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1.
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   

2.
In support of requirements for the U.S. Air Force Cambridge Research Laboratories, gravity anomalies have been upward continued to several elevations in different areas of the United States. One area was 340 to 400 N in latitude and 960 to 1030 W in longitude, generally called the Oklahoma area. The computations proceeded from 26, 032 point anomalies to the prediction of mean anomalies in 14, 704, 2.5′×2.5′ blocks and 9,284, 5′×5′ blocks. These anomalies were upward continued along 28 profiles at 5′ intervals for every 30′ in latitude and longitude. These anomalies at elevations were meaned in various patterns to form mean 30′×30″, 10×10, 50×50 blocks. Comparisons were then made to the corresponding ground values. The results of these comparisons lead to practical recommendations on the arrangement of flight profiles in airborne gravimetry.  相似文献   

3.
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   

4.
Summary The absolute deviations of the vertical detectable at Potsdam from astronomical-gravity comparisons differ significantly from earlier values obtained from the astronomic-geodetic observations which form the starting elements of the European triangulation network. It is possible to show, by the use of values of the deviation of the vertical extending over the whole of Europe as far as longitude 30°, and referred to the undulations of the geoid ofTanni, that the starting elements adopted at Potsdam are too large by 3″.0 in latitude and 1″.4 in longitude.
Resumen Las desviaciones absolutas de la vertical obtenidas en Potsdam por procedimiento astronómico-gravimétrico, se alejan sensiblemente de los valores encontrados enteriormente por procedimiento astronómicogeodésico, y que constituyen la base de partida de la red de conjunto europea. Es posible demostrar, basándose en el material de desviaciones de la vertical extendido a toda Europa hasta la longitud de 30°, partiendo de las ondulaciones del geoide deTanni, que los datos de partida adoptados en Potsdam son demasiado grandes en 3″,0 de latitud y 1″,4 de longitud.
Résumé Les déviations absolues de la verticale relevées à Potsdam par voie astronomico-gravimétrique s’écartent sensiblement des valeurs trouvées autrefois par voie astronomico-géodésique, et qui forment la base de départ du réseau d’ensemble de l’Europe. Il est possible de démontrer, en s’appuyant sur le matériel de déviations de la verticale étendu sur toute l’Europe jusqu’à la longitude de 30°, en partant des ondulations du géo?de deTanni, que les données de départ adoptées à Potsdam sont trop grandes de 3″.0 en latitude et de 1″.4 en longitude.
Sommario La deviazione assoluta della verticale determinata a Postdam per via astronomico-gravimetrica, si scosta sensibilmente dal valore trovato in precedenza per via astronomico-geodetica, che forma la base della compensazione delle reti europee. Si può dimostrare, appoggiandosi sulle deviazioni della verticale conosciute in Europa fino alla longitudine di 30°, e partendo dalle ondulazioni del geoide diTanni, che i dati di partenza adottati a Postdam sono troppo grandi di 3″,0 in latitudine e di 1″,4 in longitudine.

Communication présentée à l’Assemblée Générale de Bruxelles  相似文献   

5.
On the basis of gravity field model （EIGEN_CG01C）, together with multi-altimeter data, the improved deflection of the vertical gridded in 2＇×2＇ in China marginal sea and gridded in 5＇×5＇ in the global sea was determined by using the weighted method of along-track least squares, and the accuracy is better than 1.2^# in China marginal sea. As for the quality of the deflection of the vertical, it meets the challenge for the gravity field of high resolution and accuracy, it shows that, compared with the shipboard gravimetry in the sea, the accuracy of the gravity anomalies computed with the marine deflection of the vertical by inverse Vening-Meinesz formula is 7.75 m.s ^-2.  相似文献   

