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1.
An analysis of vertical deflections derived from high-degree spherical harmonic models 总被引:1,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
2.
Astronomical-topographic levelling using high-precision astrogeodetic vertical deflections and digital terrain model data 总被引:1,自引:1,他引:1
At the beginning of the twenty-first century, a technological change took place in geodetic astronomy by the development of
Digital Zenith Camera Systems (DZCS). Such instruments provide vertical deflection data at an angular accuracy level of 0.̋1
and better. Recently, DZCS have been employed for the collection of dense sets of astrogeodetic vertical deflection data in
several test areas in Germany with high-resolution digital terrain model (DTM) data (10–50 m resolution) available. These
considerable advancements motivate a new analysis of the method of astronomical-topographic levelling, which uses DTM data
for the interpolation between the astrogeodetic stations. We present and analyse a least-squares collocation technique that
uses DTM data for the accurate interpolation of vertical deflection data. The combination of both data sets allows a precise
determination of the gravity field along profiles, even in regions with a rugged topography. The accuracy of the method is
studied with particular attention on the density of astrogeodetic stations. The error propagation rule of astronomical levelling
is empirically derived. It accounts for the signal omission that increases with the station spacing. In a test area located
in the German Alps, the method was successfully applied to the determination of a quasigeoid profile of 23 km length. For
a station spacing from a few 100 m to about 2 km, the accuracy of the quasigeoid was found to be about 1–2 mm, which corresponds
to a relative accuracy of about 0.05−0.1 ppm. Application examples are given, such as the local and regional validation of
gravity field models computed from gravimetric data and the economic gravity field determination in geodetically less covered
regions. 相似文献
3.
The structure of normal matrices occurring in the problem of weighted least-squares spherical harmonic analysis of measurements
scattered on a sphere with random noises is investigated. Efficient algorithms for the formation of the normal matrices are
derived using fundamental relations inherent to the products of two surface spherical harmonic functions. The whole elements
of a normal matrix complete to spherical harmonic degree L are recursively obtained from its first row or first column extended to degree 2L with only O(L
4) computational operations. Applications of the algorithms to the formation of surface normal matrices from geoid undulations
and surface gravity anomalies are discussed in connection with the high-degree geopotential modeling.
Received: 22 March 1999 / Accepted: 23 December 1999 相似文献
4.
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
5.
Journal of Geodesy - TheNWL9D (orNSWC9Z2) coordinate system is known to have thex andy coordinates of its origin approximately1 or2 meters from the Earth’s gravity center, but its zero... 相似文献
6.
The determination of gravimetric deflections of the vertical for the area of Greece is attempted by combining a spherical hamonics model and gravity nomalies using the method of least squares collocation. The components of deflections of the vertical are estimated on a grid with spacing 15′ in latitude and 20′ in longitude covering only the continental area of Greece, where a sufficient number of point gravity anomalies is available. In order to test the accuracy of the determination, gravimetric deflections of the vertical are computed at stations where astrogeodetic data are available. The results show that in a large region of rugged topography and irregular potential field, the prediction is possible with a standard deviation of 18% ... 28% of the root mean square variation of the observations, without taking into account the topography. Furthermore, the estimation of some systematic differences between observed and computed deflections of the vertical is attempted. 相似文献
7.
针对卫星测高技术反演海洋重力场需要解算格网垂线偏差,不同的格网化方法影响垂线偏差的解算精度与空间分辨率的问题,结合Shepard格网化方法与沿轨最小二乘方法的优势提出了一种新的格网化方法,即基于Shepard 权函数的沿轨最小二乘方法.采用CryoSat-2卫星约7年的数据,选取中国黄海和南海及其周边海域作为研究区域,分别利用基于交叉点的Shepard法、距离加权沿轨最小二乘法和基于Shepard权函数的沿轨最小二乘法解算1'×1'格网的垂线偏差.将不同方法得到的结果与EGM2008模型的垂线偏差进行比较,利用本文提出的方法解算的1'×1'格网垂线偏差精度最高.研究表明,在基于Shepard权函数的沿轨最小二乘方法在垂线偏差格网化中是可靠的,且该方法可获得高精度结果. 相似文献
8.
本文介绍了球谐合成和分析问题的数值计算原理,研究分析了其内在的并行性,提出了区域划分和聚合通信的并行计算策略。基于傅立叶变换技术,应用MPI(消息传递接口)并行编程模式,实现了球谐分析及合成计算的并行化。实验结果表明,较之串行实现,并行实现大大缩短了计算时间,获得了近似线形加速比,取得很高的并行效率。 相似文献
9.
