解式。 相似文献
49.
The reflection and transmission phenomena of elastic waves incident at a corrugated interface between two dissimilar fibre‐reinforced elastic half‐spaces have been analysed. Using Rayleigh method of approximation, the expressions of the reflection and transmission coefficients are obtained in closed form for the plane interface as well as for the first order approximation of the periodic interface ζ = d cos px. All these reflection and transmission coefficients of regular and irregular waves are found to be the functions of angle of incidence and elastic parameters of the media. Moreover, the coefficients of irregularly reflected and transmitted waves are found to be proportional to the amplitude of the corrugated interface and are functions of the frequency of the incident wave. Numerical computations have been performed for a specific model to compute these coefficients and results obtained are shown graphically. The results of Singh and Singh (Sadhana 2004; 29 :249–257) and Ben‐Menahem and Singh (Seismic Waves and Sources. Springer: New York) have been derived from our analysis as particular cases. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
50.