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1.
Summary Basically two different evaluation methods are available to compute geoid heights from residual gravity anomalies in the inner zone: numerical integration and least squares collocation.If collocation is not applied to a global gravity data set, as is usually the case in practice, its result will not be equal to the numerical integration result. However, the cross covariance function between geoid heights and gravity anomalies can be adapted such that the geoid contribution is computed only from a small gravity area up to a certain distance o from the computation point. Using this modification, identical results are obtained as from numerical integration.Applying this modification makes the results less dependent on the covariance function used. The difference between numerical integration and collocation is mainly caused by the implicitly extrapolated residual gravity anomaly values, outside the original data area. This extrapolated signal depends very much on the covariance function used, while the interpolated values within the original data area depend much less on it.As a sort of by-product, this modified collocation formula also leads to a new combination technique of numerical integration and collocation, in which the optimizing practical properties of both methods are fully exploited.Numerical examples are added as illustration.  相似文献   

2.
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   

3.
In order to find short periodic oscillations in the Earth's rate of rotation, atmospheric angular momentum, solar activity the Maximum Entropy Spectral Analysis — MESA (Burg, 1967) has been applied. The MESA with moving autoregressive order has been introduced in order to detect more accurately periods of very weak short periodic variations. Oscillations with periods of about 75, 50, 27 and 18 days have been found in length of day — LOD, from which tidal oscillations were removed up to 35 days — LODR computed by the Center for Space Research — CSR from Lageos Laser Ranging data, in the axial component of atmospheric angular momentum — 3 determined by the U.S. National Meteorological Center — NMC and in the geomagnetic activity represented by the geomagnetic index —A p (Lincoln, 1967). These oscillations computed by Ormsby band pass filter (Ormsby, 1961) are in a very good phase agreement in the case of oscillations with periods of 50 and 18 days in these 3 series. The MESA of the cross covariance estimations between LODR- 3, 3-A p,A p-LODR, LODR-FLUX, 3-FLUX, andA p-FLUX has confirmed the existence of common oscillations with periods of 70, 50, 27 and 18 days. This indicates a possible relationship between solar activity and the short periodic exchange of angular momentum between the atmosphere and the solid Earth.  相似文献   

4.
Defining the distortion of a conformal map projection as the oscillation of the logarithm of its infinitesimal-scale σ, Chebyshev’s principle states that the best (minimum distortion) conformal map projection over a given region Ω of the ellipsoid is characterized by the property that σ is constant on the boundary of that region. Starting from a first map of Ω, we show how to compute the distortion δ0(Ω) of this Chebyshev’s projection. We prove that this minimum possible conformal mapping distortion associated with Ω coincides with the absolute value of the minimum of the solution of a Dirichlet boundary-value problem for an elliptic partial differential equation in divergence form and with homogeneous boundary condition. If the first map is conformal, the partial differential equation becomes a Poisson equation for the Laplace operator. As an example, we compute the minimum conformal distortion associated with peninsular Spain. Using longitude and isometric latitude as coordinates, we solve the corresponding boundary-value problem with the finite element method, obtaining δ0(Ω)=0.74869×10−3. We also quantify the distortions δl and δutm of the best conformal conic and UTM (zone 30) projections over peninsular Spain respectively. We get δl=2.30202×10−3 and δutm=3.33784×10−3.  相似文献   

5.
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   

6.
Remote sensing methods for locating and monitoring temporary ponds over large areas in arid lands were tested on a study site in Northern Senegal. Three main results are presented, validated with field data and intended to highlight different spectral, spatial and temporal characteristics of the methods: (1) Among several water indices tested, two Middle Infrared-based indices (MNDWI—Modified Normalized Difference Water Index and NDWI1—Normalized Difference Water Index) are found to be most efficient; (2) an objective method is given prescribing the necessary sensor spatial resolution in terms of minimal detected pond area; and (3) the potential of multi-temporal MODIS imagery for tracking the filling phases of small ponds is illustrated. These results should assist in epidemiological studies of vector-borne diseases that develop around these ponds, but also more generally for land and water management and preservation of threatened ecosystems in arid areas.  相似文献   

