Botswana gravity reference net

Gravity reference stations for the National Gravity Survey of Botswana have been established at twenty-three sites throughout the country in a net linked to existing bases in South Africa, Kenya and Zambia with an internal accuracy of better than 0.5 gravity units (one gravity unit, gu, equals an acceleration of 10⁻⁶ m.s⁻²). The field procedure and reduction of data are explained and a list is given of the gravity values.     

First results with the transportable absolute gravity meter JILAG-3

A transportable absolute gravity meter has been built at the Joint Institute for Laboratory Astrophysics (JILA) of the University of Colorado and delivered in January 1986 to the Institut für Erdmessung (IFE), Universität Hannover. Instrumental investigations, software improvements and absolute gravity determinations on 15 stations performed byIFE in 1986 are reported here. The main conclusion from one year experience with the instrument is that absolute gravity can be observed on a station within one day with a precision of a few μgal and an accuracy of about 10 μgal.     

A model for adjustment of differential gravity measurements with simultaneous gravimeter calibration

 A mathematical model is proposed for adjustment of differential or relative gravity measurements, involving simultaneously instrumental readings, coefficients of the calibration function, and gravity values of selected base stations. Tests were performed with LaCoste and Romberg model G gravimeter measurements for a set of base stations located along a north–south line with 1750 mGal gravity range. This line was linked to nine control stations, where absolute gravity values had been determined by the free-fall method, with an accuracy better than 10 μGal. The model shows good consistence and stability. Results show the possibility of improving the calibration functions of gravimeters, as well as a better estimation of the gravity values, due to the flexibility admitted to the values of the calibration coefficients. Received: 15 November 1999 / Accepted: 31 October 2000     

Somigliana–Pizzetti gravity: the international gravity formula accurate to the sub-nanoGal level

 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     

The new gravity base net 1976 of the Federal Republic of Germany (DSGN 76)

A new gravity base net (“Schweregrundnetz 1976 der Bundesrepublik Deutschland”, DSGN 76) has been established in the Federal Republic of Germany, to meet the increased requirements of geophysics, geology, metrology and geodesy. The net comprises 21 stations with three excenters each. The gravity values were determined using 4 absolute stations, 11 IGSN71-stations and about 3000 relative gravity meter observations with 4 gravity meters. Instrumental investigations and special treatment of local tidal and atmospheric effects improved the data for the least squares adjustment, which was performed by the method of observation equations following the use of condition equations. The final adjustment showed a point r.m.s. error of about 10μGal[10^?8 ms^?2]. Detailed results will be published in the ”Veröffentlichungen der Deutschen Geodätischen Kommission”.     

Preprocessing of gravity gradients at the GOCE high-level processing facility

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.     

Establishment of precise gravity network of airport stations in India

A precise gravity network of thirty-five stations based on the first order gravity station at Palam airport, New Delhi (979.13433 gals—University of Wisconsin 1969 value) was established during April–June 1971, covering the entire country, in order to use them as reference bases for any future gravity surveys in India with a repeatability of ±0.05 mgal or less. The instrument, a LaCoste-Romberg geodetic gravimeter No. G-84, was transported by air over the network of airport stations embracing Trivandrum in the south, Srinagar in the north, Bombay in the west and Mohanbari in the east. The four airport stations in New Delhi, Calcutta, Madras and Bombay which were more precisely established by a large number of repeat observations were utilised as base stations for facilitating easy occupation of the remaining thirty-one stations within their respective zones. The observations were reduced by procedure which permits automatic removal of instrumental drift from the observed readings. According to the depicted drift curve, the instrumental drift though comparatively small, is found not exactly linear due to the possible tare effect observed at the initial stage and also the resulting creep drift that might have been developed during transportation of the gravimeter by air. The final results along with their probable errors of the order of ±0.01 mgal for base stations and ±0.03 mgal for other stations relative to the adopted value at Palam airport, are given in Table 1. Fourteen of the sites occupied are reoccupations of stations already established by the University of Wisconsin in 1963, and the results of the old and the new measurements as given in Table 2, are in remarkable agreement, which ensures the correctness of the calibration factors of the present instrument relative to that of the Wollard's LaCoste-Romberg gravimeter No. G-1-A actually employed in the 1963 measurements.     

