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1.
The Somigliana–Pizzetti gravity field (the International gravity formula), namely the gravity field of the level ellipsoid
(the International Reference Ellipsoid), is derived to the sub-nanoGal accuracy level in order to fulfil the demands of modern
gravimetry (absolute gravimeters, super conducting gravimeters, atomic gravimeters). Equations (53), (54) and (59) summarise
Somigliana–Pizzetti gravity Γ(φ,u) as a function of Jacobi spheroidal latitude φ and height u to the order ?(10−10 Gal), and Γ(B,H) as a function of Gauss (surface normal) ellipsoidal latitude B and height H to the order ?(10−10 Gal) as determined by GPS (`global problem solver'). Within the test area of the state of Baden-Württemberg, Somigliana–Pizzetti
gravity disturbances of an average of 25.452 mGal were produced. Computer programs for an operational application of the new
international gravity formula with (L,B,H) or (λ,φ,u) coordinate inputs to a sub-nanoGal level of accuracy are available on the Internet.
Received: 23 June 2000 / Accepted: 2 January 2001 相似文献
2.
The passive satellite GFZ-1 has been orbiting the Earth since April 1995. The purpose of this mission is to improve the current
knowledge of the Earth's gravity field by analysing gravitational orbit perturbations observed at unique low altitudes, below
400 km. GFZ-1 is one target of the international satellite laser ranging ground network. An evaluation of the first 30 months
of GFZ-1 laser tracking data led to a new version of the global GRIM4-S4 satellite-only gravity field model: GRIM4-S4G. Information
was obtained from GFZ-1 data for spherical harmonic coefficients up to degree 100, which was not possible in any earlier satellite-only
gravity field solution. GFZ-1's contribution to a global 5 × 5° geoid and gravity field representations is moderate but visible
with a 1 cm and 0.1 mGal gain in accuracy on a level of 75 cm and 5 mGal, respectively.
Received: 10 November 1998 / Accepted: 19 April 1999 相似文献
3.
Two numerical techniques are used in recent regional high-frequency geoid computations in Canada: discrete numerical integration
and fast Fourier transform. These two techniques have been tested for their numerical accuracy using a synthetic gravity field.
The synthetic field was generated by artificially extending the EGM96 spherical harmonic coefficients to degree 2160, which
is commensurate with the regular 5′ geographical grid used in Canada. This field was used to generate self-consistent sets of synthetic gravity anomalies and
synthetic geoid heights with different degree variance spectra, which were used as control on the numerical geoid computation
techniques. Both the discrete integration and the fast Fourier transform were applied within a 6∘ spherical cap centered at each computation point. The effect of the gravity data outside the spherical cap was computed using
the spheroidal Molodenskij approach. Comparisons of these geoid solutions with the synthetic geoid heights over western Canada
indicate that the high-frequency geoid can be computed with an accuracy of approximately 1 cm using the modified Stokes technique,
with discrete numerical integration giving a slightly, though not significantly, better result than fast Fourier transform.
Received: 2 November 1999 / Accepted: 11 July 2000 相似文献
4.
XU Xinyu LI Jiancheng ZOU Xiancai CHU Yonghai 《地球空间信息科学学报》2007,10(3):168-172
The principle and method for solving three types of satellite gravity gradient boundary value problems by least-squares are discussed in detail. Also, kernel function expressions of the least-squares solution of three geodetic boundary value problems with the observations {Γ zz },{Γ xz , Γ yz} and {Γ xx -Γ yy ,2 Γxy}are presented. From the results of recovering gravity field using simulated gravity gradient tensor data, we can draw a conclusion that satellite gravity gradient integral formulas derived from least-squares are valid and rigorous for recovering the gravity field. 相似文献
5.
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
6.
