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1.
A gravimetric geoid computed using different techniques has been compared to a geoid derived from Geos-3 altimeter data in two 30°×30° areas: one in the Tonga Trench area and one in the Indian Ocean. The specific techniques used were the usual Stokes integration (using 1°×1° mean anomalies) with the Molodenskii truncation procedure; a modified Stokes integration with a modified truncation method; and computations using three sets of potential coefficients including one complete to degree 180. In the Tonga Trench area the standard deviation of the difference between the modified Stokes’ procedure and the altimeter geoid was ±1.1 m while in the Indian Ocean area the difference was ±0.6 m. Similar results were found from the 180×180 potential coefficient field. However, the differences in using the usual Stokes integration procedure were about a factor of two greater as was predicted from an error analysis. We conclude that there is good agreement at the ±1 m level between the two types of geoids. In addition, systematic differences are at the half-meter level. The modified Stokes procedure clearly is superior to the usual Stokes method although the 180×180 solution is of comparable accuracy with the computational effort six times less than the integration procedures.  相似文献   

2.
The paper describes results obtained from the processing of 53 Geos-3 arcs of altimeter data obtained during the first weeks after the launch of the satellite in April, 1975. The measurement from the satellite to the ocean surface was used to obtain an approximate geoid undulation which was contaminated by long wavelength errors caused primarily by altimeter bias and orbit error. This long wavelength error was reduced by fitting with a low degree polynomial the raw undulation data to the undulations implied by the GEM 7 potential coefficients, in an adjustment process that included conditions on tracks that cross. The root mean square crossover discrepancy before this adjustment was ±12.4 meters while after the adjustment it was ±0.9 m. These adjusted undulations were used to construct a geoid map in the Geos-3 calibration area using a least squares filter to remove remaining noise in the undulations. Comparing these undulations to ones computed from potential coefficients and terrestrial gravity data indicates a mean difference of 0.25 m and a root mean square difference of ±1.92 m. The adjusted undulations were also used to estimate several 5o, 2o, and 1o anomalies using the method of least squares collocation. The resulting predictions agreed well with known values although the 1o x 1o anomalies could not be considered as reliably determined.  相似文献   

3.
A detailed gravimetric geoid in the North Atlantic Ocean, named DGGNA-77, has been computed, based on a satellite and gravimetry derived earth potential model (consisting in spherical harmonic coefficients up to degree and order 30) and mean free air surface gravity anomalies (35180 1°×1° mean values and 245000 4′×4′ mean values). The long wavelength undulations were computed from the spherical harmonics of the reference potential model and the details were obtained by integrating the residual gravity anomalies through the Stokes formula: from 0 to 5° with the 4′×4′ data, and from 5° to 20° with the 1°×1° data. For computer time reasons the final grid was computed with half a degree spacing only. This grid extends from the Gulf of Mexico to the European and African coasts. Comparisons have been made with Geos 3 altimetry derived geoid heights and with the 5′×5′ gravimetric geoid derived byMarsh andChang [8] in the northwestern part of the Atlantic Ocean, which show a good agreement in most places apart from some tilts which porbably come from the satellite orbit recovery.  相似文献   

4.
Meissl has derived weighting functions for converting point gravity anomaly degree variances into mean anomaly variances over a circular cap on a sphere. If the cap is sufficiently small so that the cap on a sphere degenerates into a circle on a plane, the problem may be considered that of the gain of a circular filter for a surface wave whose wave number depends on the spherical harmonic degree. The Meissl weights then become replaced by diffraction integrals of optical physics. The expected gain for a square filter for waves coming from random directions is derived and shown to be close to the gain of a circular filter with the same area. The expected gains and cross-gains for rectangular filters are also derived. When weighted by an anomaly degree variance model, these gains and cross-gains can be used to determine rectangular anomaly variances and covariances for arbitrary bandwidths. Using the Tscherning-Rapp model, analytic gravity anomaly variances and covariances are calculated for 1°×1° blocks.  相似文献   