Dezsö Nagy 《Journal of Geodesy》1981,55(1):86-93
A spherical harmonic expansion of the gravity field up to degree and order 200 was carried out. Free air anomaly data over
Canada (10×10 block averages) with a range of 211.1 mgal were used for testing. A low degree expansion (N=30) produced a map with a range
of 63.6 mgal with contour patterns that could hardly be correlated with the original hand contoured map. A high degree expansion
(N=200) on the other hand resulted in a map with a range of 199.8 mgal which quite faithfully reproduced the original including
its local variations. Test computations verify that by monitoring the RMS values and the range of the expansion it is possible
to arrive at an optimum degree of expansion for a given data set. It was also verified by the computations, that, since the
computed expansions essentially have a zero value outside the domain of the input, it is possible to combine the results of
separate non-overlapping expansions.
Contribution of the Earth Physics Branch No. 900. Presented at the 1977 Spring Meeting, AGU, May 30–June 3, Washington, D.C. 相似文献
10.
11.
With the advent of geodetic satellite missions mapping almost globally the Earth’s gravitational field, new methods and theoretical approaches have been developed and investigated to fully exploit the potential of their new observables. Besides estimating values of numerical coefficients in harmonic series of the gravitational potential, new applications emerged such as data validation and combination. In this contribution, new integral transformations are presented which transform principal components of the terrestrial deflection of the vertical onto disturbing satellite-to-satellite tracking and gradiometric data at altitude. Using spherical approximation, necessary integral kernel functions are derived in both spectral and closed forms. The behaviour of isotropic kernel functions is studied and the new integral transformations are tested in a closed-loop simulation using synthetic terrestrial and satellite data synthesized from a global gravitational model. New integral transformations can be used for data validation and combination purposes. 相似文献
12.
Ultra-high degree spherical harmonic analysis and synthesis using extended-range arithmetic 总被引:1,自引:2,他引:1
We present software for spherical harmonic analysis (SHA) and spherical harmonic synthesis (SHS), which can be used for essentially
arbitrary degrees and all co-latitudes in the interval (0°, 180°). The routines use extended-range floating-point arithmetic,
in particular for the computation of the associated Legendre functions. The price to be paid is an increased computation time;
for degree 3,000, the extended-range arithmetic SHS program takes 49 times longer than its standard arithmetic counterpart.
The extended-range SHS and SHA routines allow us to test existing routines for SHA and SHS. A comparison with the publicly
available SHS routine GEOGFG18 by Wenzel and HARMONIC SYNTH by Holmes and Pavlis confirms what is known about the stability of these programs. GEOGFG18 gives errors <1 mm for latitudes [-89°57.5′, 89°57.5′] and maximum degree 1,800. Higher degrees significantly limit the range
of acceptable latitudes for a given accuracy. HARMONIC SYNTH gives good results up to degree 2,700 for almost the whole latitude range. The errors increase towards the North pole and
exceed 1 mm at latitude 82° for degree 2,700. For a maximum degree 3,000, HARMONIC SYNTH produces errors exceeding 1 mm at latitudes of about 60°, whereas GEOGFG18 is limited to latitudes below 45°. Further extending the latitudinal band towards the poles may produce errors of several
metres for both programs. A SHA of a uniform random signal on the sphere shows significant errors beyond degree 1,700 for
the SHA program SHA by Heck and Seitz. 相似文献
13.
The accuracy of vertical position information can be degraded by various sources of error in digital aerial photogrammetry (DAP) based point clouds. To address this issue, we propose a relatively straightforward method for automated correction of such point clouds. This method can be used in conjunction with any 3D reconstruction method in which a point cloud is generated from a pair of aerial images. The crux of the method involves separately co-registering each DAP point cloud (formed by the overlap of two or more images) to a common airborne laser scanning (ALS) based digital terrain model. The proposed method has the following essential steps: (1) Ground surface patches are identified in the normalized DAP point clouds by selecting areas in which standard deviation of vertical height is low, (2) height differences between the DAP and ALS point clouds are calculated at these patches, and (3) a correction surface is interpolated from these height differences and is then used to rectify the entire DAP point cloud. The performance of the proposed method is verified using plot data (n = 250) from a forested study area in Eastern Finland. We observed that DAP data from the area corrected using our proposed method resulted in significant increases in prediction accuracy of key forest variables. Specifically, the root mean squared error (RMSE) values for dominant height predictions decreased by up to 23.2%, while the associated model R2 values increased by 16.9%. As for stem volume, RMSEs dropped by 20.6%, while the model R2 improved by 14.6%, respectively. Hence, prediction accuracies were almost as good as with ALS data. The results suggest that vertically misaligned DAP data, if rectified using an algorithm such as the one presented here, could deliver near ALS data quality at a fraction of the cost. 相似文献
14.
