共查询到20条相似文献,搜索用时 15 毫秒
1.
In space-borne gravitational field determination, two challenges are inherent. First, the continuation of the data down to
the surface of the Earth is an ill-posed problem, requiring therefore regularization techniques. Second huge data sets result
requiring efficient numerical methods. In this paper, we show how locally supported wavelets on the sphere can be developed
by means of a spherical version of the so-called up function. By construction, the corresponding scaling functions and wavelets
are infinitely smooth, so that they can be used for regularization purposes. In particular, we show how the ill-posed pseudo-differential
equations coming from satellite missions can be regularized by efficient numerical schemes using locally supported wavelets.
These methods seem in particular to be interesting for regional gravity field modelling. 相似文献
2.
Wavelet Modeling of Regional and Temporal Variations of the Earth’s Gravitational Potential Observed by GRACE 总被引:1,自引:0,他引:1
This work is dedicated to the wavelet modeling of regional and temporal variations of the Earth’s gravitational potential
observed by the GRACE (gravity recovery and climate experiment) satellite mission. In the first part, all required mathematical
tools and methods involving spherical wavelets are provided. Then, we apply our method to monthly GRACE gravity fields. A
strong seasonal signal can be identified which is restricted to areas where large-scale redistributions of continental water
mass are expected. This assumption is analyzed and verified by comparing the time-series of regionally obtained wavelet coefficients
of the gravitational signal originating from hydrology models and the gravitational potential observed by GRACE. The results
are in good agreement with previous studies and illustrate that wavelets are an appropriate tool to investigate regional effects
in the Earth’s gravitational field.
Electronic Supplementary Material Supplementary material is available for this article at 相似文献
3.
We present an alternate mathematical technique than contemporary spherical harmonics to approximate the geopotential based
on triangulated spherical spline functions, which are smooth piecewise spherical harmonic polynomials over spherical triangulations.
The new method is capable of multi-spatial resolution modeling and could thus enhance spatial resolutions for regional gravity
field inversion using data from space gravimetry missions such as CHAMP, GRACE or GOCE. First, we propose to use the minimal
energy spherical spline interpolation to find a good approximation of the geopotential at the orbital altitude of the satellite.
Then we explain how to solve Laplace’s equation on the Earth’s exterior to compute a spherical spline to approximate the geopotential
at the Earth’s surface. We propose a domain decomposition technique, which can compute an approximation of the minimal energy
spherical spline interpolation on the orbital altitude and a multiple star technique to compute the spherical spline approximation
by the collocation method. We prove that the spherical spline constructed by means of the domain decomposition technique converges
to the minimal energy spline interpolation. We also prove that the modeled spline geopotential is continuous from the satellite
altitude down to the Earth’s surface. We have implemented the two computational algorithms and applied them in a numerical
experiment using simulated CHAMP geopotential observations computed at satellite altitude (450 km) assuming EGM96 (n
max = 90) is the truth model. We then validate our approach by comparing the computed geopotential values using the resulting
spherical spline model down to the Earth’s surface, with the truth EGM96 values over several study regions. Our numerical
evidence demonstrates that the algorithms produce a viable alternative of regional gravity field solution potentially exploiting
the full accuracy of data from space gravimetry missions. The major advantage of our method is that it allows us to compute
the geopotential over the regions of interest as well as enhancing the spatial resolution commensurable with the characteristics
of satellite coverage, which could not be done using a global spherical harmonic representation.
The results in this paper are based on the research supported by the National Science Foundation under the grant no. 0327577. 相似文献
4.
The Meissl scheme for the geodetic ellipsoid 总被引:2,自引:1,他引:1
We present a variant of the Meissl scheme to relate surface spherical harmonic coefficients of the disturbing potential of
the Earth’s gravity field on the surface of the geodetic ellipsoid to surface spherical harmonic coefficients of its first- and second-order normal derivatives on the same or any other ellipsoid.
