Earth tide gravity maps for western Europe

184

Physics of the Earth and Planetary Interiors, 13 (1976) 184—196 © Elsevier Scientific Publishing Company, Amsterdam Printed in The Netherlands

EARTH TIDE GRAVITY MAPS FOR WESTERN EUROPE P. MELCHIOR

*lJ.T.

KUO

*2

and B. DUCARME

~

*1 Royal Observatory of Belgium, Brussels (Belgium) *2 Lamont-Doherty Geological Observatory, Palisades, N. Y. (U.S.A.)

(Received July 15, 1976; revised and accepted August 17, 1976)

Melchior, P., Kuo, J.T. and Ducarme, B., 1976. Earth tide gravity maps for western Europe. Phys. Earth Planet. Inter., 13: 184—196. Tidal gravity profiles completed in western Europe by the authors (twenty stations) are complemented with some others from independent stations to provide the first tidal gravity maps of this region of the world exhibiting a quite smooth behaviour of the tidal parameters. Diurnal waves appear nearly undisturbed and could furnish an upper limit for the solid tide phase lag. Semi-diurnal waves are clearly affected by the oceanic indirect effects. Computations of these effects show that the existing oceanic cotidal charts are imperfect and should be improved by using the earth tide measurements as constraints.

1. Introduction Since tl1e IGY a great number of tidal gravity stations has been operating in Europe. However, despite a resolution taken a long time ago by the Permanent Commission for Earth Tides no intercomparison of all the instruments was ever organized until 1970. Therefore the tidal parameters obtained in these stations were often contradictory so that a geophysical interpretation seemed quite difficult. In 1970, a campaign of European profiles was started at the initiative of J.T. Kuo (Kuo et a!., 1972) and began with a comparison of calibrations of three Geodynamics gravimeters between New York (Columbia University) and Bruxelles (Royal Observatory), In this operation an agreement of 0.5% was achieved (Kuo et al., 1972). Thereafter twenty-two gravimeters from different makers (Geodynamics, La Coste-Romberg and Askania 1 5) were intercompared at the fundamental station of Bruxelles by recording the tidal variations for a minimum period of four months each. These intercomparisons were simultaneous for groups of three to five instruments. *

Chargé de Recherches au Fonds National de Ia Recherche Scientifique.

Using the tidal parameters derived from these registrations for the diurnal wave O~(amplitude and phase) and for the semi-diurnal wave M 2 (phase only), Ducarme (l975b) adjusted a rheological model defined by a calibration factor and by a frequency dependent phase lag and attenuation factor to each instrument. Comparisons of different instruments have been performed at Liverpool as well as at Paris and have provided a successful check of the models. These models are used for the reduction of the data obtained in the profiles undertaken by the authors in Europe and more recently in Asia and Australia. However, it was found in one case that during transportation a significant change in the calibration factor had occurred. Even if tlus was only an exceptional accident, it was decided to make periodic recalibration at the Bruxelles fundamental station. Consequently, the operations performed with four Geodynamics instruments have been programmed as follows:

Geod. 721 Bruxelles—Cambridge---Liverpool— Bruxelles--Herstmonceux---Strasbourg—Bruxelles-Graz—Trieste—Bruxelles

185

Geod. 730 Bruxelles—Strasbourg---Torino--Padova-Bruxelles—Oostende-—Brugge—Bruxelies—-Faeroe-Arhus—-Bruxelles—-Godhavn

TABLE I Results obtained at the Bruxelles fundamental station (22 instruments)

Geod. 804 Bruxelles—Walferdange--Bruxelles--Chur-Bruxelles—Clermont Ferrand—Grasse—Bordeaux— Bruxelles

Wave

Geod. 074 Bruxelles—Witteveen—Hannover—-Bruxelles [for this instrument see Bragard (1974)1.

In the present paper we aim to present the results obtained during this campaign together with those of some colleagues who kindly authorize us to introduce their still unpublished data on the general “tidal maps” of Europe given here: M. Bonatz (Bonn station) W. Torge and H. Wenzel (Hannover and Bad Grund stations) B. Stuckenbroker (Helgoland, Busum, Kiel and Bornholm stations) A. Sakuma (Paris station) N.N. Pariiskii and P. Varga (Tihany station) The results of Bonn, here included with the kind authorization of M. Bonatz represent the mean of fourteen Askania gravimeters (three GS 11, three GS 15 and eight BN).

