共查询到20条相似文献，搜索用时 31 毫秒
1.
L. E. Sjöberg 《Journal of Geodesy》2003,77(3-4):139-147
Assuming that the gravity anomaly and disturbing potential are given on a reference ellipsoid, the result of Sjöberg (1988, Bull Geod 62:93–101) is applied to derive the potential coefficients on the bounding sphere of the ellipsoid to order e
2 (i.e. the square of the eccentricity of the ellipsoid). By adding the potential coefficients and continuing the potential downward to the reference ellipsoid, the spherical Stokes formula and its ellipsoidal correction are obtained. The correction is presented in terms of an integral over the unit sphere with the spherical approximation of geoidal height as the argument and only three well-known kernel functions, namely those of Stokes, Vening-Meinesz and the inverse Stokes, lending the correction to practical computations. Finally, the ellipsoidal correction is presented also in terms of spherical harmonic functions. The frequently applied and sometimes questioned approximation of the constant m, a convenient abbreviation in normal gravity field representations, by e
2/2, as introduced by Moritz, is also discussed. It is concluded that this approximation does not significantly affect the ellipsoidal corrections to potential coefficients and Stokes formula. However, whether this standard approach to correct the gravity anomaly agrees with the pure ellipsoidal solution to Stokes formula is still an open question. 相似文献
2.
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
3.
Estimation of dynamic ocean topography in the Gulf Stream area using the Hotine formula and altimetry data 总被引：3，自引：2，他引：1
Changyou Zhang 《Journal of Geodesy》1998,72(9):499-510
Two modifications of the Hotine formula using the truncation theory and marine gravity disturbances with altimetry data are
developed and used to compute a marine gravimetric geoid in the Gulf Stream area. The purpose of the geoid computation from
marine gravity information is to derive the absolute dynamic ocean topography based on the best estimate of the mean surface
height from recent altimetry missions such as Geosat, ERS-1, and Topex. This paper also tries to overcome difficulties of
using Fast Fourier Transformation (FFT) techniques to the geoid computation when the Hotine kernel is modified according to
the truncation theory. The derived absolute dynamic ocean topography is compared with that from global circulation models
such as POCM4B and POP96. The RMS difference between altimetry-derived and global circulation model dynamic ocean topography
is at the level of 25cm. The corresponding mean difference for POCM4B and POP96 is only a few centimeters. This study also
shows that the POP96 model is in slightly better agreement with the results derived from the Hotine formula and altimetry
data than POCM4B in the Gulf Stream area. In addition, Hotine formula with modification (II) gives the better agreement with
the results from the two global circulation models than the other techniques discussed in this paper.
Received: 10 October 1996 / Accepted: 16 January 1998 相似文献
4.
基于窗函数法和切比雪夫逼近法设计了两类适用于航空矢量重力测量的有限冲激响应(FIR)低通数字滤波器。先采用模拟高度数据验证了滤波器的性能,然后对实测静态GPS数据进行了低通滤波处理,并详细分析了滤波器的相位延迟和边界效应等影响。结果表明:①在相同的设计指标下,依照切比雪夫逼近法所设计的滤波器比采用窗函数法设计的滤波器具有更好的低通滤波效果;②对于静态ＧＰＳ测量数据,依照切比雪夫逼近法所设计的滤波器能以±（１～２）ｍＧａｌ（１ｍＧａｌ＝１０－５ ｍ／ｓ２）的精度确定垂直加速度,以优于±１ｍＧａｌ的精度确定水平加速度 相似文献
5.
M. K. Paul 《Journal of Geodesy》1973,47(4):413-425
Neglecting distant zones in the computation of geoidal height using Stokes' formula gives rise to some truncation error. This
truncation error is expressible as a weighted summation of the zonal harmonic components of the gravity anomaly. Making use
of the well-known properties of Legendre polynomials, a compact method of computing these theoretical coefficients has been
developed in this paper. 相似文献
6.
Lars E. Sjöberg 《Journal of Geodesy》1989,63(2):213-221
Integral formulas are derived for the determination of geopotential coefficients from gravity anomalies and gravity disturbances
over the surface of the Earth. First order topographic corrections to spherical formulas are presented. In addition new integral
formulas are derived for the determination of the external gravity field from surface gravity.
