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1.
    
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   

2.
An intrresting variation on the familiar method of determining the earth's equatorial radius ae, from a knowledge of the earth's equatorial gravity is suggested. The value of equatorial radius thus found is 6378,142±5 meters. The associated parameters are GM=3.986005±.000004 × 1020 cm3 sec-−2 which excludes the relative mass of atmosphere ≅10−6 ξ GM, the equatorial gravity γe 978,030.9 milligals (constrained in this solution by the Potsdam Correction of 13.67 milligals as the Potsdam Correction is more directly, orless indirectly, measurable than the equatorial gravity) and an ellipsoidal flattening of f=1/298.255.  相似文献   

3.
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   

4.
 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   

5.
The method of Bjerhammar is studied in the continuous case for a sphere. By varying the kernel function, different types of unknowns (u*) are obtained at the internal sphere (the Bjerhammar sphere). It is shown that a necessary condition for the existence of u* is that the degree variances (σ n 2 ) of the observations are of an order less than n−2. According to Kaula’s rule this condition is not satisfied for the earth’s gravity anomaly field (σ n 2 =n−1) but well for the geopotential (σ n 2 =n−3).  相似文献   

6.
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   

7.
Summary Results of two absolute gravity surveys performed in Switzerland between 1978 and 1979 are presented and discussed in the framework of the uplift history of the Swiss Alps. Five absolute stations have been established as a contribution to the Swiss fundamental gravity net as well as to geodynamic investigations on the Alpine uplift. Two sites (Interlaken—Jungfraujoch) form the end points of a calibration line for field gravimeters. The gravity range of this line amounts to 605×10−5 ms−2 (=605 mgal). It can be traversed in a relatively short time interval of less than 3 hours. Two other sites (Brig and Chur) are located in the area of the most negative gravity anomalies and highest uplift rates encountered in Switzerland. They serve as reference stations for a more extended gravity net for studying non—periodic secular gravity variations associated with the Alpine uplift. Institut für Geod?sie und Photogrammetrie, ETH-Zürich, Separata No. 13. Institut für Geophysik, ETH-Zürich, Contribution No. 333.  相似文献   

8.
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   

9.
Due to the super rotation of the Earth＇s inner core, the tilted figure axis of the inner core would progress with respect to the mantle and thus cause the variation of the Earth＇s external gravity field. This paper improves the present model of the gravity field variation caused by the inner core super rotation. Under the assumption that the inner core is a stratifying ellipsoid whose density function is fitted out from PREM and the super rotation rate is 0.27-0.53°/yr, calculations show that the global temporal variations on the Earth＇s surface have a maximum value of about 0.79-1.54×10^3 pGal and a global average intensity of about 0.45-0.89×10^ 3 μGal in the whole year of 2007, which is beyond the accuracy of the present gravimetry and even the super conducting gravimeter data. However, both the gravity variations at Beijing and Wuhan vary like sine variables with maximal variations around 0.33 pGal and 0.29 pGal, respectively, in one cycle. Thus, continuous gravity measurements for one or two decades might be able to detect the differential motion of the inner core.  相似文献   

10.
Observations of gravity and atmospheric pressure variations during the total solar eclipse of 11 July 1991 in Mexico City are presented. An LCR-G402 gravimeter equipped with a feedback system and a digital data acquisition system scanned gravity and pressure every second around the totality. On the pressure record an oscillation, starting at the totality, with a peak to peak amplitude of 0.5 hPa and a periodicity of 40 to 50 min, can clearly be seen. This oscillation results from the thermal shock wave produced by the Moon shadow travelling at supersonic speed. At the 0.1 μGal (1 nm · s−2) level all gravity perturbations are explained by the atmospheric pressure effect. Received: 10 February 1995 / Accepted: 7 June 1996  相似文献   