2. Computations The computations have been performed by the FAGS (Federation of Astronomical and Geophysical Services) International Centre for Earth Tides (Bruxelles) on the basis of the Cartwright-TaylerEdden development of the luni-solar potential and using a least-squares method with the filters of A. Venedikov (Ducarme, 1975a). The harmonic analysis, when based upon an interval of four months, allows some ten groups of waves to be correctly separated; they are respectively called:

Q1

0~ M1

2 N2

N2

M2

(P1S1K1) L2

i1 (S2K2)

001 M3

according to the Darwin’s symbols of their principal constituents. Because of the local characteristics of the so-called S~wave which merely represents meteorological effects on the instrument as well as on the

a

=

1

+

h—

-

~

*

(0) _______________

N

2 M2 S2

1.1610 1.1474

t

1.1819 1.1946 1.2251

±0.0220 ±0.0080

±0.0054

±0.0175

—0.20 +0.03

t

+3.00 +2.80 +0.84

±1.08

±0.39

t

±0.61

The mean-squares errors given here arc obtained from the comparison of the results from the different instruments and can therefore be considered as representative of the accuracy of this station. * — = Phase lag; + = Phase lead. ~ Adopted value for Bruxelles (Ducarme, 1975b).

site itself, it is not permissible to take the group (P151K1) as representative of tFI~etidal behaviour despite its high global amplitude. One-year observations would be needed to separate S~from K1. This is incompatible with a “profile program” and can only be done in more or less permanent stations. The 0~ group is therefore far more convenient from theoretical grounds as well as from experimental grounds as it proves to be extremely stable all across the continent. In this paper we will therefore restrict ourselves to an examination of the results obtained for two tidal waves groups: the tesseral diurnal 0~group and the sectorial semi-diurnal M2 group. TABLE II Precision obtained with one instrument: Standard mean quadratic errors on M2 wave (internal error for one and the same instrument) Instrument

e(a)

e(K)

Geodynamics La Coste-Romberg Askania GS 15

0.0011—0.0035 0.0011 ---0.0036 0.0032—0.0050

0°05--0°17 0°05—0° 17 0°09—0°35

__________________________________________________

The errors on the other waves are more or less inversely proportional to their relative amplitude to M2, i.e.: M2/S2K2 = 1.7; M2/N2 = 5.8; M2/KiPi = 0.56; M2/01 = 1.0 [For a discussion about the mean quadratic errors in the Venedikov’s method see Usandivaras and Ducarme (1976).l

186 TABLE III The basic tidal gravity stations in continental western Europe

a

*

factors

K

1

Bruxelles Bonn Walferdange Hannover Kid

22 14

i

Bruxelles Bonn Walferdange Hannover Kid *

0~

7 3

1.1474 1.1483 1.1429 1.1476 1.1585

*

a

5

Phase

1.1610 1.1649 1.1537 1.1629 1.1606

1.158 1.177 1.130 1.157 1.182

factors N2

S2K2

1.1946 1.1963 1.1910 1.1925 1.1940

1.182 1.173 1.166 1.165 1.170

1.225 1.213 1.197 1.202 1.220

22 14

5 7 3

K1

01

Qi

+0.03 +0.21 +0.57 —0.21 —0.55

—-0.20 —0.18 —0.09 —0.38 0.20

—0.19

N2

S2K2

+3.00 +2.87 +4.22 +2.08 +1.75

+0.84 +0.52 +1.14 +0.53 ---0.41

Phase

M2

i~

+2.80 +1.90 +2.61 +1.30 +1.36

—1.58 —0.70 0.12

K

i = number of different instruments.

Detailed results of analysis are given elsewhere (Melchior, and Ducarme, 1976). The results obtained at the Bruxelles fundamental station, as a mean for twenty-two instruments (nine Geodynamics, six La Coste Romberg, seven Askania 15 For or BN) are given in Table I. brevity we have not introduced the standard errors in Tables III and IV as under similar environmental conditions they are always of the same order, given in Table II.

Such a ratio between diurnal and semi-diurnal components is typical for the European Atlantic coasts. Therefore one should not wonder if at almost all the stations the amplitude factor: 3k 2 6—l+h is found to be very close to its theoretical value corresponding to the Molodensky models of the earth with a liquid core (ö = 1.161 or 1.164). Simultaneously, the phase lag is everywhere very near to zero. The only exceptions are the Italian stations Torino and

3. Regional distribution of the earth tide parameters

Padova.