Taking advantage of modern satellite positioning techniques, it is suggested that, in general, the external gravity field
as well as individual coefficients are better determined from gravity disturbances than from gravity anomalies. 相似文献
7.
M. E. Ayhan 《Journal of Geodesy》1997,71(6):362-369
In the analyses of 2D real arrays, fast Hartley (FHT), fast T (FTT) and real-valued fast Fourier transforms are generally
preferred in lieu of a complex fast Fourier transform due to the advantages of the former with respect to disk storage and
computation time. Although the FHT and the FTT in one dimension are identical, they are different in two or more dimensions.
Therefore, first, definitions and some properties of both transforms and the related 2D FHT and FTT algorithms are stated.
After reviewing the 2D FHT and FTT solutions of Stokes' formula in planar approximation, 2D FHT and FTT methods are developed
for geoid updating to incorporate additional gravity anomalies. The methods are applied for a test area which includes a 64×64
grid of 3′×3′ point gravity anomalies and geoid heights calculated from point masses. The geoids computed by 2D FHT and FTT are found to
be identical. However, the RMS value of the differences between the computed and test geoid is ±15 mm. The numerical simulations
indicate that the new methods of geoid updating are practical and accurate with considerable savings on storage requirements.
Received: 15 February 1996; Accepted: 22 January 1997 相似文献
8.
9.
The earth gravity field model CDS01S of degree and order 36 has been recovered from the post processed Science Orbits and on-board accelerometer data of GFZ's CHAMP satellite. The model resolves the geoid with an accuracy of better than 4 cm at a resolution of 700 km half-wavelength. By using the degree difference variances of geopotential coefficients to compare the model CDS01S with EIGEN3P, EIGEN1S and EGM96, the result indicates that the coefficients of CDS01S are most close to those of EIGEN3P. The result of the comparison between the accuracies of geopotential coefficients in the above models, indicates that the accuracy of coefficients in CDS01S is higher than that in EGM96. The geoid undulations of CDS01S and GGM01C up to 30 degrees are calculated and the standard deviation is 4. 7 cm between them. 相似文献
10.
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
11.
基于$\frac{{{{\bar{P}}}_{nm}}\left( \cos \theta \right)}{\sin \theta }\left( m>0 \right)$的非奇异递推公式,给出了基于球坐标的引力矢量和垂线偏差非奇异计算公式;针对极点λ可任意取值引起的地方指北坐标系方向的不确定性问题,证明了引力矢量在转换到地心直角坐标系后不随λ的变化而变化,即与λ的取值无关。最终的数值计算结果表明,直角坐标系下的非奇异计算公式与本文提出的球坐标下的非奇异计算公式所得计算结果绝对值差异小于10-16m/s2,证明了该非奇异公式的正确性。最后总结了所有引力位球函数一阶导、二阶导非奇异性计算的一般思路。 相似文献
12.
L. E. Sjöberg 《Journal of Geodesy》2000,74(2):255-268
The topographic potential and the direct topographic effect on the geoid are presented as surface integrals, and the direct
gravity effect is derived as a rigorous surface integral on the unit sphere. By Taylor-expanding the integrals at sea level
with respect to topographic elevation (H) the power series of the effects is derived to arbitrary orders. This study is primarily limited to terms of order H
2. The limitations of the various effects in the frequently used planar approximations are demonstrated. In contrast, it is
shown that the spherical approximation to power H
2 leads to a combined topographic effect on the geoid (direct plus indirect effect) proportional to H˜2 (where terms of degrees 0 and 1 are missing) of the order of several metres, while the combined topographic effect on the
height anomaly vanishes, implying that current frequent efforts to determine the direct effect to this order are not needed.
The last result is in total agreement with Bjerhammar's method in physical geodesy. It is shown that the most frequently applied
remove–restore technique of topographic masses in the application of Stokes' formula suffers from significant errors both
in the terrain correction C (representing the sum of the direct topographic effect on gravity anomaly and the effect of continuing the anomaly to sea
level) and in the term t (mainly representing the indirect effect on the geoidal or quasi-geoidal height).
