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1.
Errors are introduced in orthometric height computations by the use of standard formulas to estimate mean gravity along the plumb line. Direct measurements of gravity between the Earth’s surface and sea level from bore hole gravimetry were used to determine the magnitude of these errors. For the seven cases studied, errors in orthometric height, due to the use of the Helmert method for computing mean gravity along the plumb line, were generally small (<2 cm). However, in one instance the error was substantial, being9.6 cm. The results verified the general validity of the Poincaré-Prey approach to estimation of gravity along the plumb line and demonstrated that the suggestion byVanicek (1980) that the air gradient is more appropriate is incorrect. With sufficient topographic information to compute terrain corrections, and density estimates from surface gravity, errors in mean gravity along the plumb line should contribute no more than 3cm to orthometric height computation.  相似文献   

2.
Fast and accurate relative positioning for baselines less than 20 km in length is possible using dual-frequency Global Positioning System (GPS) receivers. By measuring orthometric heights of a few GPS stations by differential levelling techniques, the geoid undulation can be modelled, which enables GPS to be used for orthometric height determination in a much faster and more economical way than terrestrial methods. The geoid undulation anomaly can be very useful for studying tectonic structure. GPS, levelling and gravity measurements were carried out along a 200-km-long highly undulating profile, at an average elevation of 4000 m, in the Ladak region of NW Himalaya, India. The geoid undulation and gravity anomaly were measured at 28 common GPS-levelling and 67 GPS-gravity stations. A regional geoid low of nearly −4 m coincident with a steep negative gravity gradient is compatible with very recent findings from other geophysical studies of a low-velocity layer 20–30 km thick to the north of the India–Tibet plate boundary, within the Tibetan plate. Topographic, gravity and geoid data possibly indicate that the actual plate boundary is situated further north of what is geologically known as the Indus Tsangpo Suture Zone, the traditionally supposed location of the plate boundary. Comparison of the measured geoid with that computed from OSU91 and EGM96 gravity models indicates that GPS alone can be used for orthometric height determination over the Higher Himalaya with 1–2 m accuracy. Received: 10 April 1997 / Accepted: 9 October 1998  相似文献   

3.
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   

4.
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   

5.
Precise gravity measurements have repeatedly been carried out in the area around Lake Biwa in Japan since 1950 in order to detect the secular change of gravity. The results obtained so far show that gravity change observed on the west line of the first order levelling route around the lake during the period of 1971∼1975 was consistent with the results of levelling surveys. This evidence shows that precise gravity measurement is one of the powerful methods for detecting vertical crustal movement.  相似文献   

6.
Recently, a new application of time-dependent gravity observations is emerging: the study of natural hydrological mass changes and their underlying processes. Complementary to GRACE data and continuous recordings with superconducting gravimeters, repeated observations with relative instruments on a local network may contribute to gain additional information on spatial changes in hydrology. The questions that need to be addressed are whether the results of these repeated measurements will be of sufficiently high resolution and accuracy, as well as how unique the information obtained will be. To examine this, a local gravity network with maximum point distances of 65 m was established in a hilly area around the Geodynamic Observatory Moxa, Germany. Using three to five LaCoste & Romberg relative gravimeters repeated measurements were carried out in a seasonal rhythm as well as at particular events like snowmelt or dryness in 17 campaigns between November 2004 and April 2007. The standard deviations obtained by least squares adjustment range from ±9 to ±14 nm/s2 for a gravity difference of one campaign, thus for gravity changes between two campaigns from ±13 to ±20 nm/s2. Between the points of the network, spatial gravity changes of up to 171 nm/s2 (139 nm/s2 between two successive campaigns) could be proven significantly. They correlate with changes in the local hydrological situation. Particularly, a steep slope next to the observatory is identified as a gravimetrically significant hydrological compartment. The results obtained contribute to an improved reduction of the local hydrological signal in continuous gravity recordings and provide constraints to hydrological models.  相似文献   