It extends the original (spherical) Meissl scheme, which only holds for harmonic coefficients computed from geodetic data
on a sphere. In our scheme, a vector of solid spherical harmonic coefficients of one quantity is transformed into spherical
harmonic coefficients of another quantity by pre-multiplication with a transformation matrix. This matrix is diagonal for
transformations between spheres, but block-diagonal for transformations involving the ellipsoid. The computation of the transformation
matrix involves an inversion if the original coefficients are defined on the ellipsoid. This inversion can be performed accurately
and efficiently (i.e., without regularisation) for transformation among different gravity field quantities on the same ellipsoid,
due to diagonal dominance of the matrices. However, transformations from the ellipsoid to another surface can only be performed
accurately and efficiently for coefficients up to degree and order 520 due to numerical instabilities in the inversion. 相似文献
5.
M. Kern T. Preimesberger M. Allesch R. Pail J. Bouman R. Koop 《Journal of Geodesy》2005,78(9):509-519
The satellite missions CHAMP, GRACE, and GOCE mark the beginning of a new era in gravity field determination and modeling. They provide unique models of the global stationary gravity field and its variation in time. Due to inevitable measurement errors, sophisticated pre-processing steps have to be applied before further use of the satellite measurements. In the framework of the GOCE mission, this includes outlier detection, absolute calibration and validation of the SGG (satellite gravity gradiometry) measurements, and removal of temporal effects. In general, outliers are defined as observations that appear to be inconsistent with the remainder of the data set. One goal is to evaluate the effect of additive, innovative and bulk outliers on the estimates of the spherical harmonic coefficients. It can be shown that even a small number of undetected outliers (<0.2 of all data points) can have an adverse effect on the coefficient estimates. Consequently, concepts for the identification and removal of outliers have to be developed. Novel outlier detection algorithms are derived and statistical methods are presented that may be used for this purpose. The methods aim at high outlier identification rates as well as small failure rates. A combined algorithm, based on wavelets and a statistical method, shows best performance with an identification rate of about 99%. To further reduce the influence of undetected outliers, an outlier detection algorithm is implemented inside the gravity field solver (the Quick-Look Gravity Field Analysis tool was used). This results in spherical harmonic coefficient estimates that are of similar quality to those obtained without outliers in the input data. 相似文献
6.
Topographic–isostatic masses represent an important source of gravity field information, especially in the high-frequency
band, even if the detailed mass-density distribution inside the topographic masses is unknown. If this information is used
within a remove-restore procedure, then the instability problems in downward continuation of gravity observations from aircraft
or satellite altitudes can be reduced. In this article, integral formulae are derived for determination of gravitational effects
of topographic–isostatic masses on the first- and second-order derivatives of the gravitational potential for three topographic–isostatic
models. The application of these formulas is useful for airborne gravimetry/gradiometry and satellite gravity gradiometry.
The formulas are presented in spherical approximation by separating the 3D integration in an analytical integration in the
radial direction and 2D integration over the mean sphere. Therefore, spherical volume elements can be considered as being
approximated by mass-lines located at the centre of the discretization compartments (the mass of the tesseroid is condensed
mathematically along its vertical axis). The errors of this approximation are investigated for the second-order derivatives
of the topographic–isostatic gravitational potential in the vicinity of the Earth’s surface. The formulas are then applied
to various scenarios of airborne gravimetry/gradiometry and satellite gradiometry. The components of the gravitational vector
at aircraft altitudes of 4 and 10 km have been determined, as well as the gravitational tensor components at a satellite altitude
of 250 km envisaged for the forthcoming GOCE (gravity field and steady-state ocean-circulation explorer) mission. The numerical
computations are based on digital elevation models with a 5-arc-minute resolution for satellite gravity gradiometry and 1-arc-minute
resolution for airborne gravity/gradiometry. 相似文献
7.