5.
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   

6.
 Four different implementations of Stokes' formula are employed for the estimation of geoid heights over Sweden: the Vincent and Marsh (1974) model with the high-degree reference gravity field but no kernel modifications; modified Wong and Gore (1969) and Molodenskii et al. (1962) models, which use a high-degree reference gravity field and modification of Stokes' kernel; and a least-squares (LS) spectral weighting proposed by Sj?berg (1991). Classical topographic correction formulae are improved to consider long-wavelength contributions. The effect of a Bouguer shell is also included in the formulae, which is neglected in classical formulae due to planar approximation. The gravimetric geoid is compared with global positioning system (GPS)-levelling-derived geoid heights at 23 Swedish Permanent GPS Network SWEPOS stations distributed over Sweden. The LS method is in best agreement, with a 10.1-cm mean and ±5.5-cm standard deviation in the differences between gravimetric and GPS geoid heights. The gravimetric geoid was also fitted to the GPS-levelling-derived geoid using a four-parameter transformation model. The results after fitting also show the best consistency for the LS method, with the standard deviation of differences reduced to ±1.1 cm. For comparison, the NKG96 geoid yields a 17-cm mean and ±8-cm standard deviation of agreement with the same SWEPOS stations. After four-parameter fitting to the GPS stations, the standard deviation reduces to ±6.1 cm for the NKG96 geoid. It is concluded that the new corrections in this study improve the accuracy of the geoid. The final geoid heights range from 17.22 to 43.62 m with a mean value of 29.01 m. The standard errors of the computed geoid heights, through a simple error propagation of standard errors of mean anomalies, are also computed. They range from ±7.02 to ±13.05 cm. The global root-mean-square error of the LS model is the other estimation of the accuracy of the final geoid, and is computed to be ±28.6 cm. Received: 15 September 1999 / Accepted: 6 November 2000  相似文献   

7.
The vertical component obtained from the Global Positioning System (GPS) observations is from the ellipsoid (a mathematical surface), and therefore needs to be converted to the orthometric height, which is from the geoid (represented by the mean sea level). The common practice is to use existing bench marks (around the four corners of a project area and interpolate for the rest of the area), but in many areas bench marks may not be available, in which case an existing geoid undulation is used. Present available global geoid undulation values are not generally as detailed as needed, and in many areas they are not known better than ±1 to ±5 m, because of many limitations. This article explains the difficulties encountered in obtaining precise geoid undulation with some example computations, and proposes a technique of applying corrections to the best available global geoid undulations using detailed free-air gravity anomalies (within a 2° × 2° area) to get relative centimeter accuracy. Several test computations have been performed to decide the optimal block sizes and the effective spherical distances to compute the regional and the local effects of gravity anomalies on geoid undulations by using the Stokes integral. In one test computation a 2° × 2° area was subdivided into smaller surface elements. A difference of 37.34 ± 1.6 cm in geoid undulation was obtained over the same 2° × 2° area when 1° × 1° block sizes were replaced by a combination of 5' × 5' and 1' × 1' subdivision integration elements (block sizes).  相似文献   

8.
Range differences, as derived by differencing simultaneously measured ranges from two stations to one and the same lunar reflector, are investigated regarding their capabilities for determining the orientation of the earth in an earth-moon reference system. Each pair of co-observing stations forms an observational unit (line) which is located preferably along a meridian or parallel. For a time interval which lasts from the instant of the first simultaneous observation of the most eastern line to the last observation of the most western line, assuming a reasonable observational rate and incorporating observations for which the zenith distance does not exceed 70 degrees, an analysis of variance shows that the pole position and the earth rotation can be computed independently of errors in the adopted lunar ephemeris and with at least measurement accuracy given a design which consists of two north-south lines being separated by 90 degrees and one east-west line. In the case of one north-south line the standard deviation of the meridional polar motion component does not exceed three times the measurement accuracy. As long as the stations are located within 10° to 15° in north-south or east-west direction the standard deviations of the parameters do not increase significantly, The lengths of north-south and east-west lines can vary between 60° to 80° and 40° to 60° respectively. The existing lunar ranging stations in Australia, Japan, Texas and Hawaii could be used to test the suggested method.  相似文献   