7.
The objective of this study is to evaluate two approaches, which use different representations of the Earth’s gravity field for downward continuation (DC), for determining Helmert gravity anomalies on the geoid. The accuracy of these anomalies is validated by 1) analyzing conformity of the two approaches; and 2) converting them to geoid heights and comparing the resulting values to GPS-leveling data. The first approach (A) consists of evaluating Helmert anomalies at the topography and downward-continuing them to the geoid. The second approach (B) downward-continues refined Bouguer anomalies to the geoid and transforms them to Helmert anomalies by adding the condensed topographical effect. Approach A is sensitive to the DC because of the roughness of the Helmert gravity field. The DC effect on the geoid can reach up to 2 m in Western Canada when the Stokes kernel is used to convert gravity anomalies to geoid heights. Furthermore, Poisson’s equation for DC provides better numerical results than Moritz’s equation when the resulting geoid models are validated against the GPS-leveling. On the contrary, approach B is significantly less sensitive to the DC because of the smoothness of the refined Bouguer gravity field. In this case, the DC (Poisson’s and Moritz’s) contributes only at the decimeter level to the geoid model in Western Canada. The maximum difference between the geoid models from approaches A and B is about 5 cm in the region of interest. The differences may result from errors in the DC such as numerical instability. The standard deviations of the h−H−N for both approaches are about 8 cm at the 664 GPS-leveling validation stations in Western Canada.  相似文献   

8.
Global time series of low resolution images are available with high repeat frequency and at low cost, but their analysis is hampered by the presence of mixed pixels and the difficulty in locating detailed spatial features. This study examined the potential of sub-pixel classification for regional crop area estimation using time series of monthly NDVI-composites of the 1 km resolution sensor SPOT-VEGETATION. Belgium was selected as test zone, because of the availability of ample reference data in the form of a vectorial GIS with the boundaries and cover type of the large majority of agricultural fields. Two different methods were investigated: the linear mixture model and neural networks. Both result in area fraction images (AFIs), which contain for each 1 km pixel the estimated area proportions occupied by the different cover types (crops or other land use). Both algorithms were trained with part of the reference data and validated with the remainder. Validation was repeated at three different levels: the 1 km pixel, the municipality and the agro-statistical district. In general, the neural network outperformed the linear mixture model. For the major classes (winter wheat, maize, forest) the obtained acreage estimates showed good agreement with the true values, especially when aggregated to the level of the municipality (R2 ≈ 85%) or district (R2 ≈ 95%). The method seems attractive for wide-scale, regional area estimation in data-poor countries.  相似文献   

9.
A set of2261 5°×5° mean anomalies were used alone and with satellite determined harmonic coefficients of the Smithsonian' Institution to determine the geopotential expansion to various degrees. The basic adjustment was carried out by comparing a terrestrial anomaly to an anomaly determined from an assumed set of coefficients. The (14, 14) solution was found to agree within ±3 m of a detailed geoid in the United States computed using1°×1° anomalies for an inner area and satellite determined anomalies in an outer area. Additional comparisons were made to the input anomaly field to consider the accuracy of various harmonic coefficient solutions. A by-product of this investigation was a new γE=978.0463 gals in the Potsdam system or978.0326 gals in an absolute system if −13.7 mgals is taken as the Potsdam correction. Combining this value of γE withf=1/298.25, KM=3.9860122·10 22 cm 3 /sec 2 , the consistent equatorial radius was found to be6378143 m.  相似文献   

10.
The formulas for the determination of the coefficients of the spherical harmonic expansion of the disturbing potential of the earth are defined for data given on a sphere. In order to determine the spherical harmonic coefficients, the gravity anomalies have to be analytically downward continued from the earth's surface to a sphere—at least to the ellipsoid. The goal of this paper is to continue the gravity anomalies from the earth's surface downward to the ellipsoid using recent elevation models. The basic method for the downward continuation is the gradient solution (theg 1 term). The terrain correction has also been computed because of the role it can play as a correction term when calculating harmonic coefficients from surface gravity data. Theg 1 term and the terrain correction were expanded into the spherical harmonics up to180 th order. The corrections (theg 1 term and the terrain correction) have the order of about 2% of theRMS value of degree variance of the disturbing potential per degree. The influences of theg 1 term and the terrain correction on the geoid take the order of 1 meter (RMS value of corrections of the geoid undulation) and on the deflections of the vertical is of the order 0.1″ (RMS value of correction of the deflections of the vertical).  相似文献   

