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Measurement of the acceleration due to gravity (g) began in the mid-seventeenth century when C Huygens constructed the first pendulum clock. Until 1818 all gravity determinations were absolute (i.e. the value of g was evaluated). In that year a pendulum device suitable for relative gravimetry in the field (the gravity difference between two sites being the observed quantity) was first employed. Since then the use of relative gravimetry has increased rapidly, first with the development of sophisticated pendulum devices and then with spring-type gravimeters. A very high level of accuracy, sometimes a few parts in 10⁹, can now be achieved.

However, relative gravimetry relies on absolute gravimetry for the determination of the gravity datum and of the gravity scale, the latter being important for the calibration of relative gravimeters. After the Second World War, with the development of lasers and of high-precision time-interval counters, the ballistic method began to be employed in the measurement of g. Today some thirty absolute gravimeters are available world wide and are used in classical geodetic projects (gravity datum and scale) and in projects dealing with crustal deformations, volcanic and seismic hazards, sea level fluctuation and so on.

The International Gravity Commission, a body of the International Association of Geodesy, has since 1981 recognized the need for periodic comparisons of absolute gravimeters in order to detect possible systematic errors and to define the accuracy level of the methodology. A Working Group (WG6 - Intercomparison of Absolute Gravimeters) is responsible for the organization of these comparisons.

This special issue of Metrologia is devoted to the Fourth International Comparison of Absolute Gravimeters (ICAG94) which was held in Sèvres, at the Bureau International des Poids et Mesures, from 24 May to 8 June 1994. Eleven absolute gravimeters from Austria, Canada, Finland, Germany, Italy, Japan, the USA and the BIPM took part in the comparison. At the same time, fourteen relative gravimeters were used to observe a microgravity network covering the five sites chosen for the absolute gravimeters and to measure the vertical gradient of g at each site.

ICAG94 also provided the opportunity to intercompare relative gravimeters and measuring techniques, as well as new calibration tools for these devices.

A workshop, where instrument features, data processing and analysis procedures were discussed in detail, completed the meeting.

Following the 1994 series of measurements, WG6 has decided to continue the comparisons at the BIPM on a four-yearly basis, supplemented by secondary comparisons to be organized on a continental scale (North America, Europe and Asia) to allow for an easier and possibly wider participation. The first such meeting has since been held at the Table Mountain Geophysical Observatory, NOAA, Boulder, CO, USA, in 1995.

Technological progress and the development of new devices for ballistic gravimetry call for a constant effort to be made in the comparison and validation of the gravimeters, both absolute and relative, used in scientific research and services to third parties.

In 1994, from 24 May to 8 June, the fourth International Comparison of Absolute Gravimeters was held at the Bureau International des Poids et Mesures, Sèvres, France. Eleven absolute gravimeters were operated at five sites and then compared by means of a high-precision gravity network which was itself observed throughout the period. The results demonstrate that absolute gravimetry can be carried out to an accuracy of 3 μGal to 4 μGal, which represents a substantial improvement since the first international comparison (1981, 10 μGal). The relatively low rate of improvement, one third of an order of magnitude in fifteen years, is certainly limited by current technology for measuring small time and space intervals. A notable finding of the comparison was an unsuspected source of systematic error which can be eliminated by new hardware or corrected through a correction algorithm.

On the occasion of the fourth International Comparison of Absolute Gravimeters carried out at Sèvres in 1994 an extensive series of microgravimetric measurements was organized. In total, fifteen LaCoste, four Scintrex CG-3M and one Sodin gravimeter measured, within a small network, vertical gravity gradients and a calibration baseline. The results show that the accuracy for single instruments is in the range of 3 μGal to 5 μGal in gravity difference, for the Scintrex and the LaCoste meters. Data from the series were also used to intercompare different ways of calibrating the gravimeter electrostatic feedback systems. The calibration platform of the Institut für Angewandte Geodäsie, (IFAG), Frankfurt, and the calibration lift of the Observatoire Royal de Belgique (ORB) were installed at Sèvres and the results compared with those for the calibration line. This paper gives the first results and a review of the techniques used.

