共查询到20条相似文献，搜索用时 31 毫秒
1.
O. N. Savina P. A. Bespalov V. O. Rapoport N. A. Ryzhov 《Geomagnetism and Aeronomy》2006,46(2):247-253
The nonlinear equation of the first order of the Riccati type has been obtained for the wave impedance of acoustic gravity waves in the nonisothermal atmosphere. The vertically nonuniform horizontal wind and the effect of viscosity on the horizontal components of the velocity field have been taken into account in the calculations. The boundary-value problem for the Riccati equation is defined by the boundary emission condition at high altitudes. Upon finding the wave impedance along with the generalized polarization relationship, all remaining disturbances of the atmospheric parameters related to acoustic gravity waves are found with the help of a simple integration. The results of using a developed formalism are illustrated by the numerical computation of acoustic gravity wave fields in the atmosphere with real vertical profiles of temperature and horizontal field velocity. 相似文献
2.
Martinec and Grafarend (1997) have shown how the construction of Green's function in the Stokes boundary-value problem with gravity data distributed on an ellipsoid of revolution is approached in the O(e
0
2
)-approximation. They have also expressed the ellipsoidal Stokes function describing the effect of ellipticity of the boundary as a finite sum of elementary functions. We present an effective method of avoiding the singularity of spherical and the ellipsoidal Stokes functions, and also an analytical expression for the ellipsoidal Stokes integral around the computational point suitable for numerical solution. We give the numerical results of solving the ellipsoidal Stokes boundary-value problem and their difference with respect to the spherical Stoke boundary-value problem. 相似文献
3.
Atmospheric masses play an important role in precise downward continuation and validation of satellite gravity gradiometry data. In this paper we present two alternative ways to formulate the atmospheric potential. Two density models for the atmosphere are proposed and used to formulate the external and internal atmospheric potentials in spherical harmonics. Based on the derived harmonic coefficients, the direct atmospheric effects on the satellite gravity gradiometry data are investigated and presented in the orbital frame over Fennoscandia. The formulas of the indirect atmospheric effects on gravity anomaly and geoid (downward continued quantities) are also derived using the proposed density models. The numerical results show that the atmospheric effect can only be significant for precise validation or inversion of the GOCE gradiometric data at the mE level. 相似文献
4.
Explicit formula for the geoid-quasigeoid separation 总被引：1，自引：0，他引：1
The explicit formula for the geoid-to-quasigeoid correction is derived in this paper. On comparing the geoidal height and
height anomaly, this correction is found to be a function of the mean value of gravity disturbance along the plumbline within
the topography. To evaluate the mean gravity disturbance, the gravity field of the Earth is decomposed into components generated
by masses within the geoid, topography and atmosphere. Newton’s integration is then used for the computation of topography-and
atmosphere-generated components of the mean gravity, while the combined solution for the downward continuation of gravity
anomalies and Stokes’ boundary-value problem is utilized in computing the component of mean gravity disturbance generated
by mass irregularities within the geoid. On application of this explicit formulism a theoretical accuracy of a few millimetres
can be achieved in evaluation of the geoid-to-quasigeoid correction. However, the real accuracy could be lower due to deficiencies
within the numerical methods and to errors within the input data (digital terrain and density models and gravity observations). 相似文献
5.
Zdeněk Martinec 《Studia Geophysica et Geodaetica》1990,34(4):313-326
Summary A new method for computing the potential coefficients of the Earth's external gravity field is presented. The gravimetric
boundary-value problem with a free boundary is reduced to the problem with a fixed known telluroid. The main idea of the derivation
consists in a continuation of the quantities from the physical surface to the telluroid by means of Taylor's series expansion
in such a way that the terms whose magnitudes are comparable with the accuracy of today's gravity measurements are retained.
Thus not only linear, but also non-linear terms are taken into account. Explicitly, the terms up to the order of the third
power of the Earth's flattening are retained. The non-linear boundary-value problem on the telluroid is solved by an iteration
procedure with successive approximations. In each iteration step the solution of the non-linear problem is estimated by the
solutions of two linear problems utilizing the fact that the non-linear boundary condition may be split into two parts; the
linear spherical approximation of the gravity anomaly whose magnitude is significantly greater than the others and the non-linear
ellipsoidal corrections. Finally, in order to solve the problem in terms of spherical harmonics, the transform method composed
of the fast Fourier transform and Gauss Legendre quadrature is theoretically outlined. Immediate data processing of gravity
data measured on the physical Earth's surface without any continuation of gravity measurements to a reference level surface
belongs to the main advantage of the presented method. This implies that no preliminary data handling is needed and that the
error data propagation is, consequently, maximally suppressed. 相似文献
6.
In the first attempt to solve the Stokes boundary-value problem in ellipsoidal coordinates numerically (Ardestani and Martinec, 2000), we focused on the near-zone contribution since the effect of the ellipsoidal Stokes function in the far-zone contribution is not considered. We present a method for solving the ellipsoidal Stokes integral in far-zone contribution. The numerical results of computing the magnitude of this term for an area in north of Canada are presented. 相似文献
7.
