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1.
Mission design,operation and exploitation of the gravity field and steady-state ocean circulation explorer mission 总被引:6,自引:3,他引:3
The European Space Agency’s Gravity field and steady-state ocean circulation explorer mission (GOCE) was launched on 17 March
2009. As the first of the Earth Explorer family of satellites within the Agency’s Living Planet Programme, it is aiming at
a better understanding of the Earth system. The mission objective of GOCE is the determination of the Earth’s gravity field
and geoid with high accuracy and maximum spatial resolution. The geoid, combined with the de facto mean ocean surface derived
from twenty-odd years of satellite radar altimetry, yields the global dynamic ocean topography. It serves ocean circulation
and ocean transport studies and sea level research. GOCE geoid heights allow the conversion of global positioning system (GPS)
heights to high precision heights above sea level. Gravity anomalies and also gravity gradients from GOCE are used for gravity-to-density
inversion and in particular for studies of the Earth’s lithosphere and upper mantle. GOCE is the first-ever satellite to carry
a gravitational gradiometer, and in order to achieve its challenging mission objectives the satellite embarks a number of
world-first technologies. In essence the spacecraft together with its sensors can be regarded as a spaceborne gravimeter.
In this work, we describe the mission and the way it is operated and exploited in order to make available the best-possible
measurements of the Earth gravity field. The main lessons learned from the first 19 months in orbit are also provided, in
as far as they affect the quality of the science data products and therefore are of specific interest for GOCE data users. 相似文献
2.
The problem of “global height datum unification” is solved in the gravity potential space based on: (1) high-resolution local
gravity field modeling, (2) geocentric coordinates of the reference benchmark, and (3) a known value of the geoid’s potential.
The high-resolution local gravity field model is derived based on a solution of the fixed-free two-boundary-value problem
of the Earth’s gravity field using (a) potential difference values (from precise leveling), (b) modulus of the gravity vector
(from gravimetry), (c) astronomical longitude and latitude (from geodetic astronomy and/or combination of (GNSS) Global Navigation
Satellite System observations with total station measurements), (d) and satellite altimetry. Knowing the height of the reference
benchmark in the national height system and its geocentric GNSS coordinates, and using the derived high-resolution local gravity
field model, the gravity potential value of the zero point of the height system is computed. The difference between the derived
gravity potential value of the zero point of the height system and the geoid’s potential value is computed. This potential
difference gives the offset of the zero point of the height system from geoid in the “potential space”, which is transferred
into “geometry space” using the transformation formula derived in this paper. The method was applied to the computation of
the offset of the zero point of the Iranian height datum from the geoid’s potential value W
0=62636855.8 m2/s2. According to the geometry space computations, the height datum of Iran is 0.09 m below the geoid. 相似文献
3.
Geoid determination using one-step integration 总被引:1,自引:1,他引:0
P. Novák 《Journal of Geodesy》2003,77(3-4):193-206
A residual (high-frequency) gravimetric geoid is usually computed from geographically limited ground, sea and/or airborne gravimetric data. The mathematical model for its determination from ground gravity is based on the transformation of observed discrete values of gravity into gravity potential related to either the international ellipsoid or the geoid. The two reference surfaces are used depending on height information that accompanies ground gravity data: traditionally orthometric heights determined by geodetic levelling were used while GPS positioning nowadays allows for estimation of geodetic (ellipsoidal) heights. This transformation is usually performed in two steps: (1) observed values of gravity are downward continued to the ellipsoid or the geoid, and (2) gravity at the ellipsoid or the geoid is transformed into the corresponding potential. Each of these two steps represents the solution of one geodetic boundary-value problem of potential theory, namely the first and second or third problem. Thus two different geodetic boundary-value problems must be formulated and solved, which requires numerical evaluation of two surface integrals. In this contribution, a mathematical model in the form of a single Fredholm integral equation of the first kind is presented and numerically investigated. This model combines the solution of the first and second/third boundary-value problems and transforms ground gravity disturbances or anomalies into the harmonically downward continued disturbing potential at the ellipsoid or the geoid directly. Numerical tests show that the new approach offers an efficient and stable solution for the determination of the residual geoid from ground gravity data. 相似文献
4.