11.
Terrestrial free-air gravity anomalies form a most essential data source in the framework of gravity field determination. Gravity anomalies depend on the datums of the gravity, vertical, and horizontal networks as well as on the definition of a normal gravity field; thus gravity anomaly data are affected in a systematic way by inconsistencies of the local datums with respect to a global datum, by the use of a simplified free-air reduction procedure and of different kinds of height system. These systematic errors in free-air gravity anomaly data cause systematic effects in gravity field related quantities like e.g. absolute and relative geoidal heights or height anomalies calculated from gravity anomaly data. In detail it is shown that the effects of horizontal datum inconsistencies have been underestimated in the past. The corresponding systematic errors in gravity anomalies are maximum in mid-latitudes and can be as large as the errors induced by gravity and vertical datum and height system inconsistencies. As an example the situation in Australia is evaluated in more detail: The deviations between the national Australian horizontal datum and a global datum produce a systematic error in the free-air gravity anomalies of about −0.10 mgal which value is nearly constant over the continent  相似文献   

12.
    
An analysis is made of the results from all repeated gravity measurements of the Fennoscandian land uplift gravity line 63°. The line is, thereby, divided into two separate parts: one part west of the land uplift maximum, and the other part east of the land uplift maximum. A statistically significant change of gravity is found both for the western part and the eastern one. Both parts give a relation between gravity change and land uplift of about −0.22μgal/mm. Paper presented at the 10th General Meeting of the Nordic Geodetic Commission, Helsinki 1986. (Addresses of the authors at the end of the article).  相似文献   

13.
Modern models of the Earth's gravity field are developed in the IERS (International Earth Rotation Service) terrestrial reference frame. In this frame the mean values for gravity coefficients of the second degree and first order, C 21(IERS) and S 21(IERS), by the current IERS Conventions are recommended to be calculated by using the observed polar motion parameters. Here, it is proved that the formulae presently employed by the IERS Conventions to obtain these coefficients are insufficient to ensure their values as given by the same source. The relevant error of the normalized mean values for C 21(IERS) and S 21(IERS) is 3×10−12, far above the adopted cutoff (10−13) for variations of these coefficients. Such an error in C 21 and S 21 can produce non-modeled perturbations in motion prediction of certain artificial Earth satellites of a magnitude comparable to the accuracy of current tracking measurements. Received: 14 September 1998 / Accepted: 20 May 1999  相似文献   

14.
A 2×2 arc-minute resolution geoid model, CARIB97, has been computed covering the Caribbean Sea. The geoid undulations refer to the GRS-80 ellipsoid, centered at the ITRF94 (1996.0) origin. The geoid level is defined by adopting the gravity potential on the geoid as W 0=62 636 856.88 m2/s2 and a gravity-mass constant of GM=3.986 004 418×1014 m3/s2. The geoid model was computed by applying high-frequency corrections to the Earth Gravity Model 1996 global geopotential model in a remove-compute-restore procedure. The permanent tide system of CARIB97 is non-tidal. Comparison of CARIB97 geoid heights to 31 GPS/tidal (ITRF94/local) benchmarks shows an average offset (h–H–N) of 51 cm, with an Root Mean Square (RMS) of 62 cm about the average. This represents an improvement over the use of a global geoid model for the region. However, because the measured orthometric heights (H) refer to many differing tidal datums, these comparisons are biased by localized permanent ocean dynamic topography (PODT). Therefore, we interpret the 51 cm as partially an estimate of the average PODT in the vicinity of the 31 island benchmarks. On an island-by-island basis, CARIB97 now offers the ability to analyze local datum problems which were previously unrecognized due to a lack of high-resolution geoid information in the area. Received: 2 January 1998 / Accepted: 18 August 1998  相似文献   

