Seismic noise is the major obstacle to performing sensitive

measurements of the gravitational field on the ground. The INFN (Istituto Nazionale di Fisica Nucleare) underground laboratory in Gran Sasso, L’Aquila(Italy), seems to be a favourable place from the environmental noise point of view.

This paper describes briefly two, relatively low cost, gravity experiments that can be performed in the underground laboratory: a) A measurement of preferred-frame and preferred-location effects. b) A test of the equivalence principle. Preliminary experimental data of the seismic noise are also presented

Fuligni, F.

Iafolla, V.

Milyukov, V.

Nozzoli, S.

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IL NUOVO CIMENTO Settembre-Ottobre 1997VOL. 20 C, N. 5Experimental gravitation and geophysics (*)F. FULIGNI (1) †, V. IAFOLLA (1), V. MILYUKOV (2) and S. NOZZOLI (1)(1) Istituto di Fisica dello Spazio Interplanetario, CNR - Frascati 00044, Italy(2) Sternberg Astronomical Institute, Moscow State University - Moscow, Russia(ricevuto il 5 Dicembre 1996; approvato il 27 Febbraio 1997)Summary. — Seismic noise is the major obstacle to performing sensitivemeasurements of the gravitational field on the ground. The INFN (IstitutoNazionale di Fisica Nucleare) underground laboratory in Gran Sasso, L’Aquila(Italy), seems to be a favourable place from the environmental noise point of view.This paper describes briefly two, relatively low cost, gravity experiments that can beperformed in the underground laboratory: a) A measurement of preferred-frame andpreferred-location effects. b) A test of the equivalence principle. Preliminary experi-mental data of the seismic noise are also presented.PACS 91.10 – Geodesy and gravity.PACS 01.30.Cc – Conference proceedings.1. – IntroductionThe gravity gradiometer under development at IFSI has a sensitivity goal, in itsnon-cryogenic version, of 1022 EUOkHz or 10211 s22 OkHz. Short descriptions of theinstrument can be found elsewhere [1, 2]. We only want to stress here that the designcharacteristics and the materials used allow an almost immediate translation of thepresent version into a cryogenic one. It is a well-known story that of the perturbations,at ground, which prevent tests and calibrations of this kind of devices at their fullsensitivity, being impossible, in practice, the construction of an efficient dampingsystem for the seismic “noise” at the frequencies of interest, typically below a few Hz.However, in addition to sensitivity, other performances are of great importance fora gradiometer, first of all common mode rejection, which is strictly connected with long-term stability of accelerometers. To assess this latter property, an accelerometer,especially equipped for long runs, was installed at the Gran Sasso undergroundlaboratory near one supporting pier of the interferometer. This location has theadvantage of being relatively free from human activity and rather stable intemperature, with variations within 0.1 degrees.(*) Paper presented at the VII Cosmic Physics National Conference, Rimini, October 26-28, 1994.† Deceased.G Società Italiana di Fisica 637F. FULIGNI, V. IAFOLLA, V. MILYUKOV and S. NOZZOLI638The instrument appears to be very stable provided temperature is kept constant.Thanks to this good performance of the accelerometer, a number of data were collectedwhich may be of some interest for geophysics. At the same time they give usencouraging suggestions that the noise level, at certain frequencies, allows performingsome experiments which are of great significance for general relativity and the theoryof gravitation. In the following we describe a number of preliminary results we haveobtained (analysis is still in progress) and then discuss two possible experiments thatcan be performed with our instrumentation, and the improvements that can be reachedwith respect to the presently available data.2. – ResultsThe accelerometer was mounted with its sensitive axis horizontal so that it workedalso as a tiltmeter. It was housed in an aluminium box which, in addition, containedbuffer batteries for power supply, feeding both the DC circuits and the pump for theAC bridge, as well as the amplifier and the digital circuits in which data where finallystored. All was supported by a very rigid plate which could be finely adjusted in thehorizontal plane by micrometric screws.Fig. 1. – Power spectral density of horizontal seismic noise measured at the Gran SassoLaboratory. The lower curve (straight line) represents the lowest expected seismic noise, verticalcomponent. See ref. [3].EXPERIMENTAL GRAVITATION AND GEOPHYSICS 639F i g . 