A data-driven approach to local gravity field modelling using spherical radial basis functions 总被引:3,自引:0,他引:3
We propose a methodology for local gravity field modelling from gravity data using spherical radial basis functions. The methodology
comprises two steps: in step 1, gravity data (gravity anomalies and/or gravity disturbances) are used to estimate the disturbing
potential using least-squares techniques. The latter is represented as a linear combination of spherical radial basis functions
(SRBFs). A data-adaptive strategy is used to select the optimal number, location, and depths of the SRBFs using generalized
cross validation. Variance component estimation is used to determine the optimal regularization parameter and to properly
weight the different data sets. In the second step, the gravimetric height anomalies are combined with observed differences
between global positioning system (GPS) ellipsoidal heights and normal heights. The data combination is written as the solution
of a Cauchy boundary-value problem for the Laplace equation. This allows removal of the non-uniqueness of the problem of local
gravity field modelling from terrestrial gravity data. At the same time, existing systematic distortions in the gravimetric
and geometric height anomalies are also absorbed into the combination. The approach is used to compute a height reference
surface for the Netherlands. The solution is compared with NLGEO2004, the official Dutch height reference surface, which has
been computed using the same data but a Stokes-based approach with kernel modification and a geometric six-parameter “corrector
surface” to fit the gravimetric solution to the GPS-levelling points. A direct comparison of both height reference surfaces
shows an RMS difference of 0.6 cm; the maximum difference is 2.1 cm. A test at independent GPS-levelling control points, confirms
that our solution is in no way inferior to NLGEO2004. 相似文献
8.
Space-wise approach to satellite gravity field determination in the presence of coloured noise 总被引:2,自引:2,他引:2
For many years, the gravity field of the Earth was only seen by satellite geodesy as the main factor affecting the orbit and consequently it was retrieved together with a number of other orbital perturbations. Since the advent of a new generation of accelerometers, non-gravitational perturbations can be separated from the gravity effects and a new era of gravity field estimates from space has been born. During preparatory data analysis for new missions performed by the geodetic community, three approaches have been proposed and numerically tested: the brute force method (direct approach), the semi-analytical (time-wise) method and the space-wise method. In particular, the time-wise method takes advantage of the incoming time flow of data and, after performing a Fourier transform of the observation equations, exploits the prevailing block diagonal structure of the normal equations to estimate the spherical harmonic coefficients of the gravity field. Complementary to this is the space-wise approach, which goes back to the traditional computation of the harmonic coefficients by an integration technique or by least-squares collocation. Some advantages and disadvantages are peculiar to both methods, particularly the space-wise approach, which has for a long time ignored the marked signature of the noise spectrum due to the specific measuring conditions of space-borne accelerometers. The application of a proper Wiener filter, exploiting the correlation along the orbit, embedded into an iterative scheme, seems to be the answer. The solution to this major problem of the space-wise approach is illustrated and simulation results are discussed. 相似文献
9.
Regional geoid determination in Antarctica utilizing airborne gravity and topography data 总被引:2,自引:2,他引:0
Mirko Scheinert Jan Müller Reinhard Dietrich Detlef Damaske Volkmar Damm 《Journal of Geodesy》2008,82(7):403-414
Antarctica is the only continent that suffers major gaps in terrestrial gravity data coverage. To overcome this problem and
to close these gaps as well as to densify the global satellite gravity field solutions, the International Association of Geodesy
(IAG) Commission Project 2.4 “Antarctic Geoid” was set into action. This paper reviews the current situation concerning the
gravity field in Antarctica. It is shown that airborne geophysical surveys are the most promising tools to gain new gravity
data in Antarctica. In this context, a number of projects to be carried out during the International Polar Year 2007/2008
will contribute to this goal. To demonstrate the feasibility of the regional geoid improvement in Antarctica, we present a
case study using gravity and topography data of the southern Prince Charles Mountains, East Antarctica. During the processing,
the remove–compute– restore (RCR) technique and least-squares collocation (LSC) were applied. Adding signal parts of up to
6 m to the global gravity field model that was used as a basis, the calculated regional quasigeoid reveals the dominant features
of bedrock topography in that region, namely the graben structure of the Lambert glacier system. The accuracy of the improved
regional quasigeoid is estimated to be at the level of 15 cm. 相似文献
10.