Johannes Bouman Sietse Rispens Thomas Gruber Radboud Koop Ernst Schrama Pieter Visser Carl Christian Tscherning Martin Veicherts 《Journal of Geodesy》2009,83(7):659-678
One of the products derived from the gravity field and steady-state ocean circulation explorer (GOCE) observations are the
gravity gradients. These gravity gradients are provided in the gradiometer reference frame (GRF) and are calibrated in-flight
using satellite shaking and star sensor data. To use these gravity gradients for application in Earth scienes and gravity
field analysis, additional preprocessing needs to be done, including corrections for temporal gravity field signals to isolate
the static gravity field part, screening for outliers, calibration by comparison with existing external gravity field information
and error assessment. The temporal gravity gradient corrections consist of tidal and nontidal corrections. These are all generally
below the gravity gradient error level, which is predicted to show a 1/f behaviour for low frequencies. In the outlier detection, the 1/f error is compensated for by subtracting a local median from the data, while the data error is assessed using the median absolute
deviation. The local median acts as a high-pass filter and it is robust as is the median absolute deviation. Three different
methods have been implemented for the calibration of the gravity gradients. All three methods use a high-pass filter to compensate
for the 1/f gravity gradient error. The baseline method uses state-of-the-art global gravity field models and the most accurate results
are obtained if star sensor misalignments are estimated along with the calibration parameters. A second calibration method
uses GOCE GPS data to estimate a low-degree gravity field model as well as gravity gradient scale factors. Both methods allow
to estimate gravity gradient scale factors down to the 10−3 level. The third calibration method uses high accurate terrestrial gravity data in selected regions to validate the gravity
gradient scale factors, focussing on the measurement band. Gravity gradient scale factors may be estimated down to the 10−2 level with this method. 相似文献
7.
Exploring gravity field determination from orbit perturbations of the European Gravity Mission GOCE 总被引:5,自引:0,他引:5
A comparison was made between two methods for gravity field recovery from orbit perturbations that can be derived from global
positioning system satellite-to-satellite tracking observations of the future European gravity field mission GOCE (Gravity
Field and Steady-State Ocean Circulation Explorer). The first method is based on the analytical linear orbit perturbation
theory that leads under certain conditions to a block-diagonal normal matrix for the gravity unknowns, significantly reducing
the required computation time. The second method makes use of numerical integration to derive the observation equations, leading
to a full set of normal equations requiring powerful computer facilities. Simulations were carried out for gravity field recovery
experiments up to spherical harmonic degree and order 80 from 10 days of observation. It was found that the first method leads
to large approximation errors as soon as the maximum degree surpasses the first resonance orders and great care has to be
taken with modeling resonance orbit perturbations, thereby loosing the block-diagonal structure. The second method proved
to be successful, provided a proper division of the data period into orbital arcs that are not too long.
Received: 28 April 2000 / Accepted: 6 November 2000 相似文献
8.
Christopher Jekeli 《Journal of Geodesy》1980,54(2):137-147
Errors are considered in the outer zone contribution to oceanic undulation differences as obtained from a set of potential
coefficients complete to degree 180. It is assumed that the gravity data of the inner zone (a spherical cap), consisting of
either gravity anomalies or gravity disturbances, has negligible error. This implies that error estimates of the total undulation
difference are analyzed. If the potential coefficients are derived from a global field of 1°×1° mean anomalies accurate to
εΔg=10 mgal, then for a cap radius of 10°, the undulation difference error (for separations between 100 km and 2000 km) ranges
from 13 cm to 55 cm in the gravity anomaly case and from 6 cm to 36 cm in the gravity disturbance case. If εΔg is reduced to 1 mgal, these errors in both cases are less than 10 cm. In the absence of a spherical cap, both cases yield
identical error estimates: about 68 cm if εΔg=1 mgal (for most separations) and ranging from 93 cm to 160 cm if εΔg=10 mgal. Introducing a perfect 30-degree reference field, the latter errors are reduced to about 110 cm for most separations. 相似文献
9.
K. H. Neumayer 《Journal of Geodesy》1998,72(12):698-704
An attempt is made to bridge the gap between closed-form harmonic upward continuation (HUC) of analytic covariance functions
of the disturbing potential of the anomalous local gravity field and the numerical shaping filter construction when the local
gravity vector is modelled in the framework of Kalman filtering. Some fundamental concepts of the local gravity field, interpreted
as a stochastic process that is stationary in the plane and harmonic in the upper half space, are reviewed. The shaping-filter
modelling technique for the local gravity vector is introduced. To determine the relation between the disturbing potential
covariance function and the gravity vector covariance matrix, the role of the so-called admissible pair is established. It
is shown that rescaling an admissible pair leads to an analogue rescaling of the shaping filter matrices derived hereof; no
cumbersome numerical recalculations are necessary. The class of covariance functions whose corresponding shaping filters possess
a closed-form HUC are identified as models whose HUC can be interpreted as a rescaling.
Received: 17 December 1997 / Accepted: 7 September 1998 相似文献
10.
