Absolute Measurement Of The Acceleration Due To Gravity In Greece

1
TECHNICAL REPORT
R 482
ABSOLUTE MEASUREMENT
OF THE ACCELERATION DUE TO GRAVITY
IN ITALY, GREECE, FRANCE AND GERMANY
G. CERUTTI, P. DE MARIA, S. DESOGUS,
A. GERMAK, F. MAZZOLENI
Torino, September 1998

2
ABSOLUTE MEASUREMENT
OF THE ACCELERATION DUE TO GRAVITY
IN ITALY, GREECE, FRANCE AND GERMANY
G. Cerutti, P. De Maria, S. Desogus,
A. Germak, F. Mazzoleni.
Istituto di Metrologia "G. Colonnetti" - Torino
INTRODUCTION
The work described in the present report was carried out between September 1996 and
June 1998 by the Istituto di Metrologia "G. Colonnetti" (IMGC) of the National
Research Council of Italy.
The program was carried out under the contract N°3 dated 1996/07/22 between the
University of Bologna, Dipartimento di Fisica and the Istituto di Metrologia “G.
Colonnetti” del C.N.R., sponsored by the European Community under the contract for
the S.E.L.F. II project (Sea Level Fluctuation: geophysical interpretation and
environmental impact).
The absolute measurements were carried out by G. Cerutti, P. De Maria, S. Desogus, A.
Germak and F. Mazzoleni by means of a gravimeter designed and constructed at IMGC
(Fig. 1) in cooperation with the Bureau International des Poids et Mesures (BIPM) [1].
This instrument had been used in past years for the absolute determination of "g" at
several places in Europe, the USA, in the People's Republic of China and in Antarctica [
2 to 8]. Five international comparisons, in 1982, 1985, 1989, 1994 and 1997 at the
BIPM in Sèvres, made it possible to compare the performances of the IMGC gravimeter
with those of analogous instruments of other foreign laboratories [9].
THE IMGC GRAVIMETER
A) MEASUREMENT METHOD
The method applied is that of the free fall of a body subjected to the gravity force alone.
More precisely, the motion of this body is observed along a trajectory symmetric to the
trajectory top.
This symmetry of motion affords significant advantages in respect of the simple free fall
as regards the measurement technique; among them, let us mention a lesser influence of
air friction and the higher intrinsic accuracy of the method.
A body is thrown upwards vertically and in its flight it passes through a great number of
mutually equidistant points or stations. The measurement method, called multiple-
station method, consists in measuring the time taken by the body to travel the distance
between two successive stations. The data of every launch are memorised and
subsequently processed by a microprocessor, which calculates the "g" value best fitting
to the law of motion.

3
B) TECHNICAL DESCRIPTION OF THE GRAVIMETER
The basic parts of the instrument are a Mach-Zehnder interferometer and a long-term
(about 20 s) seismometer (Fig. 2). The inertial mass of the seismometer supports a cube-
corner reflector, which is the reference mirror of the interferometer. The radiation of a
He-Ne stabilised laser is used as the length standard.
The second mirror of the interferometer is another cube corner, analogous to the first.
This reflector is thrown upwards vertically by means of a catapult device, which causes
the mirror to travel a trajectory of the order of 0.5 m inside an evacuated (about 0.1 Pa)
cylinder. The two cube corners are on the same vertical line, to avoid possible errors in
the measurement, due to tilt of the interferometer during the flight. A number of
interference fringes emerging from the interferometer pass during the flight of the cube
corner (trihedron) and are detected by a photomultiplier and converted into an electric
signal suitable to monitor the electronic measurement circuitry.
The system does not include an artefact length standard; consequently, a measurement
begins at a pre-determined but arbitrary instant during the upward flight along the
trajectory. Stations equidistant is obtained from successive counting of a constant
integer number of interference fringes (in the present case, 2048); in other words,
each of the stations is separated from the preceding and the successive by a
distance d = 2048 λ/2, λ being the wavelength of the laser radiation.
The time taken by the body to travel these distances is measured by means of a counter
having a resolution of the order of 100 ps. A rubidium atomic clock gives the counter
sufficient stability to act as a time standard. As already mentioned, the data pairs, i.e.,
for distances (constant) and the time intervals taken to travel them, are first memorised
and subsequently processed by a microprocessor, so that a value of "g" is obtained for
every launch.
This value is referred to a point situated below the top of the trajectory, at a distance
equal to about 1/6 of the exploitable trajectory length. The data sheet for each of the
launches (examples are given in Figs. 3.1÷3.18) indicates the level of this point and
gives an evaluation of the braking coefficient of residual air.
A graph is also given of the calculated deviations of inter-station distance values,
referred to the imposed value d = 2048 λ/2. This provides a useful indication of ground
disturbance.
The "g" value must obviously be corrected for lunisolar attraction (gravimetric
tide).This correction is obtained by the program “ETGTAB” that compute model tide
using different tidal potential developments (Doodson, Cartwright-Tayler-Edden,
Tamura or Buellesfeld) for a number of different tidal components using observed or
estimated tidal parameters.
The effect of air pressure changes is corrected according to IAG 1983 resolution n° 9:
δg (P) = 0,3 ⋅ δP (µgal)
where
δP = Pa - Pn (mbar)
Pa = actual observed air pressure