The distribution of the tidal parameters in western Europe exhibits a fairly smooth regional trend as shown on the four maps (Figs. 1—4) here reproduced. The diurnal waves (Table IV, Figs. 1 and 2) are not much affected by the indirect oceanic effects. it is

It is observed also that the ~ factor is large at Padova, Trieste and Graz. This may be due to a particular effect exerted by the Adriatic Sea. At Trieste the respective amplitudes of the oceanic tides are:

Oi:

6cm;

K 1:

well known that these tides have indeed a reduced amplitude in the Atlantic Ocean and in the North Sea. As an example, at Oostende, the amplitudes of the oceanic tides are respectively: 01:

S2:

9 cm; 52 cm;

K1: 5 cm; N2: 31 cm

M2:

180 cm;

18cm;

M2: 27cm;

S2: 16cm; N2: 4cm Here the diurnal components have comparatively large amplitudes with respect to the semi-diurnal ones. It is perhaps worth while to point out the existence

of a zoneFrankfurt of lower 5(1.147) value which includes Strasbourg (1.147), and Walferdange (1.154),

187 TABLE IV Trans-world tidal gravity profiles for western Europe: diurnal waves

N

*

Factor a

=

1

+

h --

K

1

Bruxelles Oostende Brugge Walferdange Strasbourg 3 Clermont Paris* Ferrand Grasse Bordeaux Chur Torino Padova Trieste Graz Tihany *3 Frankfurt am Main Bonn*3 BadGrund*3 Hannover Kiel*3 Arhus Bornholm *3 Helgoland*3 Liverpool Cambridge l-lerstmonceux Faeroes ~‘

N

=

*2

G

=

*3

2,302 104 60 2,426 154 296 98 96 86 130 90 34 104 166 256 2,160 2,625 64 1,233 158 118 32 100 200 60 114 180

1.1493 1.1370 1.1528 1.1335 1.1353 1.1557 1.1573 1.1445 1.1575 1.1418 1.1183 1.1833 1.1584 1.1709 1.1453 1.1358 1.1483 1.1598 1.1476 1.1585 1.1597 1.1480 1.1844 1.1490 1.1183 1.1460 1.1926

01 1.1610 1.1658 1.1934 1.1573 1.1474 1.1632 1.1711 1.1575 1.1539 1.1572 1.1543 1.1751 1.1769 1.1822 1.1575 1.1470 1.1649 1.1521 1.1629 1.1606 1.1724 1.1686 1.1735 1.1382 1.1191 1.1520 1.1384

Phase

Instrument

K

K1

Oi

0.03 0.30 0.18 —0.07 —0.15 0.59 0.40 0.09 0.45 0.37 2.43 1.47 0.53 —0.28 —0.13 --0.18 0.21 0.35 —0.21 —0.55 0.63 0.70 --0.07 ---0.17 -4.54 0.09 1.47

--0.20 0.03 0.46 —0.09 -—0.52 0.05 --0.42 —0.27 —0.43 -—0.01 —1.02 —1.37 ---0.11 —0.23 0.05 --0.25 ---0.18 0.71 —0.38 0.20 --0.18 ---0.39 —0.58 --0.38 —0.76 —0.39 0.95

X G G X SX G G G G G G G G A X X A X X G A A G G G G

*2

22 730 730 4 21 804 804 804 804 730 730 721 721 220 2 14 130 7 3 730 204 210 721 721 721 730

number of days of available tidal registration. Geodynamics gravimeter; A = Askania gravimeter; X = several miscellaneous instruments, in each case number of them fol-

lows. *3

These stations are not profile stations (with appropriate authorizatiun they are included for comparision).

extending perhaps as far as Chur (1 .157) and Torino (1.154). A similar minimum appears in the 5(M 2) values but this seems limited to the Strasbourg—Frankfurt area. An important remark in this respect is that these stations have been occupied with four different instruments. Diurnal waves are of a tesseral character and therefore they have no action upon the speed of rotation of the earth but they are associated with the precession-nutation phenomena (Melchior and Georis, 1968; Melchior 1971). Nevertheless, the’se waves are

also subjected to the retardation effect due to internal friction related to the transport properties of matter (viscosity). Their phase lag (see Fig. 2) could be therefore more representative of the viscosity of the earth as a whole than the phase obtained from semi-diurnal components which is an advance and represents mainly the interaction of oceanic loading effects on the upper crust (see Fig. 4). If such a lag of 0.20 was accepted as an upper limit the lag of the bulge itself should be 1 .7° and the Q value about 60 while the estimated tidal heat flow should not exceed some 4% of the observed

188

r.-~___’

1.139’

~U3I

1.119

1.152

1.I13~...