Received: 18 August 1998 / Accepted: 4 October 1999 相似文献
13.
基于卫星动力学理论,采用德国地球科学中心GFZ提供的CHAMP精密轨道数据和星载加速度计数据,反演了36阶地球重力场模型CDS01S。用不同模型之间的位系数差比较模型CDS01S、EIGEN3P、EIGEN1S及EGM96,表明CDS01S模型的位系数最接近于EIGEN3P;比较上述几种模型的位系数精度,表明CDS01S模型的位系数精度高于EGM96;用CDS01S和GGM01C的前30阶位系数分别计算全球2°×2°网格的大地水准面起伏,两者之间的标准偏差为4.7 cm。 相似文献
14.
R. H. Rapp 《Journal of Geodesy》1977,51(4):301-323
A set of 38406 1°×1° mean free air anomalies were used to derive a set of 1507 5° equal area anomalies that were supplemented
by 147 predicted anomalies to form a global coverage of 1654 anomalies. These anomalies were used to derive potential coefficients
to degree 52 using the summation formulae. In these computations, a smoothing operator was introduced and found to significantly
effect the results at higher degrees. In addition, the effects of the atmosphere, spherical approximation and terrain were
studied. It was found that the atmospheric effects and spherical approximation effects were about 0.3% of the actual coefficients.
The terrain correction effects amounted to 10 to 25% of the low degree coefficients depending on a specific terrain correction
model chosen; however, the correction terms found from the models did not yield solutions that agreed better with current
satellite derived potential coefficient determinations.
Anomalies were computed from the derived potential coefficients for comparison to the original anomalies. These comparisons
showed that the agreement between the two anomalies became significantly better as the degree of expansion increased to the
maximum considered. These comparisons shed some doubt on the rule of thumb that a block of size θ° can be represented by a spherical harmonic expansion to 180°/θ°. 相似文献
15.
Calibrating the GOCE accelerations with star sensor data and a global gravity field model 总被引：1，自引：0，他引：1
A reliable and accurate gradiometer calibration is essential for the scientific return of the gravity field and steady-state
ocean circulation explorer (GOCE) mission. This paper describes a new method for external calibration of the GOCE gradiometer
accelerations. A global gravity field model in combination with star sensor quaternions is used to compute reference differential
accelerations, which may be used to estimate various combinations of gradiometer scale factors, internal gradiometer misalignments
and misalignments between star sensor and gradiometer. In many aspects, the new method is complementary to the GOCE in-flight
calibration. In contrast to the in-flight calibration, which requires a satellite-shaking phase, the new method uses data
from the nominal measurement phases. The results of a simulation study show that gradiometer scale factors can be estimated
on a weekly basis with accuracies better than 2 × 10−3 for the ultrasensitive and 10−2 for the less sensitive axes, which is compatible with the requirements of the gravity gradient error. Based on a 58-day data
set, scale factors are found that can reduce the errors of the in-flight-calibrated measurements. The elements of the complete
inverse calibration matrix, representing both the internal gradiometer misalignments and scale factors, can be estimated with
accuracies in general better than 10−3. 相似文献
16.
为了进一步改进地球重力场模型 ,美国科学院 (NRC)于 1997年提出一个报告 ,号召美国和欧洲学者们组成一个由空间探测地球重力场委员会。他们评比了大约 10个计划的或想象的卫星重力任务 ,最后提出了 5种卫星重力任务的方案 ,称为专用重力任务。本文介绍这 5种任务的内容以及地球科学将由这些任务获得重大进展的研究领域。 相似文献
17.
核幔边界（core-mantle boundary,CMB）是地球内部最重要的物理化学界面之一,地核和地幔通过核幔边界发生多种相互作用,这对地球重力场、地球自转及地磁场等都能产生重要影响。大地水准面异常是地球重力场的重要观测量,反映了地球内部的物质密度异常及界面变化等重要信息。推导了通过大地水准面异常反演核幔边界起伏的公式,利用2~4阶大地水准面异常反演了大尺度核幔边界起伏形态。结果显示,核幔边界起伏的径向幅度达±5 km、与Morelli的地震层析成像结果的幅度接近,但在形态上略有差异。以高为5 km、底边长为1 000 km的棱柱体模型模拟计算了核幔边界密度异常引起的大地水准面异常响应,结果与观测大地水准面异常比较接近。 相似文献
18.