4
Pn = normal pressure, obtained by the relation:
Pn = 1,01325 ⋅ 103 (1 - 0,0065 ⋅ H/288,15)5,2559 (mbar)
H = station elevation (m)
The effect of the polar motion is corrected using the relation:
δg (pol. mot.) = -1,164⋅108
⋅ω2
⋅a⋅2sinφ⋅cosφ⋅(x⋅cosλ-y⋅sinλ) [10-8
m/s2
]
where
x, y pole coordinates in IERS system in radian (publ. IERS-Bull.)
ω = 0,7292115⋅10-4
[rad/s] angular velocity
a = 6,378136⋅106
[m] semimajor axis
φ, λ geographic coordinates of the observation station, referred to CIO pole
(longitude positive east of Greenwich).
MEASUREMENT UNCERTAINTY EVALUATION
The following terms of the measurement uncertainty must be considered as type B, and
have a rectangular distribution.
A description and evaluation of the these terms is given.
1) DISTANCE MEASUREMENT
The uncertainty in such measurements is proportional to the reproducibility and stability
of the wavelength of the laser radiation.
In the measurements in question, a He-Ne iodine stabilised laser was used. A maximum
relative-uncertainty contribution of the order of 1⋅10-9 corresponding to 1 µgal can be
expected in the "g" value.
Distance measurement values can be affected also by microseismic noise, which may
alter the reference trihedron position. With the use of a long-period seismometer, the
inertial mass of which acts as a support for the fixed trihedron, microseismic effects can
be reduced by about twenty times.
Since mobile-trihedron vibrations caused by mechanical shock in launching operations
may also cause disturbance, measurements begin with a pre-established delay in respect
of the starting instant, so as to avoid vibrations of the trihedron. These two effect can
only be considered as part of statistical fluctuation (see figure from 5.1 to 5.18).
2) LASER BEAM VERTICALITY
Beam verticality is checked by means of a mercury bath. Departures from verticality
must be less than 10-4 rad, to ensure that contribution to measurement uncertainty are
less than 4 µgal.
This value is assumed in the evaluation of the uncertainty.
3) TRAJECTORY VERTICALITY

5
The visibility of interference fringes must be homogeneous and higher than 80% over
the whole trajectory; in this way, the uncertainty concerning launch verticality is less
than 10-4 rad so that the corresponding component of the uncertainty is negligible.
4) MOBILE-TRIHEDRON ROTATION
Rotations must be less that 0,03 rad/s. In addition, the trihedron must be so constructed
that its centre of gravity and its optical centre coincide to within 0,1 mm Sometimes this
conditions are not satisfied and an uncertainty of few microgal occurs. An evaluation of
these effects leads to an uncertainty of 2 µgal in the measurement due to this
component.
5) TIME MEASUREMENTS
An atomic rubidium clock having relative stability of the order of 10-10 is used as the
frequency standard.
The resolution of the time-interval measuring device is about 100 ps. Uncertainty
contributions of the order of 1 µgal in time measurements to the "g" value can
reasonably be estimated.
6) UNCERTAINTY CONTRIBUTIONS BY OTHER FACTORS
Since magnetic fields introduce electric currents in the metal of the trihedron during its
flight, in order to limit their effects all metal parts were made of non-magnetic
materials.
Electrostatic charges may accumulate on the trihedron, on the rubber band of the
catapult, and on the internal wall of the cylinder. As far as possible, ground-connected
shields were used; however, the influence of such charges can be estimated as
corresponding to 2 µgal.
Buoyancy due to residual air is negligible since measurements are carried out in the
vacuum, and symmetrical free motion is used.
7) TIDE CORRECTION
The Earth tide reduction is dependent by the tidal parameters used in the program for
each station. These parameters are observed or estimated and an uncertainty of 1 µgal
is usually accepted for this term.
8) PRESSURE CORRECTION
The correction for atmospheric pressure variation and for polar motion are affect by
uncertainty that are negligible in the evaluation of the total B type uncertainty.
The total type B standard uncertainty, uB(g) is defined as:
and is constant for all the stations.
gal
u
g
u
i
i
B
B µ
2
,
5
)
(
8
1
2
=
= ∑
=

