Stability comparison of two absolute gravimeters: optical versus atomic interferometers

Absolute gravimeters measure the free fall acceleration of a test body. The most used is the state-of-the-art commercial gravimeter FG5 [1]. It measures the free fall of a corner cube with a Mach–Zehnder interferometer. Since the beginning of the 1990s [2], laboratories started to devise gravimeters using cold atoms as a test mass [3–5]. This led to the development of transportable instruments [6–9] able to participate in International Comparisons of Absolute Gravimeters (ICAG) as the LNE-SYRTE Cold Atom Gravimeter (CAG) has since 2009 [10, 11].

Usually, users of free fall corner cubes and in particular FG5 operators record gravity by sets consisting of a number of drops (of the order of 100) that get repeated every hour. The repetition rate is usually of the order of one drop every 10 s, in order to wait for the damping of the vibrations due to the carriage free fall and to preserve the device from mechanical wear. In [12], one free fall per 30 s was chosen, leading to an Allan standard deviation about twice as bad as if one drop per 10 s had been chosen. On the one hand, the FG5 dropping chamber [13] allows drops of 2 s which can improve the stability of FG5 notably. On the other hand, like the FG5, which uses a sophisticated super-spring system [14], various vibration rejection systems have been demonstrated and gradually improved in recent years to reject ground noise for atom sensors. They are based on the combination of a passive isolation and a low noise seismometer [4, 15]. Eventually, this turned into an active system [5, 9, 16], using the signal of the seismometer to even better stabilize the position of the reference mirror. Using such an optimized active system, a stability³ of 4.2 µGal in 1 s measurement time was demonstrated in [17]. Using a passive system, or set directly on the ground, the CAG demonstrated a stability of 1 µGal in 100 s measurement time interval [18]. To compare the stability performances of both technologies it is desirable to perform measurements at the same place and at the same time, under the influence of the same vibration noise. We took advantage of the last ICAG which took place in the Walferdange Underground Laboratory for Geodynamics (WULG) in Luxembourg at the end of 2013 to test the capabilities of the FG5X#216 and CAG on a common view measurement.

Both gravimeters were installed on the platform B of the WULG [11]. The common view measurements were performed during the night between the 24th and the 25th of October 2013. The drop interval of the FG5X was chosen at 3 s, close to its best capability of 2 s. We decided to use 3 s over 2 h to spare the moving mechanical part of the instrument. The CAG measured continuously, all night long, using the protocol already used in [18] which is based on two interleaved integrations leading to a measurement time of 720 ms. Measurements are represented in figure 1. It started at 20h15 for CAG and 15 min later for the FG5X. We realized only after the measurement was performed that the seismic noise was relatively high initially, due to an earthquake of magnitude 6.7 that occurred in the East of South Sandwich Islands. This excess noise can be seen on the FG5X first half hour measurement as well as on the superconducting gravimeter OSG-CT040 that records gravity variation continuously just a few metres from platform B. Usually, FG5 users compute the 'drop scatter' (the standard deviation of a set) to characterize the dispersion of the measurements. Here the drop scatter of the FG5X first half hour measurement is 21.7 µGal and 9.1 µGal after. A zoom on the first hours of the gravity signals corrected for tides and atmospheric pressure effects (figure 1(b)) shows that the CAG is almost unaffected by the seismic wave. The vibration rejection system [4, 15] is good enough to suppress the effect of the earthquake. This can also be seen in figure 2.

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In this paper, we choose to analyse the stabilities of the measurements using the Allan standard deviations [19] of the corrected gravity data (figure 2). Two analyses were performed for each gravimeter with and without the period during which the influence of the earthquake is significant. As we can guess from figure 1, the short-term stability of the FG5X is about 30% better when excluding the first half hour. After 200 s of measurement time the Allan standard deviation calculated with and without the earthquake noise is similar. The 1 μGal level is obtained after 86 s of measurement and the Allan standard deviation continues to decrease down to 0.3 µGal and maybe even better. However, the FG5X measurements would have to be longer to perform this analysis. For shorter averaging times, the Allan standard deviation decreases faster than a τ^−1/2 slope. This behaviour is due to the averaging of the low-frequency noise which is reasonably well sampled by the FG5X. As a consequence the statistical error se should not be estimated here using the standard formula $se=sd/\sqrt{N}$ where N is the number of free falls. In contrast, the CAG stability is not affected by the seismic wave. We find that the Allan standard deviation for the whole CAG measurements displayed with open circles on figure 2 is superimposed with the grey circles representing the Allan standard deviation calculated when excluding the earthquake. The initial bump on the Allan standard deviation is due to our measurement technique: the CAG signal is locked onto the gravity acceleration thanks to an integrator with a time constant of a few cycles [15]. Then the Allan deviation decreases with a τ^−1/2 slope up to 370 s (the 1 µGal level is obtained after less than 36 s of measurement) and continues to decrease down to 0.2 µGal. Such a long-term stability had already been obtained in the LNE laboratory [20], by comparing the CAG with a superconducting gravimeter iGrav [21]. Performing the FG5X measurement every 2 s instead of 3 s would only slightly affect the Allan standard deviation by shifting the curve to the left and it would be still above the CAG results. This can be inferred from a previous study on the uncertainty of the FG5 [22] showing that at high frequency (10⁻⁵ Hz ⩽ ν ⩽ 10⁻¹ Hz) the noise of a FG5 is white. The same study reveals that the noise increases at lower frequencies due to gravity changes linked to environmental fluctuations that are not modelled. Both Allan variance curves of the CAG and FG5X will thus overlap for an integration time greater than a quarter of a day.

We compared the stabilities of two absolute gravimeters of different technologies. Atom interferometry was already known for high cycling rate operation and the new FG5X for performing a free fall measurement every 3 s. During a quiet period the FG5X reaches a stability of 1 µGal after 86 s averaging time while the CAG needs only 36 s, even for a higher level of vibration noise. Considering the current level of accuracy of such gravimeters, of the order of a few μGal at best, a measurement time of only a few minutes is enough for the statistical uncertainty to be a negligible contribution to the combined uncertainty in the measurement.

The possibility to perform continuous measurements with atom gravimeters at high cycling rates, and to reach stabilities of 0.2 µGal in less than 2000 s, now offers the opportunity to develop such instruments for permanent installation in geophysical observatories. Moreover, the sensitivity of atom gravimeters, which scales as T², can be increased using taller vacuum chambers and larger time T between the three interrogating pulses [23]. As an example, the fountain configuration used in [17] allows one to increase T up to 300 ms, to be compared with the 80 ms we use in the CAG.

This research is carried on within the kNOW project, which acknowledges the financial support of the EMRP. The EMRP was jointly funded by the European Metrology Research Programme (EMRP) participating countries within the European Association of National Metrology Institutes (EURAMET) and the European Union. The CAG participation in ICAG-2013 was also supported by GPhys of Observatoire de Paris.