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1.
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
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.
We would like to solve the Stokes boundary-value problem taking into consideration the ellipsoidal corrections in the boundary condition in ellipsoidal coordinates The original problem, i.e., the ellipsoidal Stokes boundary-value problem has been solved by Martinec and Grafarend (1997) We use the same philosophy expressed by Martinec (1998) to solve the spherical Stokes boundary-value problem with ellipsoidal corrections in the boundary condition We wish to show the magnitude of the integration kernel describing the effect of the ellipsoidal corrections in the boundary condition in a cap around the computational point. 相似文献
4.
We have constructed Green's function to Stokes's boundary-value problem with the gravity data distributed over an ellipsoid of revolution. We show that the problem has a unique solution provided that the first eccentricity e0
of the ellipsoid of revolution is less than 0·65041. The ellipsoidal Stokes function describing the effect of ellipticity of the boundary is expressed in the
E-approximation as a finite sum of elementary functions which describe analytically the behaviour of the ellipsoidal Stokes function at the singular point = 0. We prove that the degree of singularity of the ellipsoidal Stokes function in the vicinity of its singular point is the same as that of the spherical Stokes function. 相似文献
5.
Far-zone gravity field contributions corrected for the effect of topography by means of molodensky’s truncation coefficients 总被引：1，自引：0，他引：1
Robert Tenzer Pavel Novák Peter Vajda Artu Ellmann Ahmed Abdalla 《Studia Geophysica et Geodaetica》2011,55(1):55-71
A spectral representation of the topographic corrections to gravity field quantities is formulated in terms of spherical height
functions. When computing the far-zone contributions to the topographic corrections, various types of the truncation coefficients
are applied to a spectral representation of Newton’s integral. In this study we utilise Molodensky’s truncation coefficients
in deriving the expressions for the far-zone contributions to topographic corrections. The expressions for computing the far-zone
gravity field contributions corrected for the effect of topography are then obtained by combining the expressions for the
far-zone contributions to the gravity field quantities and to the respective topographic corrections, both expressed in terms
of Molodensky’s truncation coefficients. The numerical examples of the far-zone contributions to the topographic corrections
and to the topography-corrected gravity field quantities are given over the study area situated in the Canadian Rocky Mountains
with adjacent planes. Coefficients of the global elevation and geopotential models are used as the input data. 相似文献
6.
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
7.
Mehdi Eshagh 《Pure and Applied Geophysics》2012,169(12):2201-2215
The Earth’s gravity potential can be determined from its second-order partial derivatives using the spherical gradiometric boundary-value problems which have three integral solutions. The problem of merging these solutions by spectral combination is the main subject of this paper. Integral estimators of biased- and unbiased-types are presented for recovering the disturbing gravity potential from gravity gradients. It is shown that only kernels of the biased-type integral estimators are suitable for simultaneous downward continuation and combination of gravity gradients. Numerical results show insignificant practical difference between the biased and unbiased estimators at sea level and the contribution of far-zone gravity gradients remains significant for integration. These contributions depend on the noise level of the gravity gradients at higher levels than sea. In the cases of combining the gravity gradients, contaminated with Gaussian noise, at sea and 250?km levels the errors of the estimated geoid heights are about 10 and 3 times smaller than those obtained by each integral. 相似文献
8.
陆地可控源电磁法的观测资料可依据频段范围近似地划分为近区场、中间区场及远区场,但采用测量相互正交电、磁分量,并计算视电阻率的资料处理方式只适用于远区场数据.为更有效地利用陆地可控源电磁法不同区间场的观测资料,本文结合三维数值模拟技术并采用电场分量直接进行反演的策略,对不同区间电场的响应特征与探测效果进行了分析.数值模拟结果表明:近区电场的异常响应最明显,异常响应不随频率发生显著变化,但纵向分辨能力差;远区电场异常响应随频率发生显著变化,其探测深度取决于频率的高低;中间区场较为复杂,地表电场异常响应的等值线中心并不是位于异常体中心正上方,而是在沿场传播方向上向异常体与围岩的分界面处偏移,并且发现中间区场资料的加入会影响反演结果的准确性.综合合成数据和野外实测资料的反演结果,发现结合近区场和远区场资料而舍弃中间区场资料的反演效果更佳,这为陆地可控源电磁法资料的反演解释提供了一种有效途径. 相似文献
9.