On the basis of gravity field model (EIGEN_CG01C), together with multi-altimeter data, the improved deflection of the vertical gridded in 2'×2' in China marginal sea and gridded in 5'×5' in the global sea was determined by using the weighted method of along-track least squares, and the accuracy is better than 1.2^# in China marginal sea. As for the quality of the deflection of the vertical, it meets the challenge for the gravity field of high resolution and accuracy, it shows that, compared with the shipboard gravimetry in the sea, the accuracy of the gravity anomalies computed with the marine deflection of the vertical by inverse Vening-Meinesz formula is 7.75 m.s ^-2. 相似文献
11.
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
12.
GPS-based precise orbit determination of the very low Earth-orbiting gravity mission GOCE 总被引:5,自引:0,他引:5
A prerequisite for the success of future gravity missions like the European Gravity field and steady-state Ocean Circulation
Explorer (GOCE) is a precise orbit determination (POD). A detailed simulation study has been carried out to assess the achievable
orbit accuracy based on satellite-to-satellite tracking (SST) by the US global positioning system (GPS) and in conjunction
the implications for gravity field determination. An orbit accuracy at the few centimeter level seems possible, sufficient
to support the GOCE gravity mission and in particular its gravity gradiometer.
Received: 21 January 2000 / Accepted: 4 July 2000 相似文献
13.
Due to the super rotation of the Earth's inner core, the tilted figure axis of the inner core would progress with respect to the mantle and thus cause the variation of the Earth's external gravity field. This paper improves the present model of the gravity field variation caused by the inner core super rotation. Under the assumption that the inner core is a stratifying ellipsoid whose density function is fitted out from PREM and the super rotation rate is 0.27-0.53°/yr, calculations show that the global temporal variations on the Earth's surface have a maximum value of about 0.79-1.54×10^3 pGal and a global average intensity of about 0.45-0.89×10^ 3 μGal in the whole year of 2007, which is beyond the accuracy of the present gravimetry and even the super conducting gravimeter data. However, both the gravity variations at Beijing and Wuhan vary like sine variables with maximal variations around 0.33 pGal and 0.29 pGal, respectively, in one cycle. Thus, continuous gravity measurements for one or two decades might be able to detect the differential motion of the inner core. 相似文献
14.
Gravity recovery using COSMIC GPS data: application of orbital perturbation theory 总被引:14,自引:0,他引:14
C. Hwang 《Journal of Geodesy》2001,75(2-3):117-136
COSMIC is a joint Taiwan–US mission to study the atmosphere using the Global Positioning System (GPS) occultation technique.
Improved formulas are developed for the radial, along-track, and cross-track perturbations, which are more accurate than the
commonly used order-zero formulas. The formulas are used to simulate gravity recovery using the geodetic GPS data of COSMIC
in the operational phase. Results show that the EGM96 model can be improved up to degree 26 using 1 year of COSMIC data. TOPEX/POSEIDON
altimeter data are used to derive a temporal gravity variation. COSMIC cannot reproduce this gravity variation perfectly because
of data noise and orbital configuration, but the recovered field clearly shows the gravity signature due to mass movement
in an El Ni?o.
Received: 3 March 2000 / Accepted: 10 November 2000 相似文献
15.
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
16.
Validation of GOCE gravity field models by means of orbit residuals and geoid comparisons 总被引:6,自引:3,他引:3
Three GOCE-based gravity field solutions have been computed by ESA’s high-level processing facility and were released to the
user community. All models are accompanied by variance-covariance information resulting either from the least squares procedure
or a Monte-Carlo approach. In order to obtain independent external quality parameters and to assess the current performance
of these models, a set of independent tests based on satellite orbit determination and geoid comparisons is applied. Both
test methods can be regarded as complementary because they either investigate the performance in the long wavelength spectral
domain (orbit determination) or in the spatial domain (geoid comparisons). The test procedure was applied to the three GOCE
gravity field solutions and to a number of selected pre-launch models for comparison. Orbit determination results suggest,
that a pure GOCE gravity field model does not outperform the multi-year GRACE gravity field solutions. This was expected as
GOCE is designed to improve the determination of the medium to high frequencies of the Earth gravity field (in the range of
degree and order 50 to 200). Nevertheless, in case of an optimal combination of GOCE and GRACE data, orbit determination results
should not deteriorate. So this validation procedure can also be used for testing the optimality of the approach adopted for
producing combined GOCE and GRACE models. Results from geoid comparisons indicate that with the 2 months of GOCE data a significant
improvement in the determination of the spherical harmonic spectrum of the global gravity field between degree 50 and 200
can be reached. Even though the ultimate mission goal has not yet been reached, especially due to the limited time span of
used GOCE data (only 2 months), it was found that existing satellite-only gravity field models, which are based on 7 years
of GRACE data, can already be enhanced in terms of spatial resolution. It is expected that with the accumulation of more GOCE
data the gravity field model resolution and quality can be further enhanced, and the GOCE mission goal of 1–2 cm geoid accuracy
with 100 km spatial resolution can be achieved. 相似文献
17.