A spatiospectral localization method is discussed for processing the global geopotential coefficients from satellite mission
data to investigate time-variable gravity. The time-variable mass variation signal usually appears associated with a particular
geographical area yielding inherently regional structure, while the dependence of the satellite gravity errors on a geographical
region is not so evident. The proposed localization amplifies the signal-to-noise ratio of the (non-stationary) time-variable
signals in the geopotential coefficient estimates by localizing the global coefficients to the area where the signal is expected
to be largest. The results based on localization of the global satellite gravity coefficients such as Gravity Recovery And
Climate Experiment (GRACE) and Gravity and Ocean Circulation Explorer (GOCE) indicate that the coseismic deformation caused
by great earthquakes such as the 2004 Sumatra–Andaman earthquake can be detected by the low-low tracking and the gradiometer
data within the bandwidths of spherical degrees 15–30 and 25–100, respectively. However, the detection of terrestrial water
storage variation by GOCE gradiometer is equivocal even after localization. 相似文献
11.
A new isostatic model for the Earths gravity field is presented based on a simple hypothesis of layers approximating constant density contrasts. The spherical layer distribution used to describe the hydrostatic equilibrium of the Earths masses leads to a new set of spherical harmonic coefficients for the gravitational potential. First attempts to quantify the information content of these coefficients led to the outcome that they seem to explain the observed gravity field for a certain wavelength band, while they are insufficient for short and very long wavelengths. A synthesis of the derived coefficients over specific degree ranges provided a computation of band-limited geoid undulations on a global scale. The association of these potential quantities with known tectonic structures, such as the topography of the core–mantle boundary, strengthens the belief that the interpretation of Earth gravity models, especially those arising from global digital elevation models, should be considered in close relation with deep-Earth structure. 相似文献
12.
球近似下地球外空间任意类型场元的地形影响 总被引:1,自引:0,他引:1
传统的重力归算方法只适用于地球表面上的重力异常,不能用于扰动重力、垂线偏差、重力梯度等其他类型扰动重力场元,不适合处理除地面外其他高度上场元的地形影响问题。当前,地球重力场探测的场元类型越来越丰富,探测的高度也逐渐转向航空和卫星高度,精确处理地球外空间各种类型重力场元的地形影响已成为地球重力场领域面临的重要课题。本文通过直接分解由地形生成的具有调和性质的引力场,从而导出地球外空间任意高度、任意类型扰动重力场元的地形影响,在此基础上给出在球近似下地形影响的严密算法和高精度快速算法。利用本文推荐的地形影响计算方案,可以方便地处理各种类型地面重力、海洋重力、航空重力、卫星重力、卫星测高数据的地形影响,从而丰富重力场数据处理的内涵,改善地球重力场算法的性能。 相似文献
13.
First GOCE gravity field models derived by three different approaches 总被引:28,自引:10,他引:18
Roland Pail Sean Bruinsma Federica Migliaccio Christoph F?rste Helmut Goiginger Wolf-Dieter Schuh Eduard H?ck Mirko Reguzzoni Jan Martin Brockmann Oleg Abrikosov Martin Veicherts Thomas Fecher Reinhard Mayrhofer Ina Krasbutter Fernando Sans�� Carl Christian Tscherning 《Journal of Geodesy》2011,85(11):819-843
Three gravity field models, parameterized in terms of spherical harmonic coefficients, have been computed from 71 days of GOCE (Gravity field and steady-state Ocean Circulation Explorer) orbit and gradiometer data by applying independent gravity field processing methods. These gravity models are one major output of the European Space Agency (ESA) project GOCE High-level Processing Facility (HPF). The processing philosophies and architectures of these three complementary methods are presented and discussed, emphasizing the specific features of the three approaches. The resulting GOCE gravity field models, representing the first models containing the novel measurement type of gravity gradiometry ever computed, are analysed and assessed in detail. Together with the coefficient estimates, full variance-covariance matrices provide error information about the coefficient solutions. A comparison with state-of-the-art GRACE and combined gravity field models reveals the additional contribution of GOCE based on only 71 days of data. Compared with combined gravity field models, large deviations appear in regions where the terrestrial gravity data are known to be of low accuracy. The GOCE performance, assessed against the GRACE-only model ITG-Grace2010s, becomes superior at degree 150, and beyond. GOCE provides significant additional information of the global Earth gravity field, with an accuracy of the 2-month GOCE gravity field models of 10?cm in terms of geoid heights, and 3?mGal in terms of gravity anomalies, globally at a resolution of 100?km (degree/order 200). 相似文献
14.