9.
本文利用由多源卫星测高资料计算的新版全球重力异常Grav_Alti_WHU,联合船测水深资料,构建了全球75°S—70°N范围的1′×1′海底地形模型BAT_WHU2020。以船测水深、现有模型和多波束测深数据为参考,对模型精度进行了分析评价。结果表明,在中国海域及邻区(104°E—160°E,0°N—50°N),本文模型与船测水深之差值的标准差约70 m,与SIO V19.1模型精度相当,优于ETOPO1、DTU10、GEBCO_08等模型,较此前发布的BAT_VGG模型精度提高了约30%,说明本文模型构建方法可靠、数据处理准确、精度较高。在全球范围内,BAT_WHU2020模型与船测水深之差值的标准差为50～65 m,差值在±200 m范围内的比率超过95%,与SIO V19.1模型精度相当,优于ETOPO1、DTU10、GEBCO_08等模型,较BAT_VGG模型精度提高了27%～36%。以SIO V19.1模型为参考,模型之差的标准差为90～110 m,约90%格网点差值在±200 m以内,约95%格网点差值在±300 m以内,两者一致性良好。最后,讨论了地壳均衡、Parker公式高次项等对成果精度的影响,模型的真实空间分辨率,以及以多波束测深为参考的模型精度问题。分析认为,BAT_WHU2020模型空间分辨率为10～18 km,在马里亚纳海沟、麦夸里海岭地区相对精度为5%～6%。  相似文献   

10.
本文在顾及局部地形改正、椭球改正及大气改正的情况下,采用实测数据,应用Meissel方法和Wenzel频谱分析方法,对某盆地边缘的高程异常进行了实际计算。并将计算结果同多普勒高程异常进行了比较,证明结果是良好的。此外还对我国精确高程异常的确定提出了一些建议。  相似文献   

11.
Gravity field convolutions without windowing and edge effects   总被引：5，自引：0，他引：5  
A new set of formulas has been developed for the computation of geoid undulations and terrain corrections by FFT when the input gravity anomalies and heights are mean gridded values. The effects of the analytical and the discrete spectra of kernel functions and that of zero-padding on the computation of geoid undulations and terrain corrections are studied in detail.Numerical examples show that the discrete spectrum is superior to the analytically-defined one. By using the discrete spectrum and 100% zero-padding, the RMS differences are 0.000 m for the FFT geoid undulations and 0.200 to 0.000 mGal for the FFT terrain corrections compared with results obtained by numerical integration.  相似文献   

12.
This paper studies the use of two new methods for gravimetric geoid undulation computations: The Molodenskii's and Sjöberg's methods that both modify the original Stokes'function so that certainrms errors are minimized. These new methods were checked against the traditional methods of Stokes' and Meissl's modification with the criterion of the globalrms undulation error that each method implies. Sjöberg's method gave consistently the smallest globalrms undulation error of all the other methods for capsizes 0° to 10°. However with the exception of Stokes' method, for capsizes between 0° to 5°, all the methods gave approximately (within±5cm) the same globalrms undulation error. Actual gravity data within a cap of 2° and potential coefficient information were then combined to compute the undulation of 39 laser stations distributed around the world. Therms discrepancy between the gravimetric undulations using all the four methods and the undulations computed as the ellipsoidal minus the orthometric height of 28 at the above stations was±1.70,±1.65,±1.66,±1.65m for the Stokes', Meissl's, Molodenskii's and Sjöberg's method respectively. For five oceanic laser stations where no terrestrial gravity data was available, theGEOS-3/SEASAT altimeter sea surface heights were used to compute the undulations of these stations in a collocation method. Therms discrepancy between the altimeter derived undulation and the ellipsoidal mirus orthometric value of the undulation was ±1.30m for the above five laser stations.  相似文献   

13.
本文首先证明了三种大地水准面差距计算方法(迈塞尔方法、文策尔方法、最小二乘配置法)之间的关系。通过对某盆地的大地水准面差距的计算及和多普勒结果的比较,得到了一些对计算我国大地水准面差距有益的结论。  相似文献   