11.
Crustal deformations caused by surface load due to ocean tides are strongly dependent on the surface load closest to the observation site. In order to correctly model this ocean loading effect near irregular coastal areas, a high-resolution coastline is required. A test is carried out using two GPS sites located in Alaska, where the ocean tide loading effect is large and consequently observed easily by relative positioning with GPS. The selected sites are Fair (Fairbanks) and Chi3 (located on an island that separates Prince William Sound from the Gulf of Alaska). Processing of hourly baseline solutions between Fair and Chi3 over a period of 49 days yields a significant ocean tide loading effect. The data are processed using different strategies for the tropospheric delay correction. However, the best results are obtained when 1-h ZTD (Zenith Tropospheric Delay) parameters for hourly solutions are used. In this case ocean tide loading is not absorbed into the ZTD parameters. Hence, ocean tide loading can be well resolved in the GPS data analysis. In addition, the M 2 ocean tide wave in the Gulf of Alaska has a very large amplitude. Although the horizontal M 2 ocean tide loading amplitude in general is only about 1/4 of the vertical M 2 ocean tide loading amplitude, the differential horizontal M 2 ocean tide loading displacements are nevertheless measurable using differential GPS (DGPS). When using the GOT99.2 ocean tide model and taking the coastal structure into account, the predicted differential vertical M 2 amplitude and Greenwich phase lag due to ocean tide loading are 19.3 mm and 110.2 degrees respectively, while GPS measurements yield 21.3 ± 1.0 mm and 99.7±2.8 degrees. Similarly, the predicted differential horizontal M 2 amplitude and Greenwich phase lag (in the north–south direction) are 4.5 mm and –77.0 degrees, while GPS yields 5.4 ± 0.3 mm and –106.3±3.3 degrees. Only the north-south component of the differential horizontal M 2 ocean tide loading wave is considered, because the east–west component is too small for the processed baseline and not detectable using DGPS.  相似文献   

12.
Effect of the atmospheric pressure on surface displacements   总被引：3，自引：0，他引：3  
Summary Atmospheric pressure variations with periods of some days and months can be considered as loading functions on the Earth's surface and can induce quasi-periodic surface deformations. The influence of such surface displacements is calculated by performing a convolution sum between the mass loading Green's functions and the local and regional barometric pressure data (geographically distribution in a 1° × 1° grid system extending to more than 1000km). The results for 5 stations in Europe show that the average values reach about 22.9–30.2mm depending on the ocean response: the inverted or non-inverted barometer ocean model. The corresponding admittances are 0.576–0.758mm/mbar respectively. The horizontal displacements are not negligible but always smaller. The magnitudes are about 2–3mm for East-West component and 0.5–1.0mm for North-South component.The results of the dependence on the lateral extension of the pressure load show that the admittance for radial displacement varies from 0.250mm/mbar for a column load of 100km radius to 0.539mm/mbar for a column load of more than 1000km extension. It means that the main contribution of the loads comes from the horizontal distribution of the air pressure in a broad region.The time dependent effects of the atmospheric pressure are also computed with the two-coefficient correction equations provided by Rabbel & Zschau (1985) using ground pressure data in a 1.125° × 1.125° grid system. The computations demonstrate that the results are in good agreement with those obtained with a convolution sum. It shows that this method can provide us with a good approximation for vertical displacement caused by the deformation of the Earth.  相似文献   

13.
DEM-induced errors in developing a quasi-geoid model for Africa   总被引：2，自引：0，他引：2  
Errors in digital elevation models (DEMs) will introduce errors in geoid and quasi-geoid models, via their use in interpolating free-air gravity anomalies and (in the case of the quasi-geoid) their use in computing the Molodensky G 1 term. The effects of these errors and those of datum shifts are assessed using three independent DEMs for a test region in South Africa. It is shown that these effects are significant and that it is important to choose the best-possible DEM for use in geoid and quasi-geoid modelling. Acknowledgments.The land gravity data used for this research were provided by the South African Council for Geoscience. Marine gravity anomalies were provided by the Danish National Survey and Cadastre (Kort & Matrikelstyrelsen). The GLOBE DEM was provided by the US National Geophysical Data Centre, and the CDSM DEM was provided by the South African Chief Directorate for Surveying and Mapping. The constructive comments of the reviewers are gratefully acknowledged.  相似文献   