7.
Alternative mission architectures for a gravity recovery satellite mission   总被引：4，自引：1，他引：3  
Since its launch in 2002, the Gravity Recovery and Climate Experiment (GRACE) mission has been providing measurements of the time-varying Earth gravity field. The GRACE mission architecture includes two satellites in near-circular, near-polar orbits separated in the along-track direction by approximately 220 km (e.g. collinear). A microwave ranging instrument measures changes in the distance between the spacecraft, while accelerometers on each spacecraft are used to measure changes in distance due to non-gravitational forces. The fact that the satellites are in near-polar orbits coupled with the fact that the inter-satellite range measurements are directed in the along-track direction, contributes to longitudinal striping in the estimated gravity fields. This paper examines four candidate mission architectures for a future gravity recovery satellite mission to assess their potential in measuring the gravity field more accurately than GRACE. All satellites were assumed to have an improved measurement system, with an inter-satellite laser ranging instrument and a drag-free system for removal of non-gravitational accelerations. Four formations were studied: a two-satellite collinear pair similar to GRACE; a four-satellite architecture with two collinear pairs; a two-satellite cartwheel formation; and a four-satellite cartwheel formation. A cartwheel formation consists of satellites performing in-plane, relative elliptical motion about their geometric center, so that inter-satellite measurements are, at times, directed radially (e.g. parallel to the direction towards the center of the Earth) rather than along-track. Radial measurements, unlike along-track measurements, have equal sensitivity to mass distribution in all directions along the Earth’s surface and can lead to higher spatial resolution in the derived gravity field. The ability of each architecture to recover the gravity field was evaluated using numerical simulations performed with JPL’s GIPSY-OASIS software package. Thirty days of data were used to estimate gravity fields complete to degree and order 60. Evaluations were done for 250 and 400 km nominal orbit altitudes. The sensitivity of the recovered gravity field to under-sampled effects was assessed using simulated errors in atmospheric/ocean dealiasing (AOD) models. Results showed the gravity field errors associated with the four-satellite cartwheel formation were approximately one order of magnitude lower than the collinear satellite pair when only measurement system errors were included. When short-period AOD model errors were introduced, the gravity field errors for each formation were approximately the same. The cartwheel formations eliminated most of the longitudinal striping seen in the gravity field errors. A covariance analysis showed the error spectrum of the cartwheel formations to be lower and more isotropic than that of the collinear formations.  相似文献   

8.
 The use of GPS for height control in an area with existing levelling data requires the determination of a local geoid and the bias between the local levelling datum and the one implicitly defined when computing the local geoid. If only scarse gravity data are available, the heights of new data may be collected rapidly by determining the ellipsoidal height by GPS and not using orthometric heights. Hence the geoid determination has to be based on gravity disturbances contingently combined with gravity anomalies. Furthermore, existing GPS/levelling data may also be used in the geoid determination if a suitable general gravity field modelling method (such as least-squares collocation, LSC) is applied. A comparison has been made in the Aswan Dam area between geoids determined using fast Fourier transform (FFT) with gravity disturbances exclusively and LSC using only the gravity disturbances and the disturbances combined with GPS/levelling data. The EGM96 spherical harmonic model was in all cases used in a remove–restore mode. A total of 198 gravity disturbances spaced approximately 3 km apart were used, as well as 35 GPS/levelling points in the vicinity and on the Aswan Dam. No data on the Nasser Lake were available. This gave difficulties when using FFT, which requires the use of gridded data. When using exclusively the gravity disturbances, the agreement between the GPS/levelling data were 0.71 ± 0.17 m for FFT and 0.63 ± 0.15 for LSC. When combining gravity disturbances and GPS/levelling, the LSC error estimate was ±0.10 m. In the latter case two bias parameters had to be introduced to account for a possible levelling datum difference between the levelling on the dam and that on the adjacent roads. Received: 14 August 2000 / Accepted: 28 February 2001  相似文献   

9.
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   

10.
In general the observations within a continental levelling network have been made during day time when the sun is above the horizon. In Northern countries levelling observations have often been made during the summer months and in the morning and the evening, when the sun may be to the North of the prime vertical. This entails that special mean tidal perturbations by the sun on a levelling network may deviate with not quite negligible quantities from general mean tidal influence by the sun on the sea. For the moon the corresponding deviation will be nearly zero. The variance of the levelling (REUN 1960) between the tidal stations M-28 Fredericia and M-48 Genova is (±33 mm x kiloGal)2. The author (1965) has found for this line (hypothetical levelling 19/5–2/6 1950 on the Yielding Earth) possiblespecial mean tidal correction by the moon +27.5 mm possiblespecial mean tidal correction by the sun −4.2 mm ― in total +23.3 mm deviating 22.5 mm fromgeneral mean tidal correction of the seafor both moon and sun} +45.8 mm The deviation 22.5 mm between tidal corrections for Mean Sea Level, MSL, and for levelling line is not quite negligible.  相似文献   