The ellipsoidal Stokes boundary-value problem is used to compute the geoidal heights. The low degree part of the geoidal heights can be represented more accurately by Global Geopotential Models (GGM). So the disturbing potential is splitted into a low-degree reference potential and a higher-degree potential. To compute the low-degree part, the global geopotential model is used, and for the high-degree part, the solution of the ellipsoidal Stokes boundary-value problem in the form of the surface integral is used. We present an effective method to remove the singularity of the high-degree of the spherical and ellipsoidal Stokes functions around the computational point. Finally, the numerical results of solving the ellipsoidal Stokes boundary-value problem and the difference between the high-degree part of the solution of the ellipsoidal Stokes boundary-value problem and that of the spherical Stokes boundary-value problem is presented. 相似文献
8.
Petr Holota 《Studia Geophysica et Geodaetica》2011,55(3):397-413
In the introductory part of the paper the importance of the topic for gravity field studies is outlined. Some concepts and tools often used for the representation of the solution of the respective boundary-value problems are mentioned. Subsequently a weak formulation of Neumann??s problem is considered with emphasis on a particular choice of function basis generated by the reproducing kernel of the respective Hilbert space of functions. The paper then focuses on the construction of the reproducing kernel for the solution domain given by the exterior of an oblate ellipsoid of revolution. First its exact structure is derived by means of the apparatus of ellipsoidal harmonics. In this case the structure of the kernel, similarly as of the entries of Galerkin??s matrix, becomes rather complex. Therefore, an approximation of ellipsoidal harmonics (limit layer approach), based on an approximation version of Legendre??s ordinary differential equation, resulting from the method of separation of variables in solving Laplace??s equation, is used. The kernel thus obtained shows some similar features, which the reproducing kernel has in the spherical case, i.e. for the solution domain represented by the exterior of a sphere. A numerical implementation of the exact structure of the reproducing kernel is mentioned as a driving impulse of running investigations. 相似文献
9.
研究和实施了由卫星测高数据计算垂线偏差，用莫洛 金斯基（Molodensky）公式反演 大地水准面高，由此求得我国海域大地水准面高. 为了检核，将测高垂线偏差利用逆维宁迈 纳斯（Vening Meinesz）公式反演重力异常，与海上船测重力值进行了外部检核；同时还用 司托克斯（Stokes）公式，将上述反演的重力异常计算大地水准面高，与莫洛金斯基公式直 接解得的相应结果进行比较作为内部检核. 在积分计算中充分应用了FFT的严格公式.由重力和GPS水准数据确定的陆地大地水准面，和主要由卫星测高数据确定的海洋大地水准 面，二者之间一般都存在以系统误差为主的拼接差，本文分析了产生这一现象的主要原因, 并结合我国在陆海大地水准面拼接区重力资料稀疏的实际，提出了新的拼接技术，最后将拟 合参数校正中国全部海域的重 力大地水准面，以最大限度地削弱拼接点和制约测高海洋大地水准面可能存在的系统误差. 相似文献
10.
根据重力场的频谱理论,本文建立了重力异常阶方差的经验模型,并导出了外空扰动引力场与地面数据分辨率及其覆盖范围之间的关系,从理论上研究和揭示了各种地形类别下外空场的传播特性。为验证理论分析结果,还应用重力异常逐级余差方法,以实际资料计算并分析了外空扰动引力场的传播特性。结果表明,理论分析和实际计算得到的结论完全一致。 相似文献
11.
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
12.
Mariya I. Yurkina 《Studia Geophysica et Geodaetica》1996,40(1):9-13
Summary On the basis of the fundamental relations of the Molodensky's Earth's figure theory (1945), admitting the inequality of the
gravity potentials at the Major Vertical Datum W0 and on the surface of the reference level ellipsoid U0, and taken into account that potential W0 enters into equations directly, it is recomended, W0 should be adopted as a primary geodetic constant. Parameters of the best fitting ellipsoid are not needed for the solution
of geodetic problems and for the investigation of the Earth's gravity field. The reason for requiring the reference and actual
fields be close is only that the boundary-value problem can be solved in the linear approximation.
Dedicated to the Memory of M.S. Molodensky
Contribution to the I.A.G. Special Commission SC3 Fundamental Constants (SCFC). 相似文献
13.
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15.
The inversion gravity problem formulated as follows is solved. The excess density in each layer of a fixed horizontal stratified model is a function of horizontal coordinates (σ(ξ, η)) approximated by a specially constructed function. The problem is to reconstruct the function σ = σ(ξ, η) from the external gravity field. If the geological model includes more than one layer, the problem is solved with the use of a set of reference points at which the sought function is given. Variations in a gravity anomaly with respect to the field at a fixed point are used in solving this problem. 相似文献
16.