Comparisons between high-degree models of the Earth’s topographic and gravitational potential may give insight into the quality and resolution of the source data sets, provide feedback on the modelling techniques and help to better understand the gravity field composition. Degree correlations (cross-correlation coefficients) or reduction rates (quantifying the amount of topographic signal contained in the gravitational potential) are indicators used in a number of contemporary studies. However, depending on the modelling techniques and underlying levels of approximation, the correlation at high degrees may vary significantly, as do the conclusions drawn. The present paper addresses this problem by attempting to provide a guide on global correlation measures with particular emphasis on approximation effects and variants of topographic potential modelling. We investigate and discuss the impact of different effects (e.g., truncation of series expansions of the topographic potential, mass compression, ellipsoidal versus spherical approximation, ellipsoidal harmonic coefficient versus spherical harmonic coefficient (SHC) representation) on correlation measures. Our study demonstrates that the correlation coefficients are realistic only when the model’s harmonic coefficients of a given degree are largely independent of the coefficients of other degrees, permitting degree-wise evaluations. This is the case, e.g., when both models are represented in terms of SHCs and spherical approximation (i.e. spherical arrangement of field-generating masses). Alternatively, a representation in ellipsoidal harmonics can be combined with ellipsoidal approximation. The usual ellipsoidal approximation level (i.e. ellipsoidal mass arrangement) is shown to bias correlation coefficients when SHCs are used. Importantly, gravity models from the International Centre for Global Earth Models (ICGEM) are inherently based on this approximation level. A transformation is presented that enables a transformation of ICGEM geopotential models from ellipsoidal to spherical approximation. The transformation is applied to generate a spherical transform of EGM2008 (sphEGM2008) that can meaningfully be correlated degree-wise with the topographic potential. We exploit this new technique and compare a number of models of topographic potential constituents (e.g., potential implied by land topography, ocean water masses) based on the Earth2014 global relief model and a mass-layer forward modelling technique with sphEGM2008. Different to previous findings, our results show very significant short-scale correlation between Earth’s gravitational potential and the potential generated by Earth’s land topography (correlation +0.92, and 60% of EGM2008 signals are delivered through the forward modelling). Our tests reveal that the potential generated by Earth’s oceans water masses is largely unrelated to the geopotential at short scales, suggesting that altimetry-derived gravity and/or bathymetric data sets are significantly underpowered at 5 arc-min scales. We further decompose the topographic potential into the Bouguer shell and terrain correction and show that they are responsible for about 20 and 25% of EGM2008 short-scale signals, respectively. As a general conclusion, the paper shows the importance of using compatible models in topographic/gravitational potential comparisons and recommends the use of SHCs together with spherical approximation or EHCs with ellipsoidal approximation in order to avoid biases in the correlation measures. 相似文献
19.
A model for adjustment of differential gravity measurements with simultaneous gravimeter calibration
A mathematical model is proposed for adjustment of differential or relative gravity measurements, involving simultaneously
instrumental readings, coefficients of the calibration function, and gravity values of selected base stations. Tests were
performed with LaCoste and Romberg model G gravimeter measurements for a set of base stations located along a north–south
line with 1750 mGal gravity range. This line was linked to nine control stations, where absolute gravity values had been determined
by the free-fall method, with an accuracy better than 10 μGal. The model shows good consistence and stability. Results show
the possibility of improving the calibration functions of gravimeters, as well as a better estimation of the gravity values,
due to the flexibility admitted to the values of the calibration coefficients.
Received: 15 November 1999 / Accepted: 31 October 2000 相似文献
20.
从快速 Hartley变换 (FHT)基本概念入手 ,给出了 Hotine核在平面近似、球面近似、Molodenskii近似下的反演模型。另对 FHT处理中所需的坐标转换以及边缘效应等问题加以讨论。同时 ,为了改善长波特性的重力场信息 ,利用 M阶次的参考重力场对上述 Molo-denskii模型进行了改化。 相似文献