In the evaluation of the geoid done according to the Stokes-Helmert method, the following topographical effects have to be computed: the direct topographical effect, the primary indirect topographical effect and the secondary indirect topographical effect. These effects have to be computed through integration over the surface of the earth. The integration is usually split into integration over an area immediately adjacent to the point of interest, called the near zone, and the integration over the rest of the world, called the far zone. It has been shown in the papers by Martinec and Vaníek (1994), and by Novák et al. (1999) that the far-zone contributions to the topographical effects are, even for quite extensive near zones, not negligible.Various numerical approaches can be applied to compute the far-zone contributions to topographical effects. A spectral form of solution was employed in the paper by Novák et al. (2001). In the paper by Smith (2002), the one-dimensional Fast Fourier Transform was introduced to solve the problem in the spatial domain. In this paper we use two-dimensional numerical integration. The expressions for the far-zone contributions to topographical effects on potential and on gravitational attraction are described, and numerical values encountered over the territory of Canada are shown in this paper. 相似文献
10.
In this contribution we continue our earlier research, concerning the ellipsoidal harmonic expansions of the Earth disturbing gravitational potential and its derivatives on an external reference ellipsoid confocal with respect to the normal ellipsoid and close to it. One of the results of the previous investigation is represented by a new expression for the derivative of the Jekeli’s Legendre function of the second kind, entering the ellipsoidal harmonics in the potential derivative. The derived expression depends on two Gauss hypergeometric functions which converge better than the hypergeometric functions of other authors. In the present paper we construct another expression for the derivative of the Jekeli’s Legendre function, depending on two alternative hypergeometric functions. While our earlier hypergeometric series in the expression for the derivative of this function converge better when the orders of the terms do not exceed a half of their degrees, the series constructed in the present paper converge more rapidly when the orders surpass a half of the degrees. We deduce an improved expression for the derivative of the Jekeli’s Legendre function by combining these results and then construct a corresponding new expression for the derivative of the disturbing potential. This expression is applied for constructing non-singular expressions for the components of the gradient of the potential in the local north-oriented ellipsoidal reference frame. The new expressions for these components have no these deficiencies and the expression for the potential gradient depends on very quickly convergent hypergeometric series. 相似文献
11.
The estimation of the Earth’s gravitational potential energy E was obtained for different density distributions and rests
on the expression E = − (Wmin + ΔW) derived from the conventional relationship for E. The first component Wmin expresses minimum amount of the work W and the second component ΔW represents a deviation from Wmin interpreted in terms of Dirichlet’s integral applied on the internal potential. Relationships between the internal potential
and E were developed for continuous and piecewise continuous density distributions. The global 3D density model inside an
ellipsoid of revolution was chosen as a combined solution of the 3D continuous distribution and the reference PREM radial
piecewise continuous profile. All the estimates of E were obtained for the spherical Earth since the estimated (from error
propagation rule) accuracy σE of the energy E is at least two orders greater than the ellipsoidal reduction and the contribution of lateral density inhomogeneities
of the 3D global density model. The energy E contained in the 2nd degree Stokes coefficients was determined. A good agreement
between E = EGauss derived from Gaussian distribution and other E, in particular for E = EPREM based on the PREM piecewise continuous density model and E-estimates derived from simplest Legendre-Laplace, Roche, Bullard
and Gauss models separated into core and mantle only, suggests the Gaussian distribution as a basic radial model when information
about density jumps is absent or incomplete. 相似文献
12.