卫星重力梯度测量与地球引力场的精度研究 总被引：1，自引：0，他引：1
本文根据地球引力位的球谐函数展开式,利用重力梯度张量各分量导出了位系数模型的精度估计公式.从三方面进行了研究:假定卫星重力梯度仪测量精度,探讨用重力梯度数据确定地球重力场模型的精度;求出位系数模型和大气阻力引起的重力梯度卫星的轨道误差;最后,反求轨道误差和位系数误差对重力梯度测量值的影响.数值计算表明,与地面技术和常规卫星方法相比,卫星梯度测量可使重力场模型的精度至少提高3-5倍;利用重力梯度张量全分量求得的重力值精度比单用径向分量Vrr的结果提高40％以上;若仅顾及位系数模型和大气阻力误差,则轨道误差对梯度测量值的影响△Vi3（i=3,2,1）至少可分别在1/4和1/3弧圈内达到△Vi3≤σ（仪器精度）. 相似文献
17.
Three-Dimensional Gravity Modeling In All Space 总被引：11，自引：2，他引：9
We review available analytical algorithms for the gravity effect and gravity gradients especially the vertical gravity gradient due to a right rectangular prism, a right polygonal prism, and a polyhedron. The emphasis is placed on an investigation of validity, consistency, and especially singularities of different algorithms, which have been traditionally proposed for calculation of the gravity effect on ground (or outside anomalous bodies), when they are applied to all points in space. The rounding error due to the computer floating point precision is estimated. The gravity effect and vertical gradient of gravity in three dimensions caused by a cubic model are calculated by different types of algorithms. The reliability of algorithms for the calculation of gravity of a right polygonal prism and a polyhedron is further verified by using a regular polygonal prism approximating a vertical cylinder and a regular polyhedron approximating a sphere, respectively. By highlighting Haáz-Jung-Plouff and Okabe-Steiner-Zilahi-Sebess' formulae for a right rectangular prism, Plouff's algorithm for a right polygonal prism, and Gouml;tze and Lahmeyer's algorithm for a polyhedron and removing their singularities, we demonstrate that these formulae and algorithms can be used to model the gravity anomaly and its vertical gradient at all possible computation positions. 相似文献
18.
在云南省西部，跨越中、缅两国交界的横断山系地区（97°E~102°E，24°N~30°N）有近一半的面积尚没有重力测点、即重力数据空白区和重力测点稀少的普查级测区.以前的有关文献、图集中所给出对此地区的重力场都是十分模糊的结果与图件.因此应用这些资料无法详细地研究该地区重力场特征与深部地壳结构（构造）.本文应用卫星重力异常资料作为“近似空间重力异常”，经中间层改正后给出的“计算布格重力异常”，其分布特征与该地区的地形高程呈很好的镜像相关.对相应山脉、河谷以及断裂构造都有所反映.特别是在横断山系地区该布格重力异常呈现为近南北的走向.为此，据该“计算布格重力异常”,并选定对该区有代表性的一条重力异常剖面作正反演计算，以得到其地壳深部结构剖面.结果表明，在横断山脉地区的地壳厚度在51~56 km间起伏变化；滇西北云岭山系以及玉龙山区的地壳厚度约在60 km以上. 最后，对所得结果与图件进行了讨论，并提出了几点认识和纠正的建议. 相似文献
19.
Due to the influence of volcanic rock or weathering crust coverage, the quality of deep seismic data is often not reliable and it is difficult to identify small deep buried hill structure beneath the cover. However, the gravity exploration technology can use the remarkable density differences between the object and the overlying strata to identify this special geological reservoir. Although recently several rounds of seismic exploration have been carried out in Raoyang depression, Huabei Oilfield, North China to determine the existence of Hu 8 north deep buried hill, whether the buried hill really exists or not as well as its scale is still in controversial. In this paper, based on the information of seismic data and formation density, deep processing of 3D high precision ground gravity data has been carried out for 3D forward and inversion computation. The dimensional gravity forward calculation results show that the density of the deep anomaly body forms a relatively low gravity anomaly in the earth's surface. By using the potential processing method of vertical second derivative, and sliding filtering, the residual anomaly is separated from regional or background field, which illustrates the existence of a local high gravity anomaly at Hu 8 north area. According to the amplitude of residual gravity anomaly and formation density difference modeling, through a number of 3D forward calculations and 3D inversion of gravity data, the existence of Hu 8 north buried hill and its possible scale are basically determined. The results prove that the 3D high precision gravity method is effective in determining the deep buried hill structure in case that seismic data is not reliable. 相似文献
20.
利用卫星观测和地面实测资料统一归算的全球空间重力异常,探讨重力异常对全球冬夏大气活动中心、热带气旋以及温带气旋和高原低涡多发区的影响,并对其物理机理作一简要讨论.认为重力异常是大气运动发生发展不可忽视的因子之一. 相似文献