6.
 The Somigliana–Pizzetti gravity field (the International gravity formula), namely the gravity field of the level ellipsoid (the International Reference Ellipsoid), is derived to the sub-nanoGal accuracy level in order to fulfil the demands of modern gravimetry (absolute gravimeters, super conducting gravimeters, atomic gravimeters). Equations (53), (54) and (59) summarise Somigliana–Pizzetti gravity Γ(φ,u) as a function of Jacobi spheroidal latitude φ and height u to the order ?(10−10 Gal), and Γ(B,H) as a function of Gauss (surface normal) ellipsoidal latitude B and height H to the order ?(10−10 Gal) as determined by GPS (`global problem solver'). Within the test area of the state of Baden-Württemberg, Somigliana–Pizzetti gravity disturbances of an average of 25.452 mGal were produced. Computer programs for an operational application of the new international gravity formula with (L,B,H) or (λ,φ,u) coordinate inputs to a sub-nanoGal level of accuracy are available on the Internet. Received: 23 June 2000 / Accepted: 2 January 2001  相似文献   

7.
The method of analytical downward continuation has been used for solving Molodensky’s problem. This method can also be used to reduce the surface free air anomaly to the ellipsoid for the determination of the coefficients of the spherical harmonic expansion of the geopotential. In the reduction of airborne or satellite gradiometry data, if the sea level is chosen as reference surface, we will encounter the problem of the analytical downward continuation of the disturbing potential into the earth, too. The goal of this paper is to find out the topographic effect of solving Stoke’sboundary value problem (determination of the geoid) by using the method of analytical downward continuation. It is shown that the disturbing potential obtained by using the analytical downward continuation is different from the true disturbing potential on the sea level mostly by a −2πGρh 2/p. This correction is important and it is very easy to compute and add to the final results. A terrain effect (effect of the topography from the Bouguer plate) is found to be much smaller than the correction of the Bouguer plate and can be neglected in most cases. It is also shown that the geoid determined by using the Helmert’s second condensation (including the indirect effect) and using the analytical downward continuation procedure (including the topographic effect) are identical. They are different procedures and may be used in different environments, e.g., the analytical downward continuation procedure is also more convenient for processing the aerial gravity gradient data. A numerical test was completed in a rough mountain area, 35°<ϕ<38°, 240°<λ<243°. A digital height model in 30″×30″ point value was used. The test indicated that the terrain effect in the test area has theRMS value ±0.2−0.3 cm for geoid. The topographic effect on the deflections of the vertical is around1 arc second.  相似文献   

8.
If in imagination we viewed a solar eclipse or the occultation of a star from a point outside the earth, we would see the shadow of the moon advancing across the face of the earth, the earth meanwhile turning on its axis beneath the shadow. When some point on the advancing edge of the shadow overtook a given point on the surface of the earth, an observer at that point would note the beginning of the eclipse or occultation. When the trailing edge of the shadow uncovered that point again, the observer there would note the end of the eclipse or occultation. The universal time (as distinguished from the local time) of the beginning or ending would depend on the position of the observer with reference to the body of the earth, that is, on his ideal geodetic coordinates. These universal times would not depend in the least on the direction of the observer’s vertical. This fact is the key to the usefulness of eclipses and occultations for geodetic purposes. Suppose that the prediction for the times of beginning or ending had been made on the basis of the astronomical latitude and longitude of the observer. Since there would be in general deflections of the vertical in latitude and longitude, Δπ and Δλ, these would bring about, even in the absence of any other source of discrepancy, diffe- This article is at once a condensation and an expansion. It is a condensation of a series of lectures delivered in the winter and spring of 1947 to members of the U. S. Coast and Geodetic Survey and of the Army Map Service. It is an expansion of a very informal lecture given before Section III of the International Association of Geodesy, meeting in General Assembly at Oslo in August, 1948.  相似文献   

9.
By using Halley’s third-order formula to find the root of a non-linear equation, we develop a new iterative procedure to solve an irrational form of the “latitude equation”, the equation to determine the geodetic latitude for given Cartesian coordinates. With a limit to one iteration, starting from zero height, and minimizing the number of divisions by means of the rational form representation of Halley’s formula, we obtain a new non-iterative method to transform Cartesian coordinates to geodetic ones. The new method is sufficiently precise in the sense that the maximum error of the latitude and the relative height is less than 6 micro-arcseconds for the range of height, −10 km ≤ h ≤ 30,000 km. The new method is around 50% faster than our previous method, roughly twice as fast as the well-known Bowring’s method, and much faster than the recently developed methods of Borkowski, Laskowski, Lin and Wang, Jones, Pollard, and Vermeille.  相似文献   