Computation of spherical harmonic coefficients and their error estimates using least-squares collocation 总被引:4,自引:0,他引:4
C. C. Tscherning 《Journal of Geodesy》2001,75(1):12-18
Equations expressing the covariances between spherical harmonic coefficients and linear functionals applied on the anomalous
gravity potential, T, are derived. The functionals are the evaluation functionals, and those associated with first- and second-order derivatives
of T. These equations form the basis for the prediction of spherical harmonic coefficients using least-squares collocation (LSC).
The equations were implemented in the GRAVSOFT program GEOCOL. Initially, tests using EGM96 were performed using global and
regional sets of geoid heights, gravity anomalies and second-order vertical gravity gradients at ground level and at altitude.
The global tests confirm that coefficients may be estimated consistently using LSC while the error estimates are much too
large for the lower-order coefficients. The validity of an error estimate calculated using LSC with an isotropic covariance
function is based on a hypothesis that the coefficients of a specific degree all belong to the same normal distribution. However,
the coefficients of lower degree do not fulfil this, and this seems to be the reason for the too-pessimistic error estimates.
In order to test this the coefficients of EGM96 were perturbed, so that the pertubations for a specific degree all belonged
to a normal distribution with the variance equal to the mean error variance of the coefficients. The pertubations were used
to generate residual geoid heights, gravity anomalies and second-order vertical gravity gradients. These data were then used
to calculate estimates of the perturbed coefficients as well as error estimates of the quantities, which now have a very good
agreement with the errors computed from the simulated observed minus calculated coefficients. Tests with regionally distributed
data showed that long-wavelength information is lost, but also that it seems to be recovered for specific coefficients depending
on where the data are located.
Received: 3 February 2000 / Accepted: 23 October 2000 相似文献
15.
E. W. Grafarend 《Journal of Geodesy》2001,75(7-8):363-390
In a comparison of the solution of the spherical horizontal and vertical boundary value problems of physical geodesy it is
aimed to construct downward continuation operators for vertical deflections (surface gradient of the incremental gravitational
potential) and for gravity disturbances (vertical derivative of the incremental gravitational potential) from points on the
Earth's topographic surface or of the three-dimensional (3-D) Euclidean space nearby down to the international reference sphere
(IRS). First the horizontal and vertical components of the gravity vector, namely spherical vertical deflections and spherical
gravity disturbances, are set up. Second, the horizontal and vertical boundary value problem in spherical gravity and geometry
space is considered. The incremental gravity vector is represented in terms of vector spherical harmonics. The solution of
horizontal spherical boundary problem in terms of the horizontal vector-valued Green function converts vertical deflections
given on the IRS to the incremental gravitational potential external in the 3-D Euclidean space. The horizontal Green functions
specialized to evaluation and source points on the IRS coincide with the Stokes kernel for vertical deflections. Third, the
vertical spherical boundary value problem is solved in terms of the vertical scalar-valued Green function. Fourth, the operators
for upward continuation of vertical deflections given on the IRS to vertical deflections in its external 3-D Euclidean space
are constructed. Fifth, the operators for upward continuation of incremental gravity given on the IRS to incremental gravity
to the external 3-D Euclidean space are generated. Finally, Meissl-type diagrams for upward continuation and regularized downward
continuation of horizontal and vertical gravity data, namely vertical deflection and incremental gravity, are produced.
Received: 10 May 2000 / Accepted: 26 February 2001 相似文献
16.
