Table of contents

The Sixth International Comparison of Absolute Gravimeters was held from 5 June to 28 August 2001 at the Bureau International des Poids et Mesures (BIPM), Sèvres. Seventeen absolute gravimeters were used to make measurements at five sites of the BIPM gravity network. The vertical gravity gradients at the sites and the ties between them were also measured using seventeen relative gravimeters. For the first time the ties were also measured using absolute gravimeters. Various methods of processing the absolute and relative data were tested to calculate the results. The final results of ICAG-2001 are presented. The acceleration due to gravity at a height of 0.90 m is given as (980 925 701.2 ± 5.5) µGal and (980 928 018.8 ± 5.5) µGal for sites A and B, respectively, calculated using a combined adjustment of the absolute and relative data.

The application of technological advances has dramatically improved our ability to measure the absolute value of g, the free-fall acceleration due to gravity. Over the past thirty years this improvement has been nearly three orders of magnitude! Today, the value of gcan be determined with an accuracy approaching 1 µGal (10^-8 m/s²) and measured with a precision that is at least ten times better. This paper reviews the history of and the reasons for this progress as well as taking a look to the future.

The current uses of terrestrial gravity reference stations, which have made a major contribution to world gravity standards, are discussed. Traditionally, reference networks have served a wide spectrum of applications, offering a limited number of absolute observations and a great number of relative observations. Some recent developments have significantly affected this classical procedure, such as the much wider availability of absolute gravimeters and more accurate evidence of the significant impact of environmental parameters on reference stations. The diversity of user requirements and of gravimetric observation techniques has also become more obvious. Based on these developments and on cost/benefit considerations of the system comprising observation instrument and station site, certain changes in the realization of world gravity standards are examined. For example, different applications require dedicated solutions that cannot be met by a conventional multi-purpose gravity reference network; for some applications, station monitoring is crucial. Also, as instrumental standardization is increasing, the role of classical combined absolute and relative observations adjustment is decreasing, which will in turn affect the organization of world gravity standards.

We show that the language of atom interferometry provides a unified picture for microwave and optical atomic clocks as well as for gravito-inertial sensors. The sensitivity and accuracy of these devices is now such that a new theoretical framework common to all these interferometers is required that includes: (a) a fully quantum mechanical treatment of the atomic motion in free space and in the presence of a gravitational field (most cold-atom interferometric devices use atoms in ``free fall'' in a fountain geometry); (b) an account of simultaneous actions of gravitational and electromagnetic fields in the interaction zones; (c) a second quantization of the matter fields to take into account their fermionic or bosonic character in order to discuss the role of coherent sources and their noise properties; (d) a covariant treatment including spin to evaluate general relativistic effects. A theoretical description of atomic clocks revisited along these lines is presented, using both an exact propagator of atom waves in gravito-inertial fields and a covariant Dirac equation in the presence of weak gravitational fields. Using this framework, recoil effects, spin-related effects, beam curvature effects, the sensitivity to gravito-inertial fields and the influence of the coherence of the atom source are discussed in the context of present and future atomic clocks and gravito-inertial sensors.

We describe the design of and first results from a cam-driven portable absolute gravimeter. The cambased design of a dropper allows us to build a compact system that uses 20 mm of free fall for the measurement. The instrument drops a test mass 200 times a minute (a measurement rate of more than 3 times per second). The centre of mass of the apparatus is kept fixed during the entire measurement cycle, thus avoiding ``recoil'' effects that could systematically bias the measurement. Seismic isolation is provided by a passive eddy-current-damped simple spring. Measurement results taken at Table Mountain Gravity Observatory (TMGO, Boulder, Colorado), though reproducible at a level of several microgals (1 µGal = 10^-8 m/s²), show a sensitivity to the measurement start and stop points at the 20 µGal level.

Absolute gravity measurements are performed by absolute gravimeters that sometimes show significant differences between their averaged values, as borne out by the international comparisons organized periodically by the Bureau International des Poids et Mesures. Many sources of error have been taken into consideration to evaluate each uncertainty budget; nevertheless in some cases the observed differences from a general averaged value are statistically larger than expected on the basis of these evaluations. The main reason for this is that some causes of uncertainty cannot be well quantified as they are based only on theoretical hypotheses. Having investigated some sources of error in the optical interferometer at the Istituto di Metrologia ``G. Colonnetti'' (IMGC) we propose: (a) an optical design that minimizes errors arising from relative movements between the interferometer parts; (b) a simple apparatus that is easy to use to equilibrate the corner-cube prism that constitutes the moving mirror of the interferometer. These two modifications to the IMGC absolute gravimeter have reduced the uncertainty arising from the interferometer by around a factor of ten.