11.
A comparison of different mass elements for use in gravity gradiometry   总被引：6，自引：3，他引：3  
Topographic and isostatic mass anomalies affect the external gravity field of the Earth. Therefore, these effects also exist in the gravity gradients observed, e.g., by the satellite gravity gradiometry mission GOCE (Gravity and Steady-State Ocean Circulation Experiment). The downward continuation of the gravitational signals is rather difficult because of the high-frequency behaviour of the combined topographic and isostatic effects. Thus, it is preferable to smooth the gravity field by some topographic-isostatic reduction. In this paper the focus is on the modelling of masses in the space domain, which can be subdivided into different mass elements and evaluated with analytical, semi-analytical and numerical methods. Five alternative mass elements are reviewed and discussed: the tesseroid, the point mass, the prism, the mass layer and the mass line. The formulae for the potential, the attraction components and the Marussi tensor of second-order potential derivatives are provided. The formulae for different mass elements and computation methods are checked by assuming a synthetic topography of constant height over a spherical cap and the position of the computation point on the polar axis. For this special situation an exact analytical solution for the tesseroid exists and a comparison between the analytical solution of a spherical cap and the modelling of different mass elements is possible. A comparison of the computation times shows that modelling by tesseroids with different methods produces the most accurate results in an acceptable computation time. As a numerical example, the Marussi tensor of the topographic effect is computed globally using tesseroids calculated by Gauss–Legendre cubature (3D) on the basis of a digital height model. The order of magnitude in the radial-radial component is about  ± 8 E.U. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.  相似文献   

12.
《测量评论》2013,45(100):252-261
Abstract

As part of the scientific work of the British North Greenland Expedition (1952–1954), a programme of trigonometrical levelling was carried out from the east to the west coast of Greenland, along a line across the inland ice between latitudes 76° 40′ N., and 78° 10′ N. The primary purpose of the work was to determine accurately the heights above sea level of a series of gravity stations, the gravity measurements being made in connection with determinations of ice thickness. For meteorological purposes it was necessary to know also the altitude of the Expedition's central station, situated in latitude 78° 04′ N., longitude 38° 29′ W. The accuracy necessary for the purpose of the gravity survey was a few metres for the altitudes, while the latitude of each gravity station had to be determined with an accuracy of ± 0.1 minute.  相似文献   

13.
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   

14.
陆态网络绝对重力基准的建立及应用   总被引：4，自引：0，他引：4  
利用陆态网络100个基准站的首期观测数据,建立了基本覆盖我国大陆范围的高精度绝对重力基准,各基准站点值精度均小于5.0μGal/a,为相对重力联测提供了高精度起算基准点,可获得真实的相对重力联测平差结果,避免重复重力观测获得的重力场动态变化图出现畸变。成都基准台重复重力观测获得的重力变化规律表明,汶川地震前长期重力变化率达5.01±0.7μGal/a,如此大的震前重力变化很可能是由于地下物质运移引起的。联合绝对重力和GRACE卫星长期测量数据,根据二者系统偏差确定了武汉地区的地壳沉降速率,为-3.27±0.65mm/a。  相似文献   

15.
A reliable and accurate gradiometer calibration is essential for the scientific return of the gravity field and steady-state ocean circulation explorer (GOCE) mission. This paper describes a new method for external calibration of the GOCE gradiometer accelerations. A global gravity field model in combination with star sensor quaternions is used to compute reference differential accelerations, which may be used to estimate various combinations of gradiometer scale factors, internal gradiometer misalignments and misalignments between star sensor and gradiometer. In many aspects, the new method is complementary to the GOCE in-flight calibration. In contrast to the in-flight calibration, which requires a satellite-shaking phase, the new method uses data from the nominal measurement phases. The results of a simulation study show that gradiometer scale factors can be estimated on a weekly basis with accuracies better than 2 × 10−3 for the ultrasensitive and 10−2 for the less sensitive axes, which is compatible with the requirements of the gravity gradient error. Based on a 58-day data set, scale factors are found that can reduce the errors of the in-flight-calibrated measurements. The elements of the complete inverse calibration matrix, representing both the internal gradiometer misalignments and scale factors, can be estimated with accuracies in general better than 10−3.  相似文献   

16.
Recurrence relations have been derived for truncation error coefficients of the extended Stokes' function and its partial derivatives required in the computation of the disturbing gravity vector at any elevation above the earth's surface. The corresponding formulae, the example of values of the truncation error coefficients for H=30.1 km and ψ0=30∘ and the estimations of truncation error are given in this article. Received: 26 January 1996 / Accepted: 11 June 1997  相似文献   