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ADDITIONAL UNCERTAINTY
The fifth comparison of absolute gravimeters in Sevres in November 1997 revealed an
anomaly of an optical component of the I.M.G.C. apparatus. This anomaly has then
been removed, but it may have affected the results of previous measurements. This
effect has been considered as type A additional term u′A (g) in the evaluation of
combined standard uncertainty only for the measurements carried out before November
1997. A value of 5 µgal is assumed for this term.
UNCERTAINTY OF g1 AND g2 IN THE SITE
If two measurements repeated in different time in one site have to be compared (i.e.
Medicina) the correlation of the measurements must be considered.
Then the uncertainty of the difference assumes the expression:
where:
uC1 and uC2= combined standard uncertainty of the two measurements
cov(g1, g2)= covariance of g1 and g2
Only the type B components for the same instruments are fully correlated (see the
appendix page 82).
EXPERIMENTAL RESULTS
The following results concern the absolute measurements of the acceleration due to
gravity that were carried out in Italy (eleven sites) Greece (four sites), France (two sites)
and Germany.
Figs. 4.1÷4.17 gives more information on the station location, whereas Figs. 5.1÷5.18
are the histograms of experimental results.
Figs. 6.1÷6.16 give a photographical view of the sites of the measurements.
The following tables report the results obtained for each station: the date, the number of
measurement in the station, the mean value of gravity expressed as:
- the standard deviation:
∑
=
=
n
k
k
g
n
g
1
1
( )
∑
=
−
−
=
n
k
k g
g
n
g
s
1
2
1
1
)
(
)
cov(
2
)
( 2
,
1
2
2
2
1
2
1 g
g
u
u
g
g
u C
C −
+
=
−

7
- the type A standard uncertainty:
where:
- the mean level above the pillar floor of the point of reference of the measurement
(Ho)
- the elevation of the station above the mean see level (necessary to compute the
normal air pressure Pn of the site)
- the measured mean value of the atmospheric pressure during the measurements
- the correction of g for the atmospheric pressure variation
- the correction of g for the polar motion
- the value of g at level Ho corrected for Earth Tide, pressure and Polar motion gc
- the combined standard uncertainty uc expressed as:
where uB(g) = 5,2 µgal constant for all the stations.
Combined uncertainty uc for a normal distribution corresponds to a covering
probability of 68 % approximately. Combined standard uncertainty has been evaluated
in accordance with the EAL-R2 guide.
MEDICINA AW I
The measurement point is located in the gravity laboratory of the Radio Telescopio
(C.N.R.) near Bologna (Fig. 4.1)
Date: 23rd
÷ 26th
November 1996
Number of measurements: n = 155
Measured mean value of g: g = 980 474 826,2 µgal
Standard deviation: s ( g ) = 33 µgal
Type A standard uncertainty: uA(g) = 5,6 µgal
Level of the measurement point to floor
surface: Ho = 0,9049 m
Elevation of the station above sea level H = 25 m
Normal air pressure Pn = 1010 mbar
Actual observed air pressure Pa = 1014 ± 0,2 mbar
δg = 0,3 ⋅ δP δg (P) = 1,2 µgal
Correction for polar motion: δg (pol. mot.) = -1,7 µgal
g corrected: g c = 980 474 825,7 µgal
)
(
)
( 2
2
g
u
g
u
u B
A
c +
=
2
2
)
(
)
(
)
( g
u
g
u
g
u A
A ′
+
=
n
g
s
g
u
)
(
)
( =