Observations made with the JILA2 absolute gravimeter operated by the Geological Survey of Canada, during the 1989 and 1994 International Comparisons of Absolute Gravimeters, show that orientation-dependent systematic errors are introduced at the BIPM A3 site. With improved electronics, we can better identify instrument-induced vibrations which have a deleterious effect on the observations. Observations made in 1989 are compared with the measurements made in 1994. Furthermore, instrument orientation in 1994 is shown to have a damaging effect on the observations. This may suggest better designs for absolute gravity piers located on unconsolidated material.

We describe the design improvements incorporated in a new generation of absolute gravimeters, the FG5. A vertically oriented (in-line) interferometer design is used to remove the influence of floor vibration and tilt on the optical path length. The interferometer uses an iodine-stabilized laser as a primary length standard, with circuitry for automatic peak detection and locking. The seismic isolation system is an active long-period seismometer (Super Spring). The new design has improved passive isolation and thermal drift characteristics over previous systems. Programming flexibility and control of the test mass trajectory have been improved. The computer system has also improved real-time analysis and system capability. The FG5 instrument has a higher level of robustness, reliability and ease of use. These design advances have led to an instrumental uncertainty estimate of 1,1 × 10^-8 m s^-2 (1,0 μGal). Instrument agreement among nine similar devices is 1,8 μGal and observations under optimal conditions exhibit standard deviations of 5 μGal to 8 μGal.

In the error budget for absolute measurements of g, one of the most important contributions is the uncertainty of the frequency of the stabilized laser used as the reference wavelength. This was confirmed during the third International Comparison of Absolute Gravimeters held at the BIPM in 1989, at which the frequencies of all the lasers used in the gravimeters were checked by beat frequency against a BIPM reference laser. This problem was solved by the replacement of a He-Ne laser at λ ≈ 633 nm stabilized by the requirement that the intensity of two orthogonal modes be equal by a laser stabilized with respect to the saturated absorption of iodine at the same wavelength. A new design of portable laser, realized at the BIPM and developed by commercial companies, is described and the capabilities of this laser for use as a primary standard of wavelength or reference wavelength in a new generation of absolute gravimeters are presented. The results of the frequency calibration of the lasers used in the absolute gravimeters which participated in the fourth International Comparison of Absolute Gravimeters held at the BIPM in May and June 1994 are also presented.

Data from the 1994 International Comparison of Absolute Gravimeters were processed with the National Oceanic and Atmospheric Administration (NOAA) Geosciences Lab protocols and processing algorithms. The rootmean-square discrepancy between results obtained from individual groups and the NOAA processing is 2,3 μGal; the average discrepancy is 1,5 μGal. The sources of the discrepancies are probably (i) differences in the vertical gradients used for datum level transfers, (ii) inconsistencies between processing algorithms, and (iii) differences in data editing criteria.

Data from FG5 absolute gravimeters have been analysed using processing software developed by Edinburgh University. The work aims to understand apparent inconsistencies between relative and absolute observations and the variation of absolute gravity estimates outside the 10 nm s^-2 to 20 nm s^-2 (10 nm s^-2 = 1 μGal) range expected for FG5 instruments. Data from FG5-103 at Edinburgh, Birkenhead, Teddington and Taunton, FG5-107 at Taunton, FG5-105 at Teddington and FG5-101 at Onsala, Sweden, have been reprocessed. Fitting time-distance pairs to an equation of motion without a vertical gradient of gravity gives an estimate for g at some fraction of the way down the drop. None of the current theories correctly predicts the observed fraction of 0,43, so accurate results can only be found by including the vertical gradient terms to obtain a value of gravity at the top of the drop. Observations of the vertical gradient at some absolute sites have shown it to be nonlinear, so that using the same value in the equation of motion as for datum corrections can lead to significant errors. Solving the full equation of motion should give a constant estimate of gravity for all lengths or starting positions of the drop. This is rarely the case in the samples analysed here and the estimates may vary by up to 250 nm s^-2. Systematic site- and instrument-dependent structure in the time-position residuals biases the solution. Removing the stacked residuals produces gravity estimates which are constant and independent of the drop length or starting position. In order to find the gravity offset caused by the system response, the residuals are modelled by a small number of damped sinusoids.