17.
A synthetic [simulated] Earth gravity model (SEGM) of the geoid, gravity and topography has been constructed over Australia specifically for validating regional gravimetric geoid determination theories, techniques and computer software. This regional high-resolution (1-arc-min by 1-arc-min) Australian SEGM (AusSEGM) is a combined source and effect model. The long-wavelength effect part (up to and including spherical harmonic degree and order 360) is taken from an assumed errorless EGM96 global geopotential model. Using forward modelling via numerical Newtonian integration, the short-wavelength source part is computed from a high-resolution (3-arc-sec by 3-arc-sec) synthetic digital elevation model (SDEM), which is a fractal surface based on the GLOBE v1 DEM. All topographic masses are modelled with a constant mass-density of 2,670 kg/m3. Based on these input data, gravity values on the synthetic topography (on a grid and at arbitrarily distributed discrete points) and consistent geoidal heights at regular 1-arc-min geographical grid nodes have been computed. The precision of the synthetic gravity and geoid data (after a first iteration) is estimated to be better than 30 μ Gal and 3 mm, respectively, which reduces to 1 μ Gal and 1 mm after a second iteration. The second iteration accounts for the changes in the geoid due to the superposed synthetic topographic mass distribution. The first iteration of AusSEGM is compared with Australian gravity and GPS-levelling data to verify that it gives a realistic representation of the Earth’s gravity field. As a by-product of this comparison, AusSEGM gives further evidence of the north–south-trending error in the Australian Height Datum. The freely available AusSEGM-derived gravity and SDEM data, included as Electronic Supplementary Material (ESM) with this paper, can be used to compute a geoid model that, if correct, will agree to in 3 mm with the AusSEGM geoidal heights, thus offering independent verification of theories and numerical techniques used for regional geoid modelling.Electronic Supplementary Material Supplementary material is available in the online version of this article at http://dx.doi.org/10.1007/s00190-005-0002-z  相似文献   

18.
    
The application of a Sartorius 4104 microbalance after Gast in vertical gradiometry was tested. A small mass of about 20 grams is suspended on thin fibers of different lengths Δℓ≤80 cm. From the weight difference of the small mass obtained at different levels along the plumb line the corresponding differences of gravity along the plumb line are inferred. The microbalance is mounted on a steal rack; measurements at constant low pressure (moderate vacuum) show the applicability of the balance as gravity difference sensor for field work. When environmental effects are further reduced (i,e, temperature is kept constant within ±0.1°C; pressure is controlled within 0.1 Torr etc.) the resolution of the balance can be fully exploited so a relative accuracy of ±10−9 should be feasible and for laboratory experiments should be of the order of a few parts in ±10−10. Vertical gravity gradients as observed on an improved moving platform with a LaCoste model G gravimeter are discussed. New possibilities of microgravimetry are pointed out. High precision observations and establishment of a system in an area of tectonic interest for detecting secular gravity changes are described. Paper presented at the meeting of the “International Gravity Commission”, Paris, September 1974.  相似文献   

19.
The principle and method for solving three types of satellite gravity gradient boundary value problems by least-squares are discussed in detail. Also, kernel function expressions of the least-squares solution of three geodetic boundary value problems with the observations {Γ zz },{Γ xz , Γ yz} and {Γ xx -Γ yy ,2 Γxy}are presented. From the results of recovering gravity field using simulated gravity gradient tensor data, we can draw a conclusion that satellite gravity gradient integral formulas derived from least-squares are valid and rigorous for recovering the gravity field.  相似文献   

20.
One of the products derived from the gravity field and steady-state ocean circulation explorer (GOCE) observations are the gravity gradients. These gravity gradients are provided in the gradiometer reference frame (GRF) and are calibrated in-flight using satellite shaking and star sensor data. To use these gravity gradients for application in Earth scienes and gravity field analysis, additional preprocessing needs to be done, including corrections for temporal gravity field signals to isolate the static gravity field part, screening for outliers, calibration by comparison with existing external gravity field information and error assessment. The temporal gravity gradient corrections consist of tidal and nontidal corrections. These are all generally below the gravity gradient error level, which is predicted to show a 1/f behaviour for low frequencies. In the outlier detection, the 1/f error is compensated for by subtracting a local median from the data, while the data error is assessed using the median absolute deviation. The local median acts as a high-pass filter and it is robust as is the median absolute deviation. Three different methods have been implemented for the calibration of the gravity gradients. All three methods use a high-pass filter to compensate for the 1/f gravity gradient error. The baseline method uses state-of-the-art global gravity field models and the most accurate results are obtained if star sensor misalignments are estimated along with the calibration parameters. A second calibration method uses GOCE GPS data to estimate a low-degree gravity field model as well as gravity gradient scale factors. Both methods allow to estimate gravity gradient scale factors down to the 10−3 level. The third calibration method uses high accurate terrestrial gravity data in selected regions to validate the gravity gradient scale factors, focussing on the measurement band. Gravity gradient scale factors may be estimated down to the 10−2 level with this method.  相似文献   

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