8
Combined standard uncertainty: uc = 7,7 µgal
MEDICINA AW II
(C.N.R.) near Bologna (Fig. 4.1)
Date: 1st
÷ 2nd
July, 1997
Standard deviation: s ( g ) = 21,9 µgal
Normal air pressure Pn = 1010,3 mbar
Actual observed air pressure Pa = 1012,5 ± 0,2 mbar
δg = 0,3 ⋅ δP δg (P) = 0,7 µgal
Correction for polar motion: δg (pol. mot.) = 1,7 µgal
BASOVIZZA
The station is located in the Astronomic Observatory, in a room of the building called
“cupoletta astrofili” (Fig. 4.2)
Date: 5th
÷ 6th
July 1997
δg = 0,3 ⋅ δP δg (P) = -9,7 µgal

9
PADOVA
The station is located in a garage of the Dep. of Geology and Geophysics of the
University of Padova, via Rudena 3 (Fig. 4.3)
Date: 7th
÷ 8th
July 1997
Normal air pressure Pn = 1012mbar
Actual observed air pressure Pa = 1013 ±0,2 mbar
δg = 0,3 ⋅ δP δg (P) = 0,3 µgal
GENOVA
The station is located in a room of Villa Croce, via Jacopo Ruffini 3, Genova (Fig. 4.4)
Date: 16th
September 1997
δg = 0,3 ⋅ δP δg (P) = 2,8 µgal

10
CATANIA
The measurement point is located in a room of the Institute of Geology and Geophysics
in the Catania University, Palazzo delle Scienze, C.so Italia 55 (Fig. 4.5)
Date: 27th
- 28th
October 1997
δg = 0,3 ⋅ δP δg (P) = 0,5 µgal
g corrected: g c = 980 034 818 µgal
NOTO
The measurement point is located in the basement of the V.L.B.I. antenna in the
Observatory at Noto (Fig. 4.6)
Date: 30th
- 31st
October, 1st
November 1997
δg = 0,3 ⋅ δP δg (P) = 0,3 µgal

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MATERA
The measurement point is located in the basement of the V.L.B.I. antenna of the
“Centro di Geodesia Spaziale” of the “Agenzia Spaziale Italiana” near Matera City (Fig.
4.7)
Date: 3rd
- 4th
November 1997
δg = 0,3 ⋅ δP δg (P) = 2,9 µgal
BRINDISI
The measurement point is located in a room of the scuola Elementare, 7° Circolo
Distretto 22 at Brindisi via don Monza, 1 (Fig. 4.8)
Date: 5th
- 6th
November 1997
δg = 0,3 ⋅ δP δg (P) = 1,2 µgal

12
MEDICINA AS
(C.N.R.) near Bologna, bat on the pillar called AS (Fig. 4.9)
Date: 16th
- 17th
June 1998
Actual observed air pressure Pa = 1021,5 ± 0,2 mbar
δg = 0,3 ⋅ δP δg (P) = 3,4 µgal
RAVENNA
The station is located in a laboratory of the school “Istituto Tecnico Agrario”near
Ravenna City (Fig.4.10)
Date: 19th
- 20th
June 1998
Elevation of the station above sea level H = 20m
δg = 0,3 ⋅ δP δg (P) = 4 µgal

13
DIONYSOS (GREECE)
The measurement point is located in a room of the Dionysos Satellite Observatory
(Fig. 4.11)
Date: 27th
÷ 28th
September 1996
δg = 0,3 ⋅ δP δg (P) = 0,6 µgal
ROUMELLI-CRETE (GREECE)
The station is located in a room of the town hall (Fig. 4.12)
Date: 30th
September, 1st
October 1996
δg = 0,3 ⋅ δP δg (P) = 1,8 µgal

14
ERMOUPOLI-SYROS (GREECE)
The measurement point is located in the entrance hall of the custom office of the
harbour of Ermoupoli (Fig. 4.13)
Date: 3rd
- 4th
October 1996
δg = 0,3 ⋅ δP δg (P) = 2,1 µgal
ASKITES (GREECE)
The measurement point is located in the corridor of the school of the village (Fig. 4.14)
Date: 7th
- 8th
October 1996
δg = 0,3 ⋅ δP δg (P) = 4,2 µgal