10.
The short wavelength geoid undulations, caused by topography, amount to several decimeters in mountainous areas. Up to now these effects are computed by means of digital terrain models in a grid of 100–500m. However, for many countries these data are not yet available or their collection is too expensive. This problem can be overcome by considering the special behaviour of the gravity potential along mountain slopes. It is shown that 90 per cent of the topographic effects are represented by a simple summation formula, based on the average height differences and distances between valleys and ridges along the geoid profiles, δN=[30.H.D.+16.(H−H′).D] in mm/km, (error<10%), whereH, H′, D are estimated in a map to the nearest 0.2km. The formula is valid for asymmetric sides of valleys (H, H′) and can easily be corrected for special shapes. It can be used for topographic refinement of low resolution geoids and for astrogeodetic projects. The “slope method” was tested in two alpine areas (heights up to 3800m, astrogeodetic deflection points every 170km 2) and resulted in a geoid accuracy of ±3cm. In first order triangulation networks (astro points every 1000km 2) or for gravimetric deflections the accuracy is about 10cm per 30km. Since a map scale of 1∶500.000 is sufficient, the method is suitable for developing countries, too.  相似文献   

11.
Least-squares by observation equations is applied to the solution of geodetic boundary value problems (g.b.v.p.). The procedure is explained solving the vectorial Stokes problem in spherical and constant radius approximation. The results are Stokes and Vening-Meinesz integrals and, in addition, the respective a posteriori variance-covariances. Employing the same procedure the overdeterminedg.b.v.p. has been solved for observable functions potential, scalar gravity, astronomical latitude and longitude, gravity gradients Гxz, Гyz, and Гzz and three-dimensional geocentric positions. The solutions of a large variety of uniquely and overdeterminedg.b.v.p.'s can be obtained from it by specializing weights. Interesting is that the anomalous potential can be determined—up to a constant—from astronomical latitude and longitude in combination with either {Гxz,Гyz} or horizontal coordinate corrections Δx and Δy, or both. Dual to the formulation in terms of observation equations the overdeterminedg.b.v.p.'s can as well be solved by condition equations. Constant radius approximation can be overcome in an iterative approach. For the Stokes problem this results in the solution of the “simple” Molodenskii problem. Finally defining an error covariance model with a Krarup-type kernel first results were obtained for a posteriori variance-covariance and reliability analysis.  相似文献   

12.
An inverse Poisson integral technique has been used to determine a gravity field on the geoid which, when continued by analytic free space methods to the topographic surface, agrees with the observed field. The computation is performed in three stages, each stage refining the previous solution using data at progressively increasing resolution (1o×1o, 5′×5′, 5/8′×5/8′) from a decreasing area of integration. Reduction corrections are computed at 5/8′×5/8′ granularity by differencing the geoidal and surface values, smoothed by low-pass filtering and sub-sampled at 5′ intervals. This paper discusses 1o×1o averages of the reduction corrections thus obtained for 172 1o×1o squares in western North America. The 1o×1o mean reduction corrections are predominantly positive, varying from −3 to +15mgal, with values in excess of 5mgal for 26 squares. Their mean andrms values are +2.4 and 3.6mgal respectively and they correlate well with the mean terrain corrections as predicted byPellinen in 1962. The mean andrms contributions from the three stages of computation are: 1o×1o stage +0.15 and 0.7mgal; 5′×5′ stage +1.0 and 1.6mgal; and 5/8′×5/8′ stage +1.3 and 1.8mgal. These results reflect a tendency for the contributions to become larger and more systematically positive as the wavelengths involved become shorter. The results are discussed in terms of two mechanisms; the first is a tendency for the absolute values of both positive and negative anomalies to become larger when continued downwards and, the second, a non-linear rectification, due to the correlation between gravity anomaly and topographic height, which results in the values continued to a level surface being systematically more positive than those on the topography.  相似文献   