A new technique to determine geoid and orthometric heights from satellite positioning and geopotential numbers 总被引:1,自引:0,他引:1
L. E. Sjöberg 《Journal of Geodesy》2006,80(6):304-312
This paper takes advantage of space-technique-derived positions on the Earth’s surface and the known normal gravity field to determine the height anomaly from geopotential numbers. A new method is also presented to downward-continue the height anomaly to the geoid height. The orthometric height is determined as the difference between the geodetic (ellipsoidal) height derived by space-geodetic techniques and the geoid height. It is shown that, due to the very high correlation between the geodetic height and the computed geoid height, the error of the orthometric height determined by this method is usually much smaller than that provided by standard GPS/levelling. Also included is a practical formula to correct the Helmert orthometric height by adding two correction terms: a topographic roughness term and a correction term for lateral topographic mass–density variations. 相似文献
5.
The geodetic boundary value problem is formulated which uses as boundary values the differences between the geopotential of
points at the surface of the continents and the potential of the geoid. These differences are computed by gravity measurements
and levelling data. In addition, the shape of the geoid over the oceans is assumed to be known from satellite altimetry and
the shape of the continents from satellite results together with three-dimensional triangulation. The boundary value problem
thus formulated is equivalent to Dirichlet's exterior problem except for the unknown potential of the geoid. This constant
is determined by an integral equation for the normal derivative of the gravitational potential which results from the first
derivative of Green's fundamental formula. The general solution, which exists, of the integral equation gives besides the
potential of the geoid the solution of the geodetic boundary value problem. In addition approximate solutions for a spherical
surface of the earth are derived. 相似文献
6.
J. C. Bhattacharji 《Journal of Geodesy》1980,54(2):225-233
The Everest spheroid, 1830, in general use in the Survey of India, was finally oriented in an arbitrary manner at the Indian
geodetic datum in 1840; while the international spheroid, 1924, in use for scientific purposes; was locally fitted to the
Indian geoid in 1927. An attempt is here made to obtain the initial values for the Indian geodetic datum in absolute terms
on GRS 67 by least-square solution technique, making use of the available astro-geodetic data in India, and the corresponding
generalised gravimetric values at the considered astro-geodetic points, as derived from the mean gravity anomalies over1°×1° squares of latitude and longitude in and around the Indian sub-continent, and over5° equal area blocks covering the rest of the earth’s surface. The values obtained independently by gravimetric method, were
also considered before actual finalization of the results of the present determination. 相似文献
7.
P. Schwintzer C. Reigber A. Bode Z. Kang S. Y. Zhu F.-H. Massmann J. C. Raimondo R. Biancale G. Balmino J. M. Lemoine B. Moynot J. C. Marty F. Barlier Y. Boudon 《Journal of Geodesy》1997,71(4):189-208
Summary. GFZ Potsdam and GRGS Toulouse/Grasse jointly developed a new pair of global models of the Earth's gravity field to satisfy
the requirements of the recent and future geodetic and altimeter satellite missions. A precise gravity model is a prerequisite
for precise satellite orbit restitution, tracking station positioning and altimeter data reduction. According to different
applications envisaged, the new model exists in two parallel versions: the first one being derived exclusively from satellite
tracking data acquired on 34 satellites, the second one further incorporating satellite altimeter data over the oceans and
terrestrial gravity data. The most recent “satellite-only” gravity model is labelled GRIM4-S4 and the “combined” gravity model
GRIM4-C4. The models are solutions in spherical harmonics and have a resolution up to degree and order 60 plus a few resonance
terms in the case of GRIM4-S4, and up to degree/order 72 in the case of GRIM4-C4, corresponding to a spatial resolution of
555 km at the Earth's surface. The gravitational coefficients were estimated in a rigorous least squares adjustment simultaneously
with ocean tidal terms and tracking station position parameters, so that each gravity model is associated with a consistent
ocean tide model and a terrestrial reference frame built up by over 300 optical, laser and Doppler tracking stations. Comprehensive
quality tests with external data and models, and test arc computations over a wide range of satellites have demonstrated the
state-of-the-art capabilities of both solutions in long-wavelength geoid representation and in precise orbit computation.