2 . – So l i d E a r t h ’ s t i d e s m e a s u r e d a t G r a n S a s s o . T h e a n a l y s i s w a s p e r f o r m e d b yE. Lorenzini.F. FULIGNI, V. IAFOLLA, V. MILYUKOV and S. NOZZOLI640Particular attention was devoted to the very low-frequency range which appearsmost important for the experiments we plan to perform. Figure 1 shows the powerspectral density of data collected in the period 1-17 November 1994. If, on the one side,for us this is noise against which to detect signals, for geophysicists it is a signal withuseful and interesting information. The higher part of this spectrum, above 1024 Hz, isof great interest for seismology, corresponding to slow motions of the ground inducedby far away quakes. There is, however, an additional background contribution due totilts of the soil caused by changes in atmospheric pressure loading. This explains why,in general, the vertical acceleration noise is lower than the horizontal one, being theformer of second order in the tilt angle. The reference curve (continuous line in fig. 1)gives the estimated minimum vertical acceleration noise [3]. As can be seen, our resultssuggest a very low horizontal component, which in general should be expected morethan one and perhaps two orders of magnitude larger. On the other hand, thecorrectness of our calibrations, within approximately 10%, is ensured by themeasurement of tides, that in fact dominate the lowest frequency (E1024 Hz) part ofthe spectrum (fig. 2). This behaviour is in agreement with the fact that this kind ofnoise decays rapidly with depth [4], so great advantages are obtained by placing theinstruments far from the free surface of the Earth.In addition to tides there is another group of processes, the free vibrations of theEarth, which depend on elastic constants of our planet. Their periods are on the orderof 100 minutes and less. The oscillations with the larger periods are not referred tousual elastic oscillations and can be caused by gravitational forces. These oscillationsmay also be due to motions of underground waters. Observations of long-periodoscillations (see, for example, [5]), have been performed but data are relatively poor.We performed an analysis via maximum-entropy method in the range of periodsbetween 1 and 4 hours for data collected from 17 to 28 September 1993. A similaranalysis has been performed for the data obtained by a two degree of freedom tiltmeterin Baksan (Russia) in the same period of time. The structures of spectra look similarand some of the periods are coincident within one standard deviation. However, thereare peaks in the Gran Sasso spectrum which are absent in the Baksan spectrum.Further study is needed to interpret these results, in particular cross correlation maygive useful hints.3. – Gravitational experimentsAs mentioned in the introduction, seismic noise is the major obstacle to performingsensitive measurements of gravitational fields, so that the highest sensitivities can onlybe attained in space with drag-free vehicles. In the previous section we have shown thatthe Gran Sasso laboratory seems a particularly favourable place from theenvironmental point of view. With this in mind we discuss now two experiments thatcan be performed there at a relatively low cost, and we show that significant results canstill be obtained for the field of gravitational physics.3.1. Preferred-frame and preferred-location effects. – The existence of such effectsin local gravitational experiments would represent violations of the strong equivalenceprinciple. An ideal local gravitational experiment is a Cavendish-type experimentwhere the relative accelerations of two bodies are measured as a function of theirmasses and mutual distances. The analysis, performed in the PPN formalism [6],EXPERIMENTAL GRAVITATION AND GEOPHYSICS 641assumes a test body of negligible mass kept, by a four-acceleration a, at a constantproper distance r from a massive body falling freely through space-time. The resultingfour-acceleration a divided by the mass of the source body gives the locally measuredgravitational constant GL . It turns out that GL shows a dependence on the velocity ofthe source relative to the universe rest frame with coefficients which are functions ofthe preferred frame parameters a 1 , a 2 , a 3 , and on a combination of the preferred-location parameter j and external potentials originating from possible nearby bodies.Of course, for the case of general relativity GL41 (in geometrized units).This is exactly the picture of a gravimeter fixed on the surface of the Earth, and infact the most precise tests of these effects are obtained from geophysicalmeasurements. The method consists in measuring variations in the gravitational forceas the Earth moves in space. The frequencies involved will be then, essentially, those ofvariations of the Earth velocity, that is the sidereal rotation rate V and the orbitalsidereal frequency v and harmonics and combinations of them. Thus, to solid Earthtides of Newtonian geophysics one could add further terms due to variations of GL . Ananalysis of data [7] taken in a 18-month period has given Na 2NE4 Q1024, NjNE1023. Inprinciple, with our instrument, an order of magnitude improvement in these upperlimits can be obtained.3.2. Test of the equivalence principle. – We discuss now briefly how a test of the(weak) principle of equivalence can be performed in an environment such as the