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1.
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
2.
Flight test results from a strapdown airborne gravity system 总被引：3，自引：0，他引：3
In June 1995, a flight test was carried out over the Rocky Mountains to assess the accuracy of airborne gravity for geoid
determination. The gravity system consisted of a strapdown inertial navigation system (INS), two GPS receivers with zero baseline
on the airplane and multiple GPS master stations on the ground, and a data logging system. To the best of our knowledge, this
was the first time that a strapdown INS has been used for airborne gravimetry. The test was designed to assess repeatability
as well as accuracy of airborne gravimetry in a highly variable gravity field. An east-west profile of 250 km across the Rocky
Mountains was chosen and four flights over the same ground track were made. The flying altitude was about 5.5km, i.e., between
2.5 and 5.0km above ground, and the average flying speed was about 430km/h. This corresponds to a spatial resolution (half
wavelength of cutoff frequency) of 5.07.0km when using filter lengths between 90 and 120s. This resolution is sufficient for
geoid determination, but may not satisfy other applications of airborne gravimetry. The evaluation of the internal and external
accuracy is based on repeated flights and comparison with upward continued ground gravity using a detailed terrain model.
Gravity results from repeated flight lines show that the standard deviation between flights is about 2mGal for a single profile
and a filter length of 120s, and about 3mGal for a filter length of 90s. The standard deviation of the difference between
airborne gravity upward continued ground gravity is about 3mGal for both filter lengths. A critical discussion of these results
and how they relate to the different transfer functions applied, is given in the paper. Two different mathematical approaches
to airborne scalar gravimetry are applied and compared, namely strapdown inertial scalar gravimetry (SISG) and rotation invariant
scalar gravimetry (RISG). Results show a significantly better performance of the SISG approach for a strapdown INS of this
accuracy class. Because of major differences in the error model of the two approaches, the RISG method can be used as an effective
reliability check of the SISG method. A spectral analysis of the residual errors of the flight profiles indicates that a relative
geoid accuracy of 23cm over distances of 200km (0.1 ppm) can be achieved by this method. Since these results present a first
data analysis, it is expected that further improvements are possible as more refined modelling is applied.
Received: 19 August 1996 / Accepted: 12 May 1997 相似文献
3.
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
4.
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
5.
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
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.
目前广泛使用的非全张量航空重力梯度测量系统,不能测量重力梯度全部张量,限制了航空重力梯度的应用.因此,需要研究航空重力梯度不同分量之间的位场转换.根据重力梯度与扰动重力位内在的频率微分关系,联合多参量在拟合观测参量最优的条件下反演扰动重力位,实现了联合多参量的位场转换.实验表明,相对于传统的单参量位场转换,多参量位场转... 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.
重力测量数据存在地形数据产生的高频分量的影响,高精度地形数据正演重力梯度也能较好地反映重力局部高频特征。为获得高精度重力梯度数据,实现基准梯度数据库精确快速构建,研究了利用数字高程模型正演重力梯度的频率域快速计算方法,推导出基于余弦变换的Parker正演重力梯度理论公式。数值实验结果表明,余弦变换频率域正演方法平均绝对误差可达到0.5E左右精度要求,与傅里叶变换正演方法相比误差可减小3dB左右,与棱柱法等空间域正演方法相比,该方法计算规模小,速度优势明显。 相似文献
10.
提出利用地面重力异常数据计算地面扰动位径向二阶梯度，将该梯度的积分表达式转换为卷积形式的谱表达式，便于应用ＦＦＴ／ＦＨＴ技术进行快速计算。这一将地面重力异常化为重力梯度的实用算法为将卫星重力梯度和航空重力梯度观测数据与地面重力数据的联合处理提供了一种有效途径。最后，以本文导出的数学模型为基础，给出了模型（ＷＤＭ９４）数据的试算结果并作了分析 相似文献
11.
联合使用位模型和地形信息的陆区航空重力向下延拓方法 总被引：1，自引：0，他引：1
为了规避传统逆Poisson积分向下延拓解算过程的不适定性问题,借鉴导航定位中的"差分"概念,利用超高阶位模型直接计算海域航空重力测量向下延拓改正数的方法。本文在此基础上提出联合使用重力位模型和地形高数据,计算陆部航空重力向下延拓总改正数的改进方案,以飞行高度面与地面对应点的位模型差分信息表征总改正数的中长波分量,以相对应的局部地形改正差分修正量表征总改正数的中高频成分,从而实现航空重力数据点对点向地面的全频段延拓。在地形变化不同区域,联合使用EGM2008位模型、地面实测重力和高分辨率高程数据进行了实际数值计算和精度评估,验证了该方法的有效性。 相似文献
12.