14.
Satellite gravity missions, such as CHAMP, GRACE and GOCE, and airborne gravity campaigns in areas without ground gravity will enhance the present knowledge of the Earths gravity field. Combining the new gravity information with the existing marine and ground gravity anomalies is a major task for which the mathematical tools have to be developed. In one way or another they will be based on the spectral information available for gravity data and noise. The integration of the additional gravity information from satellite and airborne campaigns with existing data has not been studied in sufficient detail and a number of open questions remain. A strategy for the combination of satellite, airborne and ground measurements is presented. It is based on ideas independently introduced by Sjöberg and Wenzel in the early 1980s and has been modified by using a quasi-deterministic approach for the determination of the weighting functions. In addition, the original approach of Sjöberg and Wenzel is extended to more than two measurement types, combining the Meissl scheme with the least-squares spectral combination. Satellite (or geopotential) harmonics, ground gravity anomalies and airborne gravity disturbances are used as measurement types, but other combinations are possible. Different error characteristics and measurement-type combinations and their impact on the final solution are studied. Using simulated data, the results show a geoid accuracy in the centimeter range for a local test area.  相似文献   

15.
CONT08 was a 15 days campaign of continuous Very Long Baseline Interferometry (VLBI) sessions during the second half of August 2008 carried out by the International VLBI Service for Geodesy and Astrometry (IVS). In this study, VLBI estimates of troposphere zenith total delays (ZTD) and gradients during CONT08 were compared with those derived from observations with the Global Positioning System (GPS), Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS), and water vapor radiometers (WVR) co-located with the VLBI radio telescopes. Similar geophysical models were used for the analysis of the space geodetic data, whereas the parameterization for the least-squares adjustment of the space geodetic techniques was optimized for each technique. In addition to space geodetic techniques and WVR, ZTD and gradients from numerical weather models (NWM) were used from the European Centre for Medium-Range Weather Forecasts (ECMWF) (all sites), the Japan Meteorological Agency (JMA) and Cloud Resolving Storm Simulator (CReSS) (Tsukuba), and the High Resolution Limited Area Model (HIRLAM) (European sites). Biases, standard deviations, and correlation coefficients were computed between the troposphere estimates of the various techniques for all eleven CONT08 co-located sites. ZTD from space geodetic techniques generally agree at the sub-centimetre level during CONT08, and??as expected??the best agreement is found for intra-technique comparisons: between the Vienna VLBI Software and the combined IVS solutions as well as between the Center for Orbit Determination (CODE) solution and an IGS PPP time series; both intra-technique comparisons are with standard deviations of about 3?C6?mm. The best inter space geodetic technique agreement of ZTD during CONT08 is found between the combined IVS and the IGS solutions with a mean standard deviation of about 6?mm over all sites, whereas the agreement with numerical weather models is between 6 and 20?mm. The standard deviations are generally larger at low latitude sites because of higher humidity, and the latter is also the reason why the standard deviations are larger at northern hemisphere stations during CONT08 in comparison to CONT02 which was observed in October 2002. The assessment of the troposphere gradients from the different techniques is not as clear because of different time intervals, different estimation properties, or different observables. However, the best inter-technique agreement is found between the IVS combined gradients and the GPS solutions with standard deviations between 0.2 and 0.7?mm.  相似文献   

16.
 This paper suggests that potential coefficient models of the Earth's gravitational potential be used to calculate height anomalies which are then reduced to geoid undulations where such quantities are needed for orthometric height determination and vertical datum definition through a potential coefficient realization of the geoid. The process of the conversion of the height anomaly into a geoid undulation is represented by a height anomaly gradient term and the usual N–ζ term that is dependent on elevation and the Bouguer anomaly. Using a degree 360 expansion of 30′ elevations and the OSU91A potential coefficient model, a degree 360 representation of the correction terms was computed. The magnitude of N–ζ reached –3.4 m in the Himalaya Mountains with smaller, but still significant, magnitudes in other mountainous regions. Received: 6 May 1996; Accepted: 30 October 1996  相似文献   

17.
Up‐to‐date and accurate digital elevation models (DEMs) are essential for many applications such as numerical modeling of mass movements or mapping of terrain changes. Today the Federal Department of Topography, swisstopo, provides Digital Terrain Models (DTMs) and Digital Surface Models (DSMs) derived from airborne LiDAR data with a high spatial resolution of 2 m covering the entire area of Switzerland below an elevation of 2000 m a.s.l.. However, above an elevation of 2000 m a.s.l., which is typical for high‐alpine terrain, the best product available is the a DTM with a spatial resolution of 25 m. This spatial resolution is insufficient for many applications in complex terrain. In this study, we investigate the quality of DSMs derived from opto‐electronic scanner data (ADS80; acquired in autumn 2010) using photogrammetric image correlation techniques based on the multispectral nadir and backward looking sensor data. As reference, we take a high precision airborne LiDAR data set with a spatial resolution of ca. 0.5 m, acquired in late summer 2010, covering the Grabengufer/Dorfbach catchment near Randa, VS. We find the deviations between the two datasets are surprisingly low. In terrain with inclination angles of less than 30° the RMSE is below 0.5 m. In extremely steep terrain of more than 50° the RMSE goes up to 2 m and outliers increase significantly. We also find dependencies of the deviations on illumination conditions and ground cover classes. Finally we discuss advantages and disadvantages of the different data acquisition methods.  相似文献   