D. Arabelos 《Journal of Geodesy》1985,59(2):109-123
The evaluation of deflections of the vertical for the area of Greece is attempted using a combination of topographic and astrogeodetic
data. Tests carried out in the area bounded by 35°≤ϕ≤42°, 19°≤λ≤27° indicate that an accuracy of ±3″.3 can be obtained in
this area for the meridian and prime vertical deflection components when high resolution topographic data in the immediate
vicinity of computation points are used, combined with high degree spherical harmonic expansions of the geopotential and isostatic
reduction potential. This accuracy is about 25% better than the corresponding topographic-Moho deflection components which
are evaluated using topographic and Moho data up to 120 km around each station, without any combination with the spherical
harmonic expansion of the geopotential or isostatic reduction potential. The accuracy in both cases is increased to about
2″.6 when the astrogeodetic data available in the area mentioned above are used for the prediction of remaining values. Furthermore
the estimation of datum-shift parameters is attempted using least squares collocation. 相似文献
15.
I. N. Tziavos 《Journal of Geodesy》1987,61(2):177-197
Mean gravity anomalies, deflections of the vertical, and a geopotential model complete to degree and order180 are combined in order to determine geoidal heights in the area bounded by [34°≦ϕ≤42°, 18°≦λ≦28°]. Moreover, employing point
gravity anomalies simultaneously with the above data, an attempt is made to predict deflections of the vertical in the same
area. The method used in the computations is least squares collocation. Using empirical covariance functions for the data,
the suitable errors for the different sources of observations, and the optimum cap radius around each point of evaluation,
an accuracy better than±0.60m for geoidal heights and±1″.5 for deflections of the vertical is obtained taking into account existing systematic effects. This accuracy refers to the
comparison between observed and predicted values. 相似文献
16.
By exchanging angular momentum with the solid earth, tidal variations in ocean currents and sea level cause the rotation of
the solid earth to change. Observations of earth rotation variations can therefore be used to evaluate ocean tide models.
The rotational predictions of a spherical harmonic ocean tide model that is not constrained by any type of data are compared
here to the predictions of numerical ocean tide models and to earth rotation observations from which atmospheric and non-tidal
oceanic effects have been removed. The spherical harmonic ocean tide model is shown to account for the observed variations
at the fortnightly tidal period in polar motion excitation but not in length-of-day. Overall, its long-period polar motion
excitation predictions fit the observed tidal signals better than do the predictions of the numerical ocean tide models studied
here. It may be possible to improve its agreement with length-of-day observations by tuning certain model parameters, as was
done to obtain the close agreement reported here between the modeled and observed polar motion excitation; alternatively,
the discrepancy in length-of-day may point to the need to revise current models of mantle anelasticity and/or models of the
oceanic response to atmospheric pressure variations. 相似文献
17.
Combining EGM2008 and SRTM/DTM2006.0 residual terrain model data to improve quasigeoid computations in mountainous areas devoid of gravity data 总被引:6,自引:4,他引:2
A global geopotential model, like EGM2008, is not capable of representing the high-frequency components of Earth’s gravity
field. This is known as the omission error. In mountainous terrain, omission errors in EGM2008, even when expanded to degree
2,190, may reach amplitudes of 10 cm and more for height anomalies. The present paper proposes the utilisation of high-resolution
residual terrain model (RTM) data for computing estimates of the omission error in rugged terrain. RTM elevations may be constructed
as the difference between the SRTM (Shuttle Radar Topography Mission) elevation model and the DTM2006.0 spherical harmonic
topographic expansion. Numerical tests, carried out in the German Alps with a precise gravimetric quasigeoid model (GCG05)
and GPS/levelling data as references, demonstrate that RTM-based omission error estimates improve EGM2008 height anomaly differences
by 10 cm in many cases. The comparisons of EGM2008-only height anomalies and the GCG05 model showed 3.7 cm standard deviation
after a bias-fit. Applying RTM omission error estimates to EGM2008 reduces the standard deviation to 1.9 cm which equates
to a significant improvement rate of 47%. Using GPS/levelling data strongly corroborates these findings with an improvement
rate of 49%. The proposed RTM approach may be of practical value to improve quasigeoid determination in mountainous areas
without sufficient regional gravity data coverage, e.g., in parts of Asia, South America or Africa. As a further application,
RTM omission error estimates will allow refined validation of global gravity field models like EGM2008 from GPS/levelling
data. 相似文献
18.
19.
G. Obenson 《Journal of Geodesy》1973,47(2):141-156
Equations, suitable for machine evaluation, are derived for computing the coefficients to be multiplied by each mean gravity
anomaly, world-wide, to obtain the deflections of the vertical and undulations at any given point. These coefficients together
with the accuracies of the anomalies are used to compute the standard of the deflections and undulations. Sample computations
done with some assumed data gave average world-wide standard errors of 0".6 for the meridian and prime vertical deflections
and 4.5 m for the undulations. 相似文献