Gravity anomaly reference fields, required e.g. in remove-compute-restore (RCR) geoid computation, are obtained from global
geopotential models (GGM) through harmonic synthesis. Usually, the gravity anomalies are computed as point values or area
mean values in spherical approximation, or point values in ellipsoidal approximation. The present study proposes a method
for computation of area mean gravity anomalies in ellipsoidal approximation (‘ellipsoidal area means’) by applying a simple
ellipsoidal correction to area means in spherical approximation. Ellipsoidal area means offer better consistency with GGM
quasigeoid heights. The method is numerically validated with ellipsoidal area mean gravity derived from very fine grids of
gravity point values in ellipsoidal approximation. Signal strengths of (i) the ellipsoidal effect (i.e., difference ellipsoidal
vs. spherical approximation), (ii) the area mean effect (i.e., difference area mean vs. point gravity) and (iii) the ellipsoidal
area mean effect (i.e., differences between ellipsoidal area means and point gravity in spherical approximation) are investigated
in test areas in New Zealand and the Himalaya mountains. The impact of both the area mean and the ellipsoidal effect on quasigeoid
heights is in the order of several centimetres. The proposed new gravity data type not only allows more accurate RCR-based
geoid computation, but may also be of some value for the GGM validation using terrestrial gravity anomalies that are available
as area mean values. 相似文献
13.
Observation-based evaluation of surface wave effects on currents and trajectory forecasts 总被引：4，自引：2，他引：2
Johannes R?hrs Kai H?kon Christensen Lars Robert Hole G?ran Brostr?m Magnus Drivdal Svein Sundby 《Ocean Dynamics》2012,62(10-12):1519-1533
Knowledge of upper ocean currents is needed for trajectory forecasts and is essential for search and rescue operations and oil spill mitigation. This paper addresses effects of surface waves on ocean currents and drifter trajectories using in situ observations. The data set includes colocated measurements of directional wave spectra from a wave rider buoy, ocean currents measured by acoustic Doppler current profilers (ADCPs), as well as data from two types of tracking buoys that sample the currents at two different depths. The ADCP measures the Eulerian current at one point, as modelled by an ocean general circulation model, while the tracking buoys are advected by the Lagrangian current that includes the wave-induced Stokes drift. Based on our observations, we assess the importance of two different wave effects: (a) forcing of the ocean current by wave-induced surface fluxes and the Coriolis–Stokes force, and (b) advection of surface drifters by wave motion, that is the Stokes drift. Recent theoretical developments provide a framework for including these wave effects in ocean model systems. The order of magnitude of the Stokes drift is the same as the Eulerian current judging from the available data. The wave-induced momentum and turbulent kinetic energy fluxes are estimated and shown to be significant. Similarly, the wave-induced Coriolis–Stokes force is significant over time scales related to the inertial period. Surface drifter trajectories were analysed and could be reproduced using the observations of currents, waves and wind. Waves were found to have a significant contribution to the trajectories, and we conclude that adding wave effects in ocean model systems is likely to increase predictability of surface drifter trajectories. The relative importance of the Stokes drift was twice as large as the direct wind drag for the used surface drifter. 相似文献
14.
R&#;hrs Johannes Christensen Kai H&#;kon Hole Lars Robert Brostr&#;m G&#;ran Drivdal Magnus Sundby Svein 《Ocean Dynamics》2012,62(10):1519-1533
Knowledge of upper ocean currents is needed for trajectory forecasts and is essential for search and rescue operations and oil spill mitigation. This paper addresses effects of surface waves on ocean currents and drifter trajectories using in situ observations. The data set includes colocated measurements of directional wave spectra from a wave rider buoy, ocean currents measured by acoustic Doppler current profilers (ADCPs), as well as data from two types of tracking buoys that sample the currents at two different depths. The ADCP measures the Eulerian current at one point, as modelled by an ocean general circulation model, while the tracking buoys are advected by the Lagrangian current that includes the wave-induced Stokes drift. Based on our observations, we assess the importance of two different wave effects: (a) forcing of the ocean current by wave-induced surface fluxes and the Coriolis–Stokes force, and (b) advection of surface drifters by wave motion, that is the Stokes drift. Recent theoretical developments provide a framework for including these wave effects in ocean model systems. The order of magnitude of the Stokes drift is the same as the Eulerian current judging from the available data. The wave-induced momentum and turbulent kinetic energy fluxes are estimated and shown to be significant. Similarly, the wave-induced Coriolis–Stokes force is significant over time scales related to the inertial period. Surface drifter trajectories were analysed and could be reproduced using the observations of currents, waves and wind. Waves were found to have a significant contribution to the trajectories, and we conclude that adding wave effects in ocean model systems is likely to increase predictability of surface drifter trajectories. The relative importance of the Stokes drift was twice as large as the direct wind drag for the used surface drifter.