Parametric least squares collocation was used in order to study the detection of systematic errors of satellite gradiometer
data. For this purpose, simulated data sets with a priori known systematic errors were produced using ground gravity data
in the very smooth gravity field of the Canadian plains. Experiments carried out at different satellite altitudes showed that
the recovery of bias parameters from the gradiometer “measurements” is possible with high accuracy, especially in the case
of crossing tracks. The mean value of the differences (original minus estimated bias parameters) was relatively large compared
to the standard deviation of the corresponding second-order derivative component at the corresponding height. This mean value
almost vanished when gravity data at ground level were combined with the second-order derivative data set at satellite altitude.
In the case of simultaneous estimation of bias and tilt parameters from ∂2
T/∂z
2“measurements”, the recovery of both parameters agreed very well with the collocation error estimation.
Received: 10 October 1996 / Accepted 25 May 1998 相似文献
13.
GOCE gravitational gradients along the orbit 总被引：6，自引：3，他引：3
Johannes Bouman Sophie Fiorot Martin Fuchs Thomas Gruber Ernst Schrama Christian Tscherning Martin Veicherts Pieter Visser 《Journal of Geodesy》2011,85(11):791-805
GOCE is ESA’s gravity field mission and the first satellite ever that measures gravitational gradients in space, that is,
the second spatial derivatives of the Earth’s gravitational potential. The goal is to determine the Earth’s mean gravitational
field with unprecedented accuracy at spatial resolutions down to 100 km. GOCE carries a gravity gradiometer that allows deriving
the gravitational gradients with very high precision to achieve this goal. There are two types of GOCE Level 2 gravitational
gradients (GGs) along the orbit: the gravitational gradients in the gradiometer reference frame (GRF) and the gravitational
gradients in the local north oriented frame (LNOF) derived from the GGs in the GRF by point-wise rotation. Because the V
XX
, V
YY
, V
ZZ
and V
XZ
are much more accurate than V
XY
and V
YZ
, and because the error of the accurate GGs increases for low frequencies, the rotation requires that part of the measured
GG signal is replaced by model signal. However, the actual quality of the gradients in GRF and LNOF needs to be assessed.
We analysed the outliers in the GGs, validated the GGs in the GRF using independent gravity field information and compared
their assessed error with the requirements. In addition, we compared the GGs in the LNOF with state-of-the-art global gravity
field models and determined the model contribution to the rotated GGs. We found that the percentage of detected outliers is
below 0.1% for all GGs, and external gravity data confirm that the GG scale factors do not differ from one down to the 10−3 level. Furthermore, we found that the error of V
XX
and V
YY
is approximately at the level of the requirement on the gravitational gradient trace, whereas the V
ZZ
error is a factor of 2–3 above the requirement for higher frequencies. We show that the model contribution in the rotated
GGs is 2–35% dependent on the gravitational gradient. Finally, we found that GOCE gravitational gradients and gradients derived
from EIGEN-5C and EGM2008 are consistent over the oceans, but that over the continents the consistency may be less, especially
in areas with poor terrestrial gravity data. All in all, our analyses show that the quality of the GOCE gravitational gradients
is good and that with this type of data valuable new gravity field information is obtained. 相似文献
14.
分别采用基于梯度、基于泊松积分和基于快速傅里叶变换（FFT）的地面重力向上延拓方案,并提出交叉检验方法估计地面重力数据误差及其空中误差传播,对毛乌素测区GT-2A航空重力测量系统采集的空中测线数据进行外符合精度评价。对比结果表明：地面重力格网插值误差和代表性误差对空中点的影响达到0.66~0.92 mGal（1 Gal=1×10-2 m/s2）,航空重力数据误差估计必须扣除这一影响;基于泊松积分和基于FFT的地面重力向上延拓方法能够客观评价航空重力观测值的外符合精度,二者表现相当;扣除地面重力误差影响后,在包含残余边界效应的情况下,毛乌素测区GT-2A航空重力空中测线重力扰动的外符合精度优于1.42 mGal。 相似文献
15.