14.
GOCE gravitational gradients along the orbit   总被引：6，自引：3，他引：3  
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   

15.
Knudsen 《Journal of Geodesy》1987,61(2):145-160
The estimation of a local empirical covariance function from a set of observations was done in the Faeroe Islands region. Gravity and adjusted Seasat altimeter data relative to theGPM2 spherical harmonic approximation were selected holding one value in celles of1/8°×1/4° covering the area. In order to center the observations they were transformed into a locally best fitting reference system having a semimajor axis1.8 m smaller than the one ofGRS80. The variance of the data then was273 mgal 2 and0.12 m 2 respectively. In the calculations both the space domain method and the frequency domain method were used. Using the space domain method the auto-covariances for gravity anomalies and geoid heights and the cross-covariances between the quantities were estimated. Furthermore an empirical error estimate was derived. Using the frequency domain method the auto-covariances of gridded gravity anomalies was estimated. The gridding procedure was found to have a considerable smoothing effect, but a deconvolution made the results of the two methods to agree. The local covariance function model was represented by a Tscherning/Rapp degree-variance model,A/((i−1)(i−2)(i+24))(R B /R E )2i+2, and the error degree-variances related to the potential coefficient setGPM2. This covariance function was adjusted to fit the empirical values using an iterative least squares inversion procedure adjusting the factor A, the depth to the Bjerhammar sphere(R E −R B ), and a scale factor associated with the error degree-variances. Three different combinations of the empirical covariance values were used. The scale factor was not well determined from the gravity anomaly covariance values, and the depth to the Bjerhammar sphere was not well determined from geoid height covariance values only. A combination of the two types of auto-covariance values resulted in a well determined model.  相似文献   

16.
At present, the modelling of terrain edges from discrete data clouds {x,y,z} is one of the ‘hot topics’ in the processing of laser scanning data. This paper proposes two different methods for the three-dimensional modelling of terrain edges. Common to both methods is the idea to describe the terrain edge as the intersection line of two surface patches zi=z(x,y), i=1,2. The first method is based on numerical integration of a differential equation describing the intersection line. The second method uses the snakes algorithm for the identification of the terrain edge. Both methods are tested for synthetic and real-world data examples, which shows that they are suitable for the practical extraction of edges from laser scanning data.  相似文献   

17.
Ellipsoidal geoid computation   总被引：1，自引：1，他引：0  
Modern geoid computation uses a global gravity model, such as EGM96, as a third component in a remove–restore process. The classical approach uses only two: the reference ellipsoid and a geometrical model representing the topography. The rationale for all three components is reviewed, drawing attention to the much smaller precision now needed when transforming residual gravity anomalies. It is shown that all ellipsoidal effects needed for geoid computation with millimetric accuracy are automatically included provided that the free air anomaly and geoid are calculated correctly from the global model. Both must be consistent with an ellipsoidal Earth and with the treatment of observed gravity data. Further ellipsoidal corrections are then negligible. Precise formulae are developed for the geoid height and the free air anomaly using a global gravity model, given as spherical harmonic coefficients. Although only linear in the anomalous potential, these formulae are otherwise exact for an ellipsoidal reference Earth—they involve closed analytical functions of the eccentricity (and the Earths spin rate), rather than a truncated power series in e2. They are evaluated using EGM96 and give ellipsoidal corrections to the conventional free air anomaly ranging from –0.84 to +1.14 mGal, both extremes occurring in Tibet. The geoid error corresponding to these differences is dominated by longer wavelengths, so extrema occur elsewhere, rising to +766 mm south of India and falling to –594 mm over New Guinea. At short wavelengths, the difference between ellipsoidal corrections based only on EGM96 and those derived from detailed local gravity data for the North Sea geoid GEONZ97 has a standard deviation of only 3.3 mm. However, the long-wavelength components missed by the local computation reach 300 mm and have a significant slope. In Australia, for example, such a slope would amount to a 600-mm rise from Perth to Cairns.  相似文献   