内核超速旋转引起的重力场变化(英文)

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.     

Absolute gravity measurements on the canadian gravity standardization network

Summary Absolute measurements of gravity have been made at 6 locations ranging from Ottawa, Ont., in southern Canada, to Alert, N.W.T., the world's most northerly permanent settlement, as part of a program to provide scale and level for the Canadian Gravity Standardization Network (CGSN). Except at Resolute, N.W.T., CGSN-74 gravity values, upon which our gravity reductions are currently based, agree with the absolute gravity meter results to within about .25µm/s². The scale of our CGSN-80 gravity network, upon which our spring-balance type gravity meter scale constants are derived, agrees with the scale defined by the absolute gravity measurements to within about one part in ten thousand.     

A new comprison of the Italian conventional' mgal and the German pendulum values

With the small dials of two Worden gravity meters, calibrated on the Italian ‘conventional’ basis, a comparison was completed in 1956 with the German pendulum stations. The result shows a difference in the slope of −0·5%. The stations in Germany of the European calibration line line have been checked.

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Riassunto Con due gravimetri Worden, tarati sulla base italiana, é stato completato nel 1956 il confronto con le misure pendolari dell'Istituto Geodetico di Potsdam, impiegando solo le viti piccole. Ne é risultata una differenza sistematica di −0·5%. Sono state pure occupate le stazioni facenti parte del tratto tedesco sulla base di taratura europea.

     

An evaluation of some systematic error sources affecting terrestrial gravity anomalies

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     

Calibrating the GOCE accelerations with star sensor data and a global gravity field model

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.     

Unification of vertical datums by GPS and gravimetric geoid models with application to Fennoscandia

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     

时变重力测量确定青藏高原地壳隆升与增厚速率

联合绝对重力和重力反演与气候实验卫星（gravity recovery and climate experiment,GRACE）重力多年观测数据,获得了青藏高原多个基准站区域的地壳垂直形变速率。研究结果表明,绝对重力呈明显的负变化,绝对重力和卫星重力的时变系统差也呈较一致的负值,鼎新（DXIN）、德令哈（DLHA）、西宁（XNIN）、拉萨（LHAS）和仲巴（XZZB）5个基准站的区域地壳垂直形变呈明显的隆升状态,即拉萨块体、祁连块体和阿拉善块体处于地壳隆升状态,隆升速率分别约为2.01±0.15 mm/a、1.88±0.19mm/a、1.91±0.10 mm/a。在印度板块和欧亚板块的双向挤压下,青藏高原的地壳在不断的隆升与增厚,平均隆升速率约为1.94±0.17 mm/a,平均增厚速率约为2.35±3.30 mm/a。     

The determination of potential difference by the joint application of measured and synthetical gravity data: a case study in Hungary

In an elementary approach every geometrical height difference between the staff points of a levelling line should have a corresponding average g value for the determination of potential difference in the Earth’s gravity field. In practice this condition requires as many gravity data as the number of staff points if linear variation of g is assumed between them. Because of the expensive fieldwork, the necessary data should be supplied from different sources. This study proposes an alternative solution, which is proved at a test bed located in the Mecsek Mountains, Southwest Hungary, where a detailed gravity survey, as dense as the staff point density (~1 point/34 m), is available along a 4.3-km-long levelling line. In the first part of the paper the effect of point density of gravity data on the accuracy of potential difference is investigated. The average g value is simply derived from two neighbouring g measurements along the levelling line, which are incrementally decimated in the consecutive turns of processing. The results show that the error of the potential difference between the endpoints of the line exceeds 0.1 mm in terms of length unit if the sampling distance is greater than 2 km. Thereafter, a suitable method for the densification of the decimated g measurements is provided. It is based on forward gravity modelling utilising a high-resolution digital terrain model, the normal gravity and the complete Bouguer anomalies. The test shows that the error is only in the order of 10⁻³mm even if the sampling distance of g measurements is 4 km. As a component of the error sources of levelling, the ambiguity of the levelled height difference which is the Euclidean distance between the inclined equipotential surfaces is also investigated. Although its effect accumulated along the test line is almost zero, it reaches 0.15 mm in a 1-km-long intermediate section of the line.     

A comparison of recent Earth gravitational models with emphasis on their contribution in refining the gravity and geoid at continental or regional scale

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.