Equatorial radius of the Earth: A dynamical determination

An intrresting variation on the familiar method of determining the earth's equatorial radius a_e, 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 γ_e 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.     

An evaluation of orthometric height accuracy using bore hole gravimetry

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.     

Interpretation of the tidal residuals during the 11 July 1991 total solar eclipse

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     

Absolute gravity measurements in Switzerland: Definition of a base network for geodynamic investigations and for the Swiss fundamental gravity net

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.     

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     

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 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.

     

Influence of the atmospheric masses on the gravitational field of the earth

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.     

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.