Received 1 February 1996; Accepted 17 July 1996 相似文献
8.
Far-zone effects for different topographic-compensation models based on a spherical harmonic expansion of the topography 总被引:1,自引:1,他引:0
The determination of the gravimetric geoid is based on the magnitude of gravity observed at the surface of the Earth or at
airborne altitude. To apply the Stokes’s or Hotine’s formulae at the geoid, the potential outside the geoid must be harmonic
and the observed gravity must be reduced to the geoid. For this reason, the topographic (and atmospheric) masses outside the
geoid must be “condensed” or “shifted” inside the geoid so that the disturbing gravity potential T fulfills Laplace’s equation everywhere outside the geoid. The gravitational effects of the topographic-compensation masses
can also be used to subtract these high-frequent gravity signals from the airborne observations and to simplify the downward
continuation procedures. The effects of the topographic-compensation masses can be calculated by numerical integration based
on a digital terrain model or by representing the topographic masses by a spherical harmonic expansion. To reduce the computation
time in the former case, the integration over the Earth can be divided into two parts: a spherical cap around the computation
point, called the near zone, and the rest of the world, called the far zone. The latter one can be also represented by a global
spherical harmonic expansion. This can be performed by a Molodenskii-type spectral approach. This article extends the original
approach derived in Novák et al. (J Geod 75(9–10):491–504, 2001), which is restricted to determine the far-zone effects for
Helmert’s second method of condensation for ground gravimetry. Here formulae for the far-zone effects of the global topography
on gravity and geoidal heights for Helmert’s first method of condensation as well as for the Airy-Heiskanen model are presented
and some improvements given. Furthermore, this approach is generalized for determining the far-zone effects at aeroplane altitudes.
Numerical results for a part of the Canadian Rocky Mountains are presented to illustrate the size and distributions of these
effects. 相似文献
9.
The international ellipsoid, 1924, was locally fitted to the Indian geoid in 1927. An attempt is here made to obtain the initial
values for the Indian geodetic datum (I.G.D.) in absolute terms by gravimetric method using the available gravity material.
The values obtained independently by the author’s least-squares solution technique, making use of the available astrogeodetic
data in India, were also utilized in the results of the present determination. 相似文献
10.
P. Moore 《Journal of Geodesy》1987,61(3):223-234
Starlette was launched in 1975 in order to study temporal variations in the Earth’s gravity field; in particular, tidal and
Earth rotation effects. For the period April 1983 to April 1984 over12,700 normal points of laser ranging data to Starlette have been sub-divided into49 near consecutive 5–6 day arcs. Normal equations for each arc as obtained from a least-squares data reduction procedure, were
solved for ocean tidal parameters along with other geodetic and geodynamic parameters. The tidal parameters are defined relative
to Wahr’s body tides and Wahr’s nutation model and show fair agreement with other satellite derived results and those obtained
from spherical harmonic decomposition of global ocean tidal models. 相似文献
11.
H. Sünkel 《Journal of Geodesy》1981,55(1):31-40
GSPP is a computer program system which has been developed for the purposes of automatically determining and representing
gravity field surfaces like the geoid, the field of gravity anomalies or deviations of the vertical at prescribed altitude,
etc. The system processes gravity field information given by a heterogeneous set of linear functionals of the anomalous potential
superimposed by noise, and provides automatically gravity field surfaces in terms of profiles, contour maps and/or 3-dimensional
representations.
The solution is generally based on least-squares collocation; for a homogeneous data set, a simple weighted average interpolation
is available as well. Based on the given data, surface function values at the grid points of a regular rectangular grid are
predicted. The representation of the surfaces is smooth using bicubic spline functions.
GSPP has a control unit which performs all necessary decision processes and such reduces the user’s decision making to a minimum.
The system has been designed for geodetic purposes only; however, because of its versatility and flexibility it presents itself
also for applications in other geosciences. 相似文献
12.