A new approach to the analysis of absolute gravimeter operation proposes that the measured value of gravity should be found as a mean-weighted value of the acceleration of a free-moving body averaged within every measurement. The weighting functions of absolute gravimeters are determined. They depend on the gravimeter model used and the allocation of chosen data points within a single measurement. The effective measurement heights of absolute gravimeters can thus be found and the corrections due to linear gravity gradient and finite speed of light established. The results presented cover both direct free-fall and symmetric rise-and-fall types of apparatus.

At the 1994 International Comparison of Absolute Gravimeters in Sèvres, a platform oscillating vertically with a sinusoidal motion was used to produce defined accelerations which were applied to gravimeters for their calibration. Gravimeters equipped with different types of feedback systems were compared. This allowed an evaluation of filtering effects. A long series of tidal recordings, and a calibration obtained by this platform method, gave tidal factors for the Bureau International des Poids et Mesures (BIPM). Comments on previous recordings are included.

Artificial accelerations are used for the absolute calibration of relative gravimeters. Such accelerations are generated by the Frankfurt calibration system. The system consists of three stepper-motor-driven spindle blocks which can be mounted on any arbitrary body: here in the experiment a platform where spring gravimeters can be placed. The vertical motions of stepper-motor-driven spindle blocks are controlled by glass gauges. In a digital feedback loop, imperfections of the screw can be compensated. The driving functions for the stepper motors are sinusoidal waves with periods between 200 s and 2400 s. With the stroke of the system (± 10 mm) artificial accelerations up to ± 1000 × 10^-8 m s^-2 can be generated. During the experiment twelve gravimeters were investigated. The calibration factors as well as the frequency transfer functions of the instruments were determined with accuracies of better than 10^-3. The results coincide well with the calibration factors derived from the gravity calibration line in Sèvres for the same instruments.

A new moving mass calibration apparatus and process for LaCoste-Romberg feedback gravimeters are presented. The apparatus is based on the well-defined and relatively simple gravity field of a cylindrical mass. The main target of the new calibration apparatus was to reach a relative accuracy of 0,1% to 0,2% in the calibration of Earth tide registering gravimeters. The authors carried out a number of calibrations with the apparatus and report their results. They also investigated the effect of several external factors influencing the calibration process. Results so far confirm that the apparatus fulfils the original target.

Two Scintrex CG3M gravimeters were calibrated and compared with other relative meters (LaCoste-Romberg and Scintrex meters) at the fourth International Comparison of Absolute Gravimeters at Sèvres, France (30 May to 2 June 1994). LaCoste-Romberg meters were used as reference. Three main experiments were carried out at the Bureau International des Poids et Mesures. First, a calibration of the two Scintrex CG3M meters on a new baseline of five points, spanning a range of about 8 mGal. It is shown that both Scintrex meters provide results similar to within 0,005 mGal, even in noisy places, and that Scintrex results are similar to those of LaCoste-Romberg instruments to within an accuracy better than 0,010 mGal. Second, measurements of vertical gradient at four points were carried out. The results for the Scintrex meters lie within 0,007 mGal/m and are similar to those of LaCoste-Romberg meters to within an accuracy of around 0,010 mGal/m. Third, a series of continuous records (each of about 10 minutes) was carried out with three LaCoste-Romberg and the Scintrex meters at four adjacent points. A repeatability of better than 0,005 mGal was obtained for one Scintrex meter. There is a difference of 0,010 mGal with LaCoste-Romberg data. These results confirm that the Scintrex meter is suitable for measuring small gravity differences, similar to those observed on active volcanoes.