排序方式: 共有43条查询结果,搜索用时 647 毫秒
31.
针对球谐函数定积分计算中Legendre函数递推问题展开研究,分析了标准向前列推法、Belikov法、跨阶次法、X数法以及顾及麦克劳林级数展开式对球谐函数定积分计算的影响。利用Eigen6c-4地球重力场模型计算扰动引力梯度径向分量,分析不同方法之间的差异。实验表明,不考虑麦克劳林级数展开式时4种方法的相对精度在高纬度地区较差,但计算模型扰动引力径向分量的精度一致,结合麦克劳林级数式可提高高纬度地区定积分计算的相对精度,但会降低中低纬度地区定积分计算的精度,并且对高纬度地区扰动引力径向分量的影响极小,但会严重降低低纬度地区扰动引力梯度计算的精度。 相似文献
32.
B. Feige 《Astronomische Nachrichten》1992,313(3):139-163
Following the discussion of some general properties and analytical formulae for cosmological models with non-zero cosmological constant, we show how the elliptic integrals for comoving distance and light travel times as function of redshift can be expressed through Legendre integrals of the first and third kind, for which standard implementations are readily available. Observational properties are then illustrated for selected but typical models using the previously derived formulae. 相似文献
33.
Robert Tenzer Pavel Novák Ilya Prutkin Artu Ellmann Peter Vajda 《Studia Geophysica et Geodaetica》2009,53(2):157-167
To reduce the numerical complexity of inverse solutions to large systems of discretised integral equations in gravimetric
geoid/quasigeoid modelling, the surface domain of Green’s integrals is subdivided into the near-zone and far-zone integration
sub-domains. The inversion is performed for the near zone using regional detailed gravity data. The farzone contributions
to the gravity field quantities are estimated from an available global geopotential model using techniques for a spherical
harmonic analysis of the gravity field. For computing the far-zone contributions by means of Green’s integrals, truncation
coefficients are applied. Different forms of truncation coefficients have been derived depending on a type of integrals in
solving various geodetic boundary-value problems. In this study, we utilise Molodensky’s truncation coefficients to Green’s
integrals for computing the far-zone contributions to the disturbing potential, the gravity disturbance, and the gravity anomaly.
We also demonstrate that Molodensky’s truncation coefficients can be uniformly applied to all types of Green’s integrals used
in solving the boundaryvalue problems. The numerical example of the far-zone contributions to the gravity field quantities
is given over the area of study which comprises the Canadian Rocky Mountains. The coefficients of a global geopotential model
and a detailed digital terrain model are used as input data. 相似文献
34.
35.
A Certain Class of Laplace Transforms with Applications to Reaction and Reaction-Diffusion Equations
A class of Laplace transforms is examined to show that particular cases of this class are associated with production-destruction and reaction-diffusion problems in physics, study of differences of independently distributed random variables and the concept of Laplacianness in statistics, α-Laplace and Mittag-Leffler stochastic processes, the concepts of infinite divisibility and geometric infinite divisibility problems in probability theory and certain fractional integrals and fractional derivatives. A number of applications are pointed out with special reference to solutions of fractional reaction and reaction-diffusion equations and their generalizations. 相似文献
36.
Joshua Ashenberg 《Celestial Mechanics and Dynamical Astronomy》2007,99(2):149-159
The mutual gravitational potential and the mutual gravitational torque of two bodies of arbitrary shape are expanded to the
fourth order. The derivations are based on Cartesian coordinates, inertia integrals with relation to the principal reference
frames of each body, and the relative rotation matrix. The current formulation is convenient to utilize in high precision
problems in rotational dynamics. 相似文献
37.
Vasily E. Tarasov 《Celestial Mechanics and Dynamical Astronomy》2006,94(1):1-15
In this paper we consider the gravitational field of fractal distribution of particles. To describe fractal distribution,
we use the fractional integrals. The fractional integrals are considered as approximations of integrals on fractals. Using
the fractional generalization of the Gauss’s law, we consider the simple examples of the fields of homogeneous fractal distribution.
The examples of gravitational moments for fractal distribution are considered. 相似文献
38.
This work addresses in‐plane pressure P and vertically polarized shear SV seismic wave propagation in a finite, laterally inhomogeneous, multilayered poroelastic geological region resting on the homogeneous elastic half‐space. The particular approach followed here is based on a combination of the (i) viscoelastic approximation (isomorphism) to Biot's equations of dynamic poroelasticity and on the (ii) boundary integral equation method (BIEM) using frequency‐dependent fundamental solutions of the governing wave equations. The problem is formulated under plane strain conditions and time‐harmonic motions are assumed. Validation of the viscoelastic isomorphism and verification of the BIEM is done by solution of benchmark examples. These simulation studies reveal that the proposed methodology is able to depict a sensitivity of the seismic signals recovered to the following parameters: (i) poroelastic properties of fluid saturated layers; (ii) lateral geological inhomogeneity; (iii) surface topography and (iv) frequency content and direction of the incident wave. It is concluded that the combination of viscoelastic isomorphism with BIEM software provides an effective numerical tool for evaluating site‐effect phenomena in multilayered, fluid saturated geological regions with complex geometry. The numerical results obtained demonstrate that dynamic poroelasticity interacting with other physical peculiarities of the Earth's surface layers, such as lateral heterogeneity, material properties along the wave path, local geological profile and type of elastic wave, gives rise to complex seismic signals on the free surface at the site of interest. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
39.
In this work, a hybrid boundary integral equation method (BIEM) is developed, based on both displacement and hypersingular traction formulations, for the analysis of time-harmonic seismic waves propagating through cracked, multi-layered geological regions with surface topography and under plane strain conditions. Specifically, the displacement-based BIEM is used for a multi-layered deposit with interface cracks, while the regularized, traction-based BIEM is used when internal cracks are present within the layers. The standard uni-dimensional boundary element with parabolic shape functions is employed for discretizing the free surface and the layer interfaces, while special discontinuous boundary elements are placed near the crack tips to model the asymptotic behaviour of both displacements and tractions. This formulation yields displacement amplitudes and phase angles on the free surface of a geological deposit, as well as stress intensity factors near the tips of the cracks. Finally, in the companion paper, numerical results are presented which show that both scattered wave and stress concentration fields are sensitive to the incidence seismic wave parameters and to specific site conditions such as surface topography, layering, the presence of cracks and crack interaction. 相似文献
40.
本文对多分层媒质并矢格林函数中的索末菲积分,用Prony方法对其被积函数分式部分用指数函数逼近.利用索末菲恒等式,无穷积分就可化为闭合的级数形式.该闭合形式可看作一串离散镜像在观察点的解.所得结果与数值积分结果吻合很好. 相似文献