Xiaopeng Li 《Journal of Geodesy》2011,85(9):597-605
Combining data from a Strapdown Inertial Navigation System and a Differential Global Positioning System (SINS/DGPS) has shown
great promise in estimating gravity on moving platforms. Previous studies on a ground-vehicle system obtained 1–3 mGal precision
with 2 km spatial resolution. High-accuracy Inertial Measurement Units (IMU) and cm-level positioning solutions are very important
in obtaining mGal-level gravity disturbance estimates. However, these ideal configurations are not always available or achievable.
Because the noise level in the SINS/DGPS gravimetric system generally decreases with an increase of speed and altitude of
the platform, the stringent constraints on the IMU and GPS may be relieved in the airborne scenario. This paper presents an
investigation of one navigation-grade and one tactical-grade IMU for the possibility of low-cost INS/GPS airborne gravimetry.
We use the data collected during the Gravity-Lidar Study of 2006 (GLS06), which contains aerogravity, GPS, and INS along the
northern coastline of the Gulf of Mexico. The gravity disturbance estimates from the navigation-grade IMU show 0.5–3.2 mGal
precision compared with the onboard gravimeter’s measurements and better than 3 mGal precision compared with the upward continued
surface control data. Due to relatively large (240 s) smoothing window, the results have about 34 km along-track resolution.
But the gravity estimates from the tactical-grade IMU have much poorer precisions. Nonetheless, useful contributions from
the tactical-grade IMU could be extracted for longer wavelengths. 相似文献
16.
Any errors in digital elevation models (DEMs) will introduce errors directly in gravity anomalies and geoid models when used
in interpolating Bouguer gravity anomalies. Errors are also propagated into the geoid model by the topographic and downward
continuation (DWC) corrections in the application of Stokes’s formula. The effects of these errors are assessed by the evaluation
of the absolute accuracy of nine independent DEMs for the Iran region. It is shown that the improvement in using the high-resolution
Shuttle Radar Topography Mission (SRTM) data versus previously available DEMs in gridding of gravity anomalies, terrain corrections
and DWC effects for the geoid model are significant. Based on the Iranian GPS/levelling network data, we estimate the absolute
vertical accuracy of the SRTM in Iran to be 6.5 m, which is much better than the estimated global accuracy of the SRTM (say
16 m). Hence, this DEM has a comparable accuracy to a current photogrammetric high-resolution DEM of Iran under development.
We also found very large differences between the GLOBE and SRTM models on the range of −750 to 550 m. This difference causes
an error in the range of −160 to 140 mGal in interpolating surface gravity anomalies and −60 to 60 mGal in simple Bouguer
anomaly correction terms. In the view of geoid heights, we found large differences between the use of GLOBE and SRTM DEMs,
in the range of −1.1 to 1 m for the study area. The terrain correction of the geoid model at selected GPS/levelling points
only differs by 3 cm for these two DEMs. 相似文献
17.
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
18.
推导了运用地球重力场模型计算单点、格网点以及格网平均的扰动重力梯度复组合分量的公式;提出了广义球谐函数及其定积分的新算法,并利用EGM96地球重力场模型试算了全球地区卫星轨道面上的重力梯度分量的格网平均观测值;通过对角线分量满足Laplace方程的精度,验证了该算法的有效性和实用性。 相似文献
19.
Gravitational gradients by tensor analysis with application to spherical coordinates 总被引：1，自引：1，他引：0
This contribution deals with the derivation of explicit expressions of the gradients of first, second and third order of the
gravitational potential. This is accomplished in the framework of tensor analysis which naturally allows to apply general
formulae to the specific coordinate systems in use in geodesy. In particular it is recalled here that when the potential field
is expressed in general coordinates on a 3D manifold, the gradient operation leads to the definition of the covariant derivative
and that the covariant derivative of a tensor can be obtained by application of a simple rule. When applied to the gravitational
potential or to any of its gradients, the rule straightforwardly provides the expressions of the higher-order gradients. It
is also shown that the tensor approach offers a clear distinction between natural and physical components of the gradients.
Two fundamental reference systems—a global, bodycentric system and a local, topocentric system, both body-fixed—are introduced
and transformation rules are derived to convert quantities between the two systems. The results include explicit expressions
for the gradients of the first three orders in both reference systems. 相似文献
20.
应用张量不变理论对利用卫星重力梯度数据确定地球重力场的方法进行了研究,对张量不变观测方程的线性化处理、非全张量观测值的数据处理策略以及采用白噪声特性下的梯度观测值恢复地球重力场的精度等进行了数值分析.结果表明,张量不变解实现了不同观测值的联合求解,基于先验重力场模型的线性化方法在实现张量不变观测模型线性化处理的同时,提... 相似文献