M. S. Petrovskaya 《Journal of Geodesy》1979,53(1):37-51
Summary The possibility of improving the convergence of Molodensky’s series is considered. Then new formulas are derived for the solution
of the geodetic boundary value problem. One of them presents an expression for the boundary condition which involves a linear
combination of Stokes’ constants and surface gravity anomalies. This differs from the usually used relation by the appearance
of additional terms dependent on second order terns with respect to the elevations of the earth’s surface. The formulas are
derived for Stokes’ constants and the anomalous potential in terms of surface anomalies. As compared to the Taylor’s series
of Molodensky, they are presented in the form of surface harmonic series. Due regard is made to the earth’s oblateness, in
addition to the terrain topography. 相似文献
13.
P. J. G. Teunissen 《Journal of Geodesy》1982,56(4):356-363
For computing the geodetic coordinates ϕ and γ on the ellipsoid one needs information of the gravity field, thus making it
possible to reduce the terrestrial observations to the reference surface. Neglect of gravity field data, such as deflections
of the vertical and geoid heights, results in misclosure effects, which can be described using the object of anholonomity. 相似文献
14.
Regional height systems do not refer to a common equipotential surface, such as the geoid. They are usually referred to the mean sea level at a reference tide gauge. As mean sea level varies (by ±1 to 2 m) from place to place and from continent to continent each tide gauge has an unknown bias with respect to a common reference surface, whose determination is what the height datum problem is concerned with. This paper deals with this problem, in connection to the availability of satellite gravity missions data. Since biased heights enter into the computation of terrestrial gravity anomalies, which in turn are used for geoid determination, the biases enter as secondary or indirect effect also in such a geoid model. In contrast to terrestrial gravity anomalies, gravity and geoid models derived from satellite gravity missions, and in particular GRACE and GOCE, do not suffer from those inconsistencies. Those models can be regarded as unbiased. After a review of the mathematical formulation of the problem, the paper examines two alternative approaches to its solution. The first one compares the gravity potential coefficients in the range of degrees from 100 to 200 of an unbiased gravity field from GOCE with those of the combined model EGM2008, that in this range is affected by the height biases. This first proposal yields a solution too inaccurate to be useful. The second approach compares height anomalies derived from GNSS ellipsoidal heights and biased normal heights, with anomalies derived from an anomalous potential which combines a satellite-only model up to degree 200 and a high-resolution global model above 200. The point is to show that in this last combination the indirect effects of the height biases are negligible. To this aim, an error budget analysis is performed. The biases of the high frequency part are proved to be irrelevant, so that an accuracy of 5 cm per individual GNSS station is found. This seems to be a promising practical method to solve the problem. 相似文献
15.
Spherical harmonic expansions of the geopotential are frequently used for modelling the earth’s gravity field. Degree and
order of recently available models go up to 360, corresponding to a resolution of about50 km. Thus, the high degree potential coefficients can be verified nowadays even by locally distributed sets of terrestrial gravity
anomalies. These verifications are important when combining the short wavelength model impact, e.g. for regional geoid determinations
by means of collocation solutions. A method based on integral formulae is presented, enabling the improvement of geopotential
models with respect to non-global distributed gravity anomalies. To illustrate the foregoing, geoid computations are carried
out for the area of Iran, introducing theGPM2 geopotential model in combination with available regional gravity data. The accuracy of the geoid determination is estimated
from a comparison with Doppler and levelling data to ±1.4m. 相似文献
16.
Many regions around the world require improved gravimetric data bases to support very accurate geoid modeling for the modernization
of height systems using GPS. We present a simple yet effective method to assess gravity data requirements, particularly the
necessary resolution, for a desired precision in geoid computation. The approach is based on simulating high-resolution gravimetry
using a topography-correlated model that is adjusted to be consistent with an existing network of gravity data. Analysis of
these adjusted, simulated data through Stokes’s integral indicates where existing gravity data must be supplemented by new
surveys in order to achieve an acceptable level of omission error in the geoid undulation. The simulated model can equally
be used to analyze commission error, as well as model error and data inconsistencies to a limited extent. The proposed method
is applied to South Korea and shows clearly where existing gravity data are too scarce for precise geoid computation. 相似文献
17.
Christopher Kotsakis 《Journal of Geodesy》2008,82(4-5):261-260
Transforming height information that refers to an ellipsoidal Earth reference model, such as the geometric heights determined
from GPS measurements or the geoid undulations obtained by a gravimetric geoid solution, from one geodetic reference frame
(GRF) to another is an important task whose proper implementation is crucial for many geodetic, surveying and mapping applications.