An analysis of vertical deflections derived from high-degree spherical harmonic models 总被引:5,自引:4,他引:1
C. Jekeli 《Journal of Geodesy》1999,73(1):10-22
The theoretical differences between the Helmert deflection of the vertical and that computed from a truncated spherical harmonic
series of the gravity field, aside from the limited spectral content in the latter, include the curvature of the normal plumb
line, the permanent tidal effect, and datum origin and orientation offsets. A numerical comparison between deflections derived
from spherical harmonic model EGM96 and astronomic deflections in the conterminous United States (CONUS) shows that correcting
these systematic effects reduces the mean differences in some areas. Overall, the mean difference in CONUS is reduced from
−0.219 arcsec to −0.058 arcsec for the south–north deflection, and from +0.016 arcsec to +0.004 arcsec for the west–east deflection.
Further analysis of the root-mean-square differences indicates that the high-degree spectrum of the EGM96 model has significantly
less power than implied by the deflection data.
Received: 9 December 1997 / Accepted: 21 August 1998 相似文献
17.
Performance of three types of Stokes's kernel in the combined solution for the geoid 总被引:8,自引:6,他引:2
When regional gravity data are used to compute a gravimetric geoid in conjunction with a geopotential model, it is sometimes
implied that the terrestrial gravity data correct any erroneous wavelengths present in the geopotential model. This assertion
is investigated. The propagation of errors from the low-frequency terrestrial gravity field into the geoid is derived for
the spherical Stokes integral, the spheroidal Stokes integral and the Molodensky-modified spheroidal Stokes integral. It is
shown that error-free terrestrial gravity data, if used in a spherical cap of limited extent, cannot completely correct the
geopotential model. Using a standard norm, it is shown that the spheroidal and Molodensky-modified integration kernels offer
a preferable approach. This is because they can filter out a large amount of the low-frequency errors expected to exist in
terrestrial gravity anomalies and thus rely more on the low-frequency geopotential model, which currently offers the best
source of this information.
Received: 11 August 1997 / Accepted: 18 August 1998 相似文献
18.
广义球谐函数定积分计算方法的改进 总被引:1,自引:0,他引:1
运用球谐函数定积分的基本递推公式,推导了在重力场球谐综合与球谐分析中出现的广义球谐函数定积分的计算公式;给出了其适用于超高阶次的改良型递推公式。数值试验表明,该改良公式具有较高的计算精度和计算速度,解决了超高阶次广义球谐函数定积分计算的溢出问题,拓展了这类定积分的计算公式。他们的数值实现为利用位模型计算高分辨率扰动重力场元格网平均值、重力场球谐综合分析等奠定了基础。 相似文献
19.
为实现大范围、高精度基准重力梯度数据库的构建,考虑到重力梯度场对地形质量的敏感效应,一般利用恒密度数字高程模型来求取重力梯度值,从而忽略了地形密度变化以及水准面以下密度异常对重力梯度的影响。根据重力位理论中求解边值问题的数值应用方法,直接利用重力异常数据求取重力梯度场,弥补了密度变化和密度异常在重力梯度上的反映。根据模型算例和实测重力异常数据求取了剖面重力梯度值,结果表明,限于重力数据空间分辨率的影响,利用重力异常数据可恢复中长波段重力梯度场。该方法与地形数据求取重力梯度和卫星重力梯度测量等方法技术相结合,对重力梯度数据库的建设具有实际应用价值。 相似文献
20.
Spherical cap harmonic analysis: a comment on its proper use for local gravity field representation 总被引:1,自引:0,他引:1
Spherical cap harmonic analysis is the appropriate analytical technique for modelling Laplacian potential and the corresponding
field components over a spherical cap. This paper describes the use of this method by means of a least-squares approach for
local gravity field representation. Formulations for the geoid undulation and the components ξ, η of the deflection of the
vertical are derived, together with some warnings in the application of the technique. Although most of the formulations have
been given by another paper, these were confusing or even incorrect, mainly because of an improper application of the spherical
cap harmonic analysis.
Received: 16 January 1996 / Accepted: 17 March 1997 相似文献