15
MARSEILLE (FRANCE)
The station is located in one custodian room of the tide-gauge building, on the coast
near the “P.nta d’Endoume” in Marseille (Fig. 4.15)
Date: 18th
September 1997
Actual observed air pressure Pa = 1023,5 ±0,2 mbar
δg = 0,3 ⋅ δP δg (P) = 3,4 µgal
GRASSE (FRANCE)
The measurement point is located in the station M10 Laser Lune of the Observatory of
C.E.R.G.A. near Caussols, Grasse (Fig. 4.16)
Date: 20th
- 21st
September 1997
Elevation of the station above sea level H = 1281,7 m
δg = 0,3 ⋅ δP δg (P) = 3,8 µgal

16
WETTZELL (GERMANY)
The measurement point is located in the Satellitenbeobachtungsstation Wettzell of the
Institut fuer Angewandte Geodaesie (Fig. 4.17)
Date: 10th
- 11th
December 1997
Elevation of the station above sea level H = 613,7 m
δg = 0,3 ⋅ δP δg (P) = -1,1 µgal
Correction for polar motion: δg (pol. mot.) = -2 µgal

17
REFERENCES
[1] Cerutti, G., Cannizzo, L., Sakuma, A., & Hostache, J. A transportable apparatus for
absolute gravity measurements. VDI-Berichte n. 212, 1974: p. 49.
[2] Cannizzo, L., Cerutti, G., Marson, I. Absolute gravity measurements in Europe. Il
Nuovo Cimento, vol. 1C (n. 1), 1978: p. 39.
[3] Marson, I., Alasia, F. Absolute measurements of gravity acceleration in the United
States of America. Bollettino di Geodesia e Scienze Affini, n. 2, 1979.
[4] Marson, I., Alasia, F. Absolute gravity measurements in Switzerland O.I., IMGC
Technical Report R 127, 1978, P. II, IMGC Technical Report R 142, 1979. P. III,
IMGC Technical Report R 156, 1980.
[5] Marson, I., Alasia, F. Absolute gravity measurements in the United States of
America. Report AFGL-TR-78-0126.
[6] Marson, I., Alasia, F. Absolute gravity measurements in USA. Technical Report
IMGC R162, Nov. 1980.
[7] Marson, I., Kahle, H.G., Mueller, S., Chaperon, F., Alasia, F. Absolute gravity
measurements in Switzerland Bull. Geodesique vol. 55, n. 3, 1981.
[8] Cerutti, G., Alasia, F., Germak, A., Bozzo, E., Caneva, G., Lanza, R., Marson, I.
The absolute gravity station and the Mt. Melbourne gravity network in Terra Nova
Bay, North Victoria Land, East Antarctica. Recent Progress in Antarctic Earth
Science: edited by Y. Yoshida et al. pp. 589-593 by Terra Scientific Publishing
Company (Terrapub), Tokyo, 1992.
[9] Marson, I, Faller, J.E., Cerutti, I., De Maria, P., et al. “Fourth International
Comparison of Absolute Gravimeters” Metrologia, 1995, 32, 137-144.
Fig. 1

18
Beam-splitter
Total reflector
Total
reflector
50 % reflector
50 %
reflector
SEISMOMETER
P.Z.T.
ACTUATOR
AUTO-
COLLIMATOR
BEAM
SPLITTER
MACH-ZEHNDER
INTERF.
LASER
MOBILE
CUBE-
CORNER
IMGC - TORINO
OPTICAL-SCHEME OF THE APPARATUS
Fig. 2
DETECTOR
MIRROR
REFERENCE
CUBE
CORNER

30
Fig. 3.12 Data processing of a single measurement at Dionysos.

31
Fig. 3.13 Data processing of a single measurement at Roumelli.

32
Fig. 3.14 Data processing of a single measurement at Ermoupoli.

33
Fig. 3.15 Data processing of a single measurement at Askites.

34
Fig. 3.16 Data processing of a single measurement at Marseille.

35
Fig. 3.17 Data processing of a single measurement at Grasse.

36
Fig. 3.18 Data processing of a single measurement at Wettzell.

47
Fig. 4.11 Monograph of the station of Dionysos.

48
Fig. 4.12 Monograph of the station of Roumelli.

49
Fig. 4.13 Monograph of the station of Ermoupoli.

50
Fig. 4.14 Monograph of the station of Askites.

51
Fig. 4.15 Monograph of the station of Marseille.

52
Fig. 4.16 Monograph of the station of Grasse.
Fig. 4.17 Monograph of the station of Wettzell.

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