Gravity reference stations for the National Gravity Survey of Botswana have been established at twenty-three sites throughout
the country in a net linked to existing bases in South Africa, Kenya and Zambia with an internal accuracy of better than 0.5
gravity units (one gravity unit, gu, equals an acceleration of 10−6 m.s−2). The field procedure and reduction of data are explained and a list is given of the gravity values. 相似文献
18.
Summary Results of two absolute gravity surveys performed in Switzerland between 1978 and 1979 are presented and discussed in the
framework of the uplift history of the Swiss Alps. Five absolute stations have been established as a contribution to the Swiss
fundamental gravity net as well as to geodynamic investigations on the Alpine uplift. Two sites (Interlaken—Jungfraujoch)
form the end points of a calibration line for field gravimeters. The gravity range of this line amounts to 605×10−5 ms−2 (=605 mgal). It can be traversed in a relatively short time interval of less than 3 hours. Two other sites (Brig and Chur)
are located in the area of the most negative gravity anomalies and highest uplift rates encountered in Switzerland. They serve
as reference stations for a more extended gravity net for studying non—periodic secular gravity variations associated with
the Alpine uplift.
Institut für Geod?sie und Photogrammetrie, ETH-Zürich, Separata No. 13.
Institut für Geophysik, ETH-Zürich, Contribution No. 333. 相似文献
19.
G. Ramillien 《Journal of Geodesy》2002,76(3):139-149
A fast spherical harmonic approach enables the computation of gravitational or magnetic potential created by a non-uniform
shell of material bounded by uneven topographies. The resulting field can be evaluated outside or inside the sphere, assuming
that density of the shell varies with latitude, longitude, and radial distance. To simplify, the density (or magnetization)
source inside the sphere is assumed to be the product of a surface function and a power series expansion of the radial distance.
This formalism is applied to compute the gravity signal of a steady, dry atmosphere. It provides geoid/gravity maps at sea
level as well as satellite altitude. Results of this application agree closely with those of earlier studies, where the atmosphere
contribution to the Earth's gravity field was determined using more time-consuming methods.
Received: 14 August 2000 / Accepted: 19 March 2001 相似文献
20.
Since the publication of the Earth gravitational model (EGM)96 considerable improvements in the observation techniques resulted
in the development of new improved models. The improvements are due to the availability of data from dedicated gravity mapping
missions (CHAMP, GRACE) and to the use of 5′ × 5′ terrestrial and altimetry derived gravity anomalies. It is expected that
the use of new EGMs will further contribute to the improvement of the resolution and accuracy of the gravity and geoid modeling
in continental and regional scale. To prove this numerically, three representative Earth gravitational models are used for
the reduction of several kinds of data related to the gravity field in different places of the Earth. The results of the reduction
are discussed regarding the corresponding covariance functions which might be used for modeling using the least squares collocation
method. The contribution of the EIGEN-GL04C model in most cases is comparable to that of EGM96. However, the big difference
is shown in the case of EGM2008, due not only to its quality but obviously to its high degree of expansion. Almost in all
cases the variance and the correlation length of the covariance functions of data reduced to this model up to its maximum
degree are only a few percentages of corresponding quantities of the same data reduced up to degree 360. Furthermore, the
mean value and the standard deviation of the reduced gravity anomalies in extended areas of the Earth such as Australia, Arctic
region, Scandinavia or the Canadian plains, vary between −1 and +1 and between 5 and 10 × 10−5 ms−2, respectively, reflecting the homogenization of the gravity field on a regional scale. This is very important in using least
squares collocation for regional applications. However, the distance to the first zero-value was in several cases much longer
than warranted by the high degree of the expansion. This is attributed to errors of medium wavelengths stemming from the lack
of, e.g., high-quality data in some area. 相似文献