15.
The second Baltic Sea Level (BSL) GPS campaign was run for one week in June 1993. Data from 35 tide gauge sites and five fiducial stations were analysed, for three fiducial stations (Onsala, Mets?hovi and Wettzell) fixed at the ITRF93 system. On a time-scale of 5 days, precision was several parts in 109 for the horizontal and vertical components. Accuracies were about 1 cm in comparison with the International GPS Geodynamical Service (IGS) coordinates in three directions. To connect the Swedish and the Finnish height systems, our numerical application utilises three approaches: a rigorous approach, a bias fit and a three-parameter fit. The results between the Swedish RH70 and the Finnish N 60 systems are estimated to −19.3 ± 6.5, −17 ± 6 and −15 ± 6 cm, respectively, by the three approaches. The results of the three indirect methods are in an agreement with those of a direct approach from levelling and gravity measurements. Received: 3 April 1996 / Accepted: 4 August 1997  相似文献   

16.
Seasonal and latitude dependent corrections to the gravity and height anomalies are developed in order to account for the neglect of the atmospheric masses outside the geold, when using Stokes’ equation. It is shown that the atmospheric correction to gravity at sea level is almost constant, equal to0.871 mgals with a variation of2 μ gals whereas the height anomaly correction varies between −0.1 cm and −1.3 cm. Further, when the combined latitudinal/seasonal dependence is neglected in the atmospheric corrections, the maximum error introduced is of the order of40 μ gals for the gravity corrections and0.7 cm for the height anomaly corrections.  相似文献   

17.
Since the publication of the Earth gravitational model (EGM)96 considerable improvements in the observation techniques resulted in the development of new improved models. The improvements are due to the availability of data from dedicated gravity mapping missions (CHAMP, GRACE) and to the use of 5′ × 5′ terrestrial and altimetry derived gravity anomalies. It is expected that the use of new EGMs will further contribute to the improvement of the resolution and accuracy of the gravity and geoid modeling in continental and regional scale. To prove this numerically, three representative Earth gravitational models are used for the reduction of several kinds of data related to the gravity field in different places of the Earth. The results of the reduction are discussed regarding the corresponding covariance functions which might be used for modeling using the least squares collocation method. The contribution of the EIGEN-GL04C model in most cases is comparable to that of EGM96. However, the big difference is shown in the case of EGM2008, due not only to its quality but obviously to its high degree of expansion. Almost in all cases the variance and the correlation length of the covariance functions of data reduced to this model up to its maximum degree are only a few percentages of corresponding quantities of the same data reduced up to degree 360. Furthermore, the mean value and the standard deviation of the reduced gravity anomalies in extended areas of the Earth such as Australia, Arctic region, Scandinavia or the Canadian plains, vary between −1 and +1 and between 5 and 10 × 10−5 ms−2, respectively, reflecting the homogenization of the gravity field on a regional scale. This is very important in using least squares collocation for regional applications. However, the distance to the first zero-value was in several cases much longer than warranted by the high degree of the expansion. This is attributed to errors of medium wavelengths stemming from the lack of, e.g., high-quality data in some area.  相似文献   

18.
Based on the gravity field models EGM96 and EIGEN-GL04C, the Earth＇s time-dependent principal moments of inertia A, B, C are obtained, and the variable rotation of the Earth is determined. Numerical results show that A, B, and C have increasing tendencies; the tilt of the rotation axis increases 2.1×10^ 8 mas/yr; the third component of the rotational angular velocity, ω3 , has a decrease of 1.0×10^ 22 rad/s^2, which is around 23% of the present observed value. Studies show in detail that both 0 and ω3 experience complex fluctuations at various time scales due to the variations of A, B and C.  相似文献   

19.
A simple formula is presented giving the value of γ−γ r to better than 0.001 mgal associated with an arbitrary reference ellipsoid, where γ is the normal gravity and γ r is its radial component. Further simplifications of this formula are possible, depending on the desired accuracy. Since in the actual field g−gr equals γ−γ r to a good approximation, this formula makes it possible to work in terms of gr rather than in terms of the measured quantity g. Such a choice is attractive mainly because the spherical harmonic expansion of gr is very simple.  相似文献   

20.
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   

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