18.
Summary The geopotential on and outside the earth is represented as a series in surface harmonics. The principal terms in it correspond to the solid harmonics of the external potential expansion with the coefficients being Stokes’ constantsC nm andS nm . The additional terms which occur near the earth’s surface due to its non-sphericity and topography are expressed in terms of Stokes’ constants too. This allows performing downward continuation of the potential derived from satellite observations. In the boundary condition which correlates Stokes’ constants and the surface gravity anomalies there occur additional terms due to the earth’s non-sphericity and topography. They are expressed in terms of Stokes’ constants as well. This improved boundary condition can be used for upward and downward continuations of the gravity field. Simple expressions are found representingC nm andS nm as explicit functions of the surface anomalies and its derivatives. The formula for the disturbing potential on the surface is derived in terms of the surface anomalies. All the formulas do not involve the earth’s surface in clinations.  相似文献   

19.
A World Bank-aided project on sodic land reclamation in Uttar Pradesh is being executed by U.P. Bhumi Sudhar Nigam, Lucknow, and Remote Sensing Applications Centre, U.P., Lucknow has the responsibility of sodic land mapping for the execution of land reclamation programme at the cadastral level. Sodic lands are mainly concentrated in the Gangetic alluvial plains but the problem of sodicity is particularly acute in the canal-irrigated areas. A study of the distribution pattern of sodic lands in canal and noncanal command areas in a reclamation site (covering 60 villages out of which sodic lands were mapped in 51 villages) of Etah district in Uttar Pradesh, indicates that 18.39 per cent area of the canal command villages was barren sodic which was 13.41 per cent of the total geographical area of the site (15417 ha), however, 11.69 per cent area was recorded to be barren sodic in the non-canal command villages which was only 3.16 per cent of the geographical area of the site. The results of soil chemical analysis indicate that barren sodic lands of canal command area are saline-sodic with higher concentration of soluble salts (pH2 >8.5, EC2 >4 dSm−1), however, those of non-canal command area are sodic (pH2 >8.5, EC2 <4 dSm−1). The post-monsoon ground level in the canal-irrigated areas was in the critical and semicritical zone (< 3.0 mbgl) whereas it was well below the semi-critical zone in the non-canal command area, which indicates that the high ground water level is a major factor to higher the area under sodicity.  相似文献   

20.
International compilations of marine gravity, such as the International Gravity Bureau (BGI) contain tens of millions of point data. Lemoine et al. (The Development of the Joint NASA GSFC and the National Imagery and Mapping Agency (NIMA) Geopotential Model EGM96, NASA/TP-1998-206861) chose not to include any marine gravity in the construction of the global gravity model EGM96. Instead they used synthetic anomalies derived from altimetry, so that no independent information about Mean Dynamic Topography (MDT) can be deduced. Software has been developed not only to identify and correct those aspects of marine gravity data that are unreliable, but to do so in a way that can be applied to very large, ocean-wide data sets. First, we select only straight-line parts of ship-tracks and fit each one with a high-degree series of Chebyshev polynomials, whose misfit standard deviation is σ line and measures the random error associated with point gravity data. Then, network adjustment determines how the gravity datum is offset for each survey. A free least squares adjustment minimises the gravity anomaly mismatch at line-crossing points, using σ line to weight the estimate for each line. For a long, well crossed survey, the instrumental drift rate is also adjusted. For some 42,000 cross-over points in the northern Atlantic Ocean, network adjustment reduces the unweighted standard deviation of the cross-over errors from 4.03 to 1.58 mGal; when quality weighted, the statistic reduces from 1.32 to 0.39 mGal. The geodetic MDT is calculated combining the adjusted gravity anomalies and satellite altimetry, and a priori global ocean model through a new algorithm called the Iterative Combination Method. This paper reports a first demonstration that geodetic oceanography can characterise the details of basin wide ocean circulation with a resolution better than global ocean circulation models. The result matches regional models of ocean circulation from hydrography measurements (Geophys Res Lett 29:1896, 2002; J Geophys Res 108:3251, 2003).  相似文献   

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