onedescribed in sect. 2. Present upper limits for the Eötvös parameter range between10211 and 10212 [8, 9]. Like in ref. [8], we use the Sun as source of the field. This gives arather low local acceleration, 0.6 cm/s2 at best, for the horizontal component, but hasthe advantage of occurring with a 24 h period, and thus with an automatic zero check. Areasonable improvement is that of requiring detection of an anomalous relativeacceleration between two test bodies of 1 part in 1014, that is at least two orders ofmagnitude better than the present upper limits. This may have important implicationsfor super symmetries [10]. Such a limit entails detection of an acceleration of6 Q10215 cm/s2. This is possible with an accelerometer like ours in its cryogenic version,provided its resonance frequency is decreased to, say, 1 mHz. We plan to do this byusing an electrostatic field, regulated by a feedback system, acting as a negativespring, thus bringing the mechanical frequency at the desired value. The intrinsic noiseof the accelerometer is mainly thermal (amplifier noise may be disregarded thanks toparametric effect), allowing a minimum detectable accelerationa4 g 4kTv 0mQ1th1/241.4 Q 10215 cm/s2(1)in an integration time t4106 s, and with reasonable values for the mass (500 g) and theQ (104 ). A gradiometer of zero baseline, that is with the accelerometers havingcoincident centers of mass, is used in a horizontal mounting. Of course the test massesare of different materials. An important factor for the performance of the gradiometeris the common mode rejection (CMR), a realistic value of which may be 104.Consider now seismic noise. At the frequency of tides, fig. 1, it is approximately1027 gOkHz or 1024 cmOs2kHz giving a contribution in the measuring bandwidth of1027 cmOs2. This corresponds to a differential acceleration of 10211 cm/s2, thanks toCMR. We need still at least four orders of magnitude of additional attenuation. Apendulum will do the job. If the horizontal accelerometer has its center of mass at aF. FULIGNI, V. IAFOLLA, V. MILYUKOV and S. NOZZOLI642distance from the suspension of the pendulum equal to the reduced length it will beperfectly isolated, as it behaves, with respect to horizontal motions, as if it were in freefall. In our case this holds also for the gradiometer, because the two accelerometershave coincident centers of mass. This is true in the ideal case. In practice losses arepresent which produce an additional coupling between pendulum and suspensionthrough their relative velocity. In this case, instead of perfect isolation, an attenuationfactor v/v p Qp will result, where v is the frequency of the signal to be measured, v pand Qp the proper frequency and the merit factor of the pendulum. It is easily seen thatan attenuation factor of around 1025 can be obtained, our signal being quasi-DC. Theproblem of seismic noise is so solved and a precision of 1 part in 1014 seems attainable atbetter than 3 sigma level.4. – ConclusionWe have seen that, starting from testing and calibration problems, data of interestfor geophysics are obtained. These data, in turn, constitute a useful information toevaluate the possibility of doing experiments of interest for the relativistic theory ofgravitation. Two examples have been briefly discussed. Of course this discussion is farfrom being complete, as many important additional (non-statistical) error sources mustbe considered. A test of the equivalence principle has been proposed [11], where aninstrument similar to that considered here is used in free fall in a vacuum chamberfrom balloon altitudes.Sensitivities not very different from those expected in the present case can bereached.* * *We thank Drs. L. CRESCENTINI and A. AMORUSO for having hosted the instrumentin their underground laboratory and for the help in setting and running theexperiment.R E F E R E N C E S[1] CIUFOLINI I., FULIGNI F., IAFOLLA V. and NOZZOLI S., Nuovo Cimento C, 15 (1992) 973.[2] FULIGNI F., IAFOLLA V. and CIUFOLINI I., in Relativistic Gravitational Experiments inSpace, edited by M. DEMIANSKI and C. W. F. EVERITT (World Scientific, Singapore) 1993, p. 324.[3] AGNEW D. C. and BERGER J., J. Geophys. Res., 83 (1978) 5420.[4] LORENZINI E. C., FULIGNI F., ZIELINSKI J. B., COSMO M. L., GROSSI M. D., IAFOLLA V. andROTHMAN T., Adv. Space Res., 14 (1994) 113. See also these Proceedings.[5] LINKOV E., PETROVA L. and OSIPOV K., Dokl. Akad. Nauk SSSR, 313 (1990) 1095, inRussian.[6] WILL C., Theory and Experiment in Gravitational Physics (Cambridge University Press)1981.[7] WARBURTON R. J. and GOODKIND J. M., Astrophys. J., 208 (1976) 881.[8] ROLL P. G., KROTKOV R. and DICKE R. H., Ann. Phys., 26 (1964) 442.[9] BRAGINSKY V. B. and PANOV V. I., Sov. Phys. JETP, 34 (1942) 463.[10] FULIGNI F. and IAFOLLA V., this issue, p. 619.[11] LORENZINI E. C., SHAPIRO I. I., FULIGNI F., IAFOLLA V., COSMO M. L., GROSSI M. D.,CHEIMETS P. N. and ZIELINSKI J. B., Nuovo Cimento B, 11 (1994) 1195.

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