13.
1　ＩｎｔｒｏｄｕｃｔｉｏｎＤｉｆｆｅｒｅｎｔｇｅｏｉｄｓｏｌｕｔｉｏｎｓｗｅｒｅｃａｒｒｉｅｄｏｕｔｆｏｒＥ ｇｙｐｔｕｓｉｎｇｈｅｔｅｒｏｇｅｎｅｏｕｓｄａｔａａｎｄｄｉｆｆｅｒｅｎｔｍｅｔｈｏｄｏｌｏｇｉｅｓ (Ｅｌ＿Ｔｏｋｈｅｙ ,1 993) .ＴｈｅｍａｉｎｇｏａｌｏｆｔｈｉｓｐａｐｅｒｉｓｔｏｄｅｔｅｒｍｉｎｅａｍｏｓｔａｃｃｕｒａｔｅｎｅｗｇｅｏｉｄｆｏｒＥｇｙｐｔｔａｋｉｎｇａｄｖａｎｔａｇｅｏｆａｎｅｗｕｐｄａｔｅｄｇｒａｖｉｔｙｄａｔａｂａｓｅ,ｔｈｅｉｎｆｏｒｍａｔｉｏｎｇｉｖｅｎｂｙ…  相似文献   

14.
The study area, Hesaraghatta watershed is located between 77° 20′ to 77° 42′ E longitude and 13° 10′ to 13° 24′ N latitude with an area of 600.01 km2. Thematic layers such as Land Use/Land Cover, drainage, soil and hydrological soil group were generated from IRS–1D LISS III satellite data (FCC). An attempt was made to estimate runoff using Soil Conservation Service (SCS) curve number model and it was estimated to be 1960, 2066, 1870 and 1810 mm for sub-watersheds 1, 2, 3 and 4 respectively. Quantitative morphometric analysis was carried out for the entire watershed and the four sub-watersheds independently by estimating their (a) linear aspects like stream order, stream length, stream length ratio, bifurcation ratio, length of overland flow, drainage pattern (b) aerial aspects like shape factor, circulatory ratio, elongation ratio and drainage density and (c) relief aspects like basin relief, relief ratio, relative relief and ruggedness number. Drainage density was estimated to be 1.23 km/km2 designating the study area as a very coarse textured watershed.  相似文献   

15.
Hydromorphogeological studies have been carried out around Agnigundala mineralised belt (longitude 70°.39′ - 16°.51′ and latitude 16°.2′ - 16°.15′) using remote sensing IRS-IB and SPOT data for ground water exploration. Based on erosional and depositional characters of various geomorphic units like Hills (Structural and denudational) Pediment, Buried pediment, plains and valley fills have been identified in various lithologies like granite, granite gneiss, biotite schist, phyllite,. quartzite and dolomite. The acclamations of individual geomorphic units through visual interpretation are verified from field data. The groundwater potentials of the individual geomorphologic units have been evaluated to obtain a complete hvdrogcological picture of the area. The field data have further helped in quanlifying various geomorphological units with reference to their potential for ground water occurrence.  相似文献   

16.
Spectral analysis by least squares as developed by Vaníček is applied to a series of transit times measurements obtained with a suspended gyrocompass (Wild) electronically equipped with three photocells and a printing chronograph. Instead of being the Fourier transform of the autocovariance function as in the usual spectral analysis of time series (Wiener theory), the spectral function used here is a function of an estimator of the variance factor obtained after a least squares fitting of a sinusoid to the data. That function is normalized to values between zero and one. For step-by-step spectral analysis by least squares each time a significant frequency appears in the spectrum it is removed by least squares fitting of the corresponding sinusoid including a damping coefficient, the residuals being again examined by spectral analysis by least squares. We find four significant frequencies: the well known principal period of about 7min in the spinning case; a very strong component with a period nearly exactly half the principal period and an amplitude of about 70″, explained by taking into account the second-order term in the theory developed by Jeudy, and two remaining periods with much smaller amplitudes (2″.9 and 0″.9). It is shown that the shortest period (0s.021), predicted by theory, exists in the measurements and cannot be neglected. The smallest component is considered to correspond to the wobble which can easily be observed in the perturbed motion.  相似文献   

17.
以经纬度坐标转换到深圳坐标为例,利用卫星遥感影像,通过全局搜寻算法选择控制点对求解仿射变换六参数值,在不同约束目标下对坐标距离偏差程度进行筛选分析,确定适合深圳坐标下能有效提高校正精度的控制点对组合及校正坐标公式。  相似文献   