The new A-10 absolute gravimeter was tested at the Sixth International Comparison of Absolute Gravimeters in 2001 and compared with the more traditional types of absolute gravimeter. Some aspects of the new software system are presented as well as some of the technical features of this automated absolute gravimeter. There is still a need for improvement and a systematic effect in the observations has to be resolved before this device can be considered to be accurate in the field.

We present an experiment in which four different FG5 absolute gravimeters (AG) were operated simultaneously alongside a superconducting relative gravimeter (SG). We demonstrate that 0.1 % precision can be achieved on the calibration factor of the SG by comparison with AG measurements, independently of the FG5 instrument used for the calibration and of the offsets among the FG5 absolute values. This experiment demonstrates the robustness of using any FG5 absolute gravimeter to calibrate any SG. This result is of value to geoscientists analysing data from (a) globally distributed SGs which most probably have been calibrated using different instruments; or (b) any individual SG calibrated with different FG5 absolute gravimeters.

High-precision measurements often resort to least-squares estimation via observation models in which the quantity of interest is one of the unknowns. The case when both the dependent and independent variables of the model are stochastic is of particular interest. An example is absolute gravimetry, where the orbit of a test mass is tracked by a laser interferometer and is reconstructed by the least-squares method. In orbit reconstruction, space and time enter symmetrically and both time and position are stochastic. We present orbit reconstruction as a total least-squares problem to establish an error model for the propagation of tracking errors. We also give an asymptotic formula expressing the relevant contribution to the uncertainty of gravity determination.

Results are presented of a comparison between different instruments (an absolute gravimeter FG5, a superconducting gravimeter C026 and a broadband seismometer STS-2) which have been operated in parallel at the same site in Strasbourg (France). Thanks to a fast sampling technique (20 Hz), we first present the position and coil output signals from the superspring of the FG5, which acts as a long-period seismograph, and compare it with the ground-motion signal directly observed with the seismometer STS-2. The effect on the absolute gravimeter (AG) measurements of a large earthquake (Peru, M = 8.1) in June 2001 is also shown. We finally investigate how well Earth tides are retrieved on both the absolute and the superconducting gravimeters and give a comparison in the spectral domain of their respective noise levels.

Absolute gravity measurements using the FG5-202 gravimeter have been conducted twice a year since September 1999 along a 120 km long profile across the Belgian Ardenne and the Roer Graben. As in this region there is a difference of an order of magnitude between the inferred vertical crustal movements deduced from the difference of levelling (about 1 mm/year) and geological information (0.1 mm/year), our goal is to better constrain the present-day deformation. The absolute gravity measurements are performed at Rochefort, Humain, Werpin, Manhay, Sprimont, Membach (Belgium) and Monschau, Jülich and Bensberg (Germany). A complete description of the network is given, and specific difficulties at some stations are presented. The precision achieved, generally less than 2.0 µGal integrated over more than 24 h of observation, is quite satisfactory at all stations but Jülich. The mining activities around Jülich cause an increase in the noise up to 7 µGal integrated over more than 72 h. We also discuss possible causes of gravity variations in this region. At present, it is still not possible to detect any trend in the available data. However, after five years of observations, we should be able to detect or constrain any possible long-term trend with a limit of 2.5 mm/year, assuming that a height change of 1 mm causes a change in gravity of 0.2 µGal. To ensure that the absolute gravimeter is giving accurate results, it has been regularly compared with the superconducting gravimeter installed at the Membach reference station.

High-precision gravity measurements and records are used to investigate geodynamic processes. The amplitude of the gravity changes induced by these phenomena is of the order of 10^-8g to 10^-9g, where the global average of g (gravity) is 9.80 m s^-2. Instrument sensitivities up to 10^-9 are therefore required to detect gravity changes. As changes in instrument sensitivity can reduce the repeatability of measurements and affect the phase and amplitude of recorded gravity signals, the accurate calibration of gravimeters in high-precision gravimetry is topical. The stability of the calibration factors in two LaCoste-Romberg gravimeters has been investigated through different calibration methods. The main results show that (a) the application of multiple calibration approaches is a powerful constraint on instrumental response and identifies real or fictitious changes in instrument sensitivity; (b) a comparison between spring and superconducting gravimeters is the most suitable way of almost completely determining the transfer function of spring gravimeters in the tidal band. Moreover, a correlation was detected between stronger changes in instrument sensitivity and the occurrence of seismic events. Thus mechanical perturbation of spring gravimeters during earthquakes can affect the stability of their calibration factors.