18.
Validation of Indian National DEM from Cartosat-1 Data   总被引：1，自引：0，他引：1  
CartoDEM is an Indian National DEM generated from Cartosat-1 stereo data. Cartosat-1, launched in May, 2005, is an along track (aft ?5°, Fore +26°) stereo with 2.5 m GSD, give base-height ratio of 0.63 with 27 km swath. The operational procedure of DEM generation comprises stereo strip triangulation of 500?×?27 km segment with 10 m posting along with 2.5 m resolution ortho image and free—access posting of 30 m has been made available (bhuvan.nrsc.gov.in). A multi approach evaluation of CartoDEM comprising (a) absolute accuracy with respect to ground control points for two sites namely Jagatsinghpur -flat and Dharamshala- hilly; second site i.e. Alwar-plain and hilly with high resolution aerial DEM, (b) relative difference between SRTM and ASTERDEM (c) absolute accuracy with ICESat GLAS for two sites namely Jagatsinghpur-plain and Netravathi river, Western Ghats-hilly (d) relative comparison of drainage delineation with respect to ASTERDEM is reported here. The absolute height accuracy in flat terrain was 4.7 m with horizontal accuracy of 7.3 m, while in hilly terrain it was 7 m height with a horizontal accuracy of 14 m. While comparison with ICESat GLAS data absolute height difference of plain and hilly was 5.2 m and 7.9 m respectively. When compared to SRTM over Indian landmass, 90 % of pixels reported were within ±8 m difference. The drainage delineation shows better accuracy and clear demarcation of catchment ridgeline and more reliable flow-path prediction in comparison with ASTER. The results qualify Indian DEM for using it operationally which is equivalent and better than the other publicly available DEMs like SRTM and ASTERDEM.  相似文献   

19.
The development of the COMPASS satellite system is introduced, and the regional tracking network and data availability are described. The precise orbit determination strategy of COMPASS satellites is presented. Data of June 2012 are processed. The obtained orbits are evaluated by analysis of post-fit residuals, orbit overlap comparison and SLR (satellite laser ranging) validation. The RMS (root mean square) values of post-fit residuals for one month’s data are smaller than 2.0 cm for ionosphere-free phase measurements and 2.6 m for ionosphere-free code observations. The 48-h orbit overlap comparison shows that the RMS values of differences in the radial component are much smaller than 10 cm and those of the cross-track component are smaller than 20 cm. The SLR validation shows that the overall RMS of observed minus computed residuals is 68.5 cm for G01 and 10.8 cm for I03. The static and kinematic PPP solutions are produced to further evaluate the accuracy of COMPASS orbit and clock products. The static daily COMPASS PPP solutions achieve an accuracy of better than 1 cm in horizontal and 3 cm in vertical. The accuracy of the COMPASS kinematic PPP solutions is within 1–2 cm in the horizontal and 4–7 cm in the vertical. In addition, we find that the COMPASS kinematic solutions are generally better than the GPS ones for the selected location. Furthermore, the COMPASS/GPS combinations significantly improve the accuracy of GPS only PPP solutions. The RMS values are basically smaller than 1 cm in the horizontal components and 3–4 cm in the vertical component.  相似文献   

20.
Crustal data of surface elevations and depth of Moho (and densities) can be utilized to form model-earth anomalies. These model-anomalies can closely approximate the free-air anomaly field of the earth, and could thus be used to predict the latter. A review of several such models is presented, with some elaboration on model developments, procedures, data analysis and accuracies. One of the models approaches a prediction accuracy of ±10 mgal for5°×5° mean free-air anomalies, whose r.m.s. value was about30% higher.  相似文献   

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