18.
New solutions for the geodetic coordinate transformation   总被引：5，自引：2，他引：5  
 The Cartesian-to-geodetic-coordinate transformation is approached from a new perspective. Existence and uniqueness of geodetic representation are presented, along with a clear geometric picture of the problem and the role of the ellipse evolute. A new solution is found with a Newton-method iteration in the reduced latitude; this solution is proved to work for all points in space. Care is given to error propagation when calculating the geodetic latitude and height. Received: 9 August 2001 / Accepted: 27 March 2002 Acknowledgments. The author would like to thank the Clifford W.␣Tompson scholarship fund, Dr. Brian DeFacio, the University of Missouri College of Arts &Sciences, and the United States Air Force. He also thanks a reviewer for suggesting and providing a prototype MATLAB code. A MATLAB program for the iterative sequence is presented at the end of the paper (Appendix A).  相似文献   

19.
An operational algorithm for computation of terrain correction (or local gravity field modeling) based on application of closed-form solution of the Newton integral in terms of Cartesian coordinates in multi-cylindrical equal-area map projection of the reference ellipsoid is presented. Multi-cylindrical equal-area map projection of the reference ellipsoid has been derived and is described in detail for the first time. Ellipsoidal mass elements with various sizes on the surface of the reference ellipsoid are selected and the gravitational potential and vector of gravitational intensity (i.e. gravitational acceleration) of the mass elements are computed via numerical solution of the Newton integral in terms of geodetic coordinates {,,h}. Four base- edge points of the ellipsoidal mass elements are transformed into a multi-cylindrical equal-area map projection surface to build Cartesian mass elements by associating the height of the corresponding ellipsoidal mass elements to the transformed area elements. Using the closed-form solution of the Newton integral in terms of Cartesian coordinates, the gravitational potential and vector of gravitational intensity of the transformed Cartesian mass elements are computed and compared with those of the numerical solution of the Newton integral for the ellipsoidal mass elements in terms of geodetic coordinates. Numerical tests indicate that the difference between the two computations, i.e. numerical solution of the Newton integral for ellipsoidal mass elements in terms of geodetic coordinates and closed-form solution of the Newton integral in terms of Cartesian coordinates, in a multi-cylindrical equal-area map projection, is less than 1.6×10–8 m2/s2 for a mass element with a cross section area of 10×10 m and a height of 10,000 m. For a mass element with a cross section area of 1×1 km and a height of 10,000 m the difference is less than 1.5×10–4m2/s2. Since 1.5× 10–4 m2/s2 is equivalent to 1.5×10–5m in the vertical direction, it can be concluded that a method for terrain correction (or local gravity field modeling) based on closed-form solution of the Newton integral in terms of Cartesian coordinates of a multi-cylindrical equal-area map projection of the reference ellipsoid has been developed which has the accuracy of terrain correction (or local gravity field modeling) based on the Newton integral in terms of ellipsoidal coordinates.Acknowledgments. This research has been financially supported by the University of Tehran based on grant number 621/4/859. This support is gratefully acknowledged. The authors are also grateful for the comments and corrections made to the initial version of the paper by Dr. S. Petrovic from GFZ Potsdam and the other two anonymous reviewers. Their comments helped to improve the structure of the paper significantly.  相似文献   

20.
This paper analyses the accuracy of vertical deflection measurements carried out with the Digital Zenith Camera System TZK2-D, an astrogeodetic state-of-the-art instrumentation developed at the University of Hannover. During 107 nights over a period of 3.5 years, the system was used for repeated vertical deflection observations at a selected station in Hannover. The acquired data set consists of about 27,300 single measurements and covers 276 h of observation time, respectively. For the data collected at an earlier stage of development (2003 to 2004), the accuracy of the nightly mean values has been found to be about 0′′.10−0′′.12. Due to applying a refined observation strategy since 2005, the accuracy of the vertical deflection measurements was enhanced into the unprecedented range of 0′′.05 − 0′′.08. Accessing the accuracy level of 0′′.05 requires usually 1 h of observational data, while the 0′′.08 accuracy level is attained after 20 min measurement time. In comparison to the analogue era of geodetic astronomy, the accuracy of vertical deflection observations is significantly improved by about one order of magnitude.  相似文献   

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