This paper presents the required methodology to deal with the above problem when we are given the Helmert transformation parameters
that link the underlying Cartesian coordinate systems to which an Earth reference ellipsoid is attached. The main emphasis
is on the effect of GRF spatial scale differences in coordinate transformations involving reference ellipsoids, for the particular
case of heights. Since every three-dimensional Cartesian coordinate system ‘gauges’ an attached ellipsoid according to its
own accessible scale, there will exist a supplementary contribution from the scale variation between the involved GRFs on
the relative size of their attached reference ellipsoids. Neglecting such a scale-induced indirect effect corrupts the values
for the curvilinear geodetic coordinates obtained from a similarity transformation model, and meter-level apparent offsets
can be introduced in the transformed heights. The paper explains the above issues in detail and presents the necessary mathematical
framework for their treatment.
An erratum to this article can be found at 相似文献
18.
Height datum definition,height datum connection and the role of the geodetic boundary value problem 总被引:3,自引:3,他引:3
Vertical datum definition is identical with the choice of a potential (or height) value for the fundamental bench mark. Also
the connection of two adjacent vertical datums poses no principal problem as long as the potential (or height) value of two
bench marks of the two systems is known and they can be connected by levelling. Only the unification of large vertical datums
and the connection of vertical datums separated by an ocean remains difficult.
Two vertical datums can be connected indirectly by means of a combination of precise geocentric positions of two points, as
derived by space techniques, their potential (or height) value in the respective height datum and their geoid height difference.
The latter requires the solution of the linear geodetic boundary value problem under the assumption that potential and gravity
anomalies refer to a variety of height datums. The unknown off-sets between the various datums appear in the solution inside
and outside the Stokes integral and can be estimated in a least squares adjustment, if geocentric positions, levelled heights
and adequate gravity material are available for all datum zones. The problem can in principle also be solved involving only
two datums, in case a precise global gravity field becomes available purely from satellite methods. 相似文献
19.
A detailed gravimetric geoid has been computed for the Nortwest Atlantic Ocean and Caribbean Sea area in support of the calibration
and evaluation of the GEOS-3 altimeter. This geoid, computed on a 15’ x 15’ grid was based upon a combination of surface gravity
data and the GSFC GEM-8 gravitational field model. This gravimetric geoid has been compared with passes of SKYLAB altimeter
data recorded in the Atlantic Ocean, and three typical passes are presented. The relative agreement of the two data types
is quite good with differences generally less than 2 meters for these passes. Sea surface manifestations of numerous short
wavelength (≈ 100 km) oceanographic features indicated in the altimeter data are also confirmed by the gravimetric geoid. 相似文献
20.
A solution to the downward continuation effect on the geoid determined by Stokes' formula 总被引:2,自引:1,他引:2
L.E. Sjöberg 《Journal of Geodesy》2003,77(1-2):94-100
The analytical continuation of the surface gravity anomaly to sea level is a necessary correction in the application of Stokes'
formula for geoid estimation. This process is frequently performed by the inversion of Poisson's integral formula for a sphere.
Unfortunately, this integral equation corresponds to an improperly posed problem, and the solution is both numerically unstable,
unless it is well smoothed, and tedious to compute. A solution that avoids the intermediate step of downward continuation
of the gravity anomaly is presented. Instead the effect on the geoid as provided by Stokes' formula is studied directly. The
practical solution is partly presented in terms of a truncated Taylor series and partly as a truncated series of spherical
harmonics. Some simple numerical estimates show that the solution mostly meets the requests of a 1-cm geoid model, but the
truncation error of the far zone must be studied more precisely for high altitudes of the computation point. In addition,
it should be emphasized that the derived solution is more computer efficient than the detour by Poisson's integral.
Received: 6 February 2002 / Accepted: 18 November 2002
Acknowledgements. Jonas ?gren carried out the numerical calculations and gave some critical and constructive remarks on a draft version of
the paper. This support is cordially acknowledged. Also, the thorough work performed by one unknown reviewer is very much
appreciated. 相似文献