相似文献15.
First, we present three different definitions of the vertical which relate to (i) astronomical longitude and astronomical
latitude as spherical coordinates in gravity space, (ii) Gauss surface normal coordinates (also called geodetic coordinates)
of type ellipsoidal longitude and ellipsoidal latitude and (iii) Jacobi ellipsoidal coordinates of type spheroidal longitude
and spheroidal latitude in geometry space. Up to terms of second order those vertical deflections agree to each other. Vertical
deflections and gravity disturbances relate to a reference gravity potential. In order to refer the horizontal and vertical
components of the disturbing gravity field to a reference gravity field, which is physically meaningful, we have chosen the
Somigliana-Pizzetti gravity potential as well as its gradient. Second, we give a new closed-form representation of Somigliana-Pizzetti
gravity, accurate to the sub Nano Gal level. Third, we represent the gravitational disturbing potential in terms of Jacobi
ellipsoidal harmonics. As soon as we take reference to a normal potential of Somigliana-Pizzetti type, the ellipsoidal harmonics
of degree/order (0,0), (1,0), (1, − 1), (1,1) and (2,0) are eliminated from the gravitational disturbing potential. Fourth,
we compute in all detail the gradient of the gravitational disturbing potential, in particular in orthonormal ellipsoidal
vector harmonics. Proper weighting functions for orthonormality on the International Reference Ellipsoid are constructed and
tabulated. In this way, we finally arrive at an ellipsoidal harmonic representation of vertical deflections and gravity disturbances.
Fifth, for an ellipsoidal harmonic Gravity Earth Model (SEGEN: http://www.uni-stuttgart.de/gi/research/paper/coefficients/coefficients.zip)
up to degree/order 360/360 we compute the global maps of ellipsoidal vertical deflections and ellipsoidal gravity disturbances
which transfer a great amount of geophysical information in a properly chosen equiareal ellipsoidal map projection. 相似文献
16.
本文给出了水平分层大地视电阻率的一种改进的定义,在这种改进了的视电阻率的远区曲线中,假极值效应有所压低,曲线的起伏度变得比原来的大,视电阻率的值也较接近于地层的真实电阻率.这些特性对于作出正确的判断都是有利的. 相似文献
17.
We present formulas for direct closed-form transformation between geodetic coordinates (φ, λ, h) and ellipsoidal coordinates
(β, λ, u) for any oblate ellipsoid of revolution. These will be useful for those dealing with ellipsoidal representations
of the Earth’s gravity field or other oblate ellipsoidal figures. The numerical stability of the transformations for near-polar
and near-equatorial regions is also considered. 相似文献
18.
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19.
A spherical approximation makes the basis for a majority of formulas in physical geodesy. However, the present-day accuracy
in determining the disturbing potential requires an ellipsoidal approximation. The paper deals with constructing Green’s function
for an ellipsoidal Earth by an ellipsoidal harmonic expansion and using it for determining the disturbing potential. From
the result obtained the part that corresponds to the spherical approximation has been extracted. Green’s function is known
to depend just on the geometry of the surface where boundary values are given. Thus, it can be calculated irrespective of
the gravity data completeness. No changes of gravity data have an effect on Green’s function and they can be easily taken
into account if the function has already been constructed. Such a method, therefore, can be useful in determining the disturbing
potential of an ellipsoidal Earth. 相似文献
20.
V. N. Koneshov V. B. Nepoklonov V. V. Pogorelov V. N. Solov’ev L. V. Afanas’eva 《Izvestiya Physics of the Solid Earth》2016,52(3):443-451
The application of the airborne gravimetry method for gravity measurements in the Arctic is considered. This method has been extensively employed in foreign studies for determining the figure of the Earth in high-latitude conditions. The possibility of conducting comparative studies along the extensive survey lines and the necessity of aerogravimetry studies for improving the global Earth’s gravity field (EGF) models are discussed. The possibility of the efficient application of the modern EGF models for estimating the systematical errors for different types of gravimetry surveys and exploring the influence of the anomalous far-zone field in the calculations of the plumb line deviations is demonstrated. 相似文献