~

1

/

1.152

~~~14i

~

1.1

~

/I ~

1.154

1.171

~

1157 _

1.154

-

-

1.175

1.177

1112

1151/

2 ‘-

~-

~

-

--

-

Fig. 1. Amplitude factor a = 1 + h — of the lunar tesseral diurnal wave 0~(Tables IV and VII). (Faeroes station, being off the map, is indicated by an arrow.) The observed amplitude is comprised between 40 jiGal in the southern stations and 30 ~zGalin the northern stations. (Brugge station is not indicated because of thermic perturbation.)

quantity which looks acceptable (Lubimova 1967; Melchior, 1973). The semi-diurnal waves (Table 5, Figs. 3 and 4) are strongly influenced by the oceanic tides but this appears as rather systematic: the amplitude factor is very much the same in all continental Europe while the observed phase advance is clearly influenced by the distance to the sea which well appears when one follows the straight line Oostende (4.3°)—Brugge(4.1°)— Bruxelles (2.8°)—Walferdange (2 .0°)—Strasbourg

(1.8°).Then Chur gives again 2.0°while the Italian stations give 1.0°.Bordeaux, on the Gascogne Gulf gives the very exceptional value of 7°.

4. The ratios A, B and C (Table VI) The ratios: A

=

5(01)15(K1)

189

L9’\

-0.9’ —0.3’

—0.4’ -9.4’

S

-S.?’

-9.2’ -

-0.3’ —0.5’

0.1’

~

- /

-~

7 _I

-0.4’

7

-U’

—1.0’

—1.4’ .6’

—

-U’

Fig. 2. Observed phase lag of the lunar tesseral diurnal wave Oi. I The minus sign represents a lag with respect to the theoretical tide (Tables IV and VII). (Brugge station is not indicated because of thermic perturbation.) 0.2°corresponds to 51.6s of time.

B = [1 — 5(O~J/[l

—

5(K1)]

are everywhere in Europe higher than unity which is in favor of the existence of dynamical effects of the liquid core of the Earth. The only exception is the Bordeaux station on the Gulf of Gascogne coast and this may indicate a peculiar behaviour of the diurnal tides in the gulf. In many stations the short duration of the observations did not allow a separation of the wave P~from the K1 group and a fortiori the wave S~from K1.

Nevertheless a general mean value for nineteen stations is: A = 1.0137; B = 1.1099 while the twenty-two instruments at Bruxelles give: A

=

1.0117 ±0.0066;

B = 1.0963 ±0.0562

The Molodensky models give: I: II:

A A

= =

1.0202; 1.0130;

B = 1.1679 B = 1.0993

190

1.60$\ 1.210

i.oiIt

1.1

.c, 1.204

~

1.1 1.19$

‘

1.21 1.193 1.201

1.132

1.1SQ/

1. .1 1.195

-

1.137 ~.1 1.205

1.136 1.130 1.1

1.203

1.193

—~:: --;I~N___~/ /_~

1.130

1.212 1.191 1. 7 1.111

Fig. 3. Amplitude factor

a

=

1

+h

—

of the lunar sectorial semi-diurnal wave M

2 (Tables V and VII). The observed amplitude is comprised between 47 MGaI in the southern stations and 28 s~Galin the northern ones.

The ratio:

C= 5(M2)/5(01) is an indicator of the size of the indirect effects acting on the M2-wave frequency. It is systematically higher than unity in all European stations, its mean value being:

and at Bruxelles: =

1 .0266

5. Calculations of the oceanic indirect effects in western Europe

C= 1.0355

C

Exceptions are Oostende, Busum, Herstmonceux and 1-lelgoland (C < 1) while Torshavn (Faeroes) gives C= 1.4122!

±0.0076

It is quite easy to evaluate the global indirect effect from the observed gravity tide. Let: I~ = total amplitude of the indirect effect for a

192 TABLE V Trans—world tidal gravity profiles or western Europe: semi—diurnal waves

N

*1

lactor a M

2

Bruxelles Oostende Brugre Walferdange Strasbourg Paris *3 Clermont lerrand Grasse Bordeaux Chur Torino Padova Trieste Graz Tihany ~ Irankfuri am Main Bonn *3 Bad Grund *3 Hannover Kid *3 3 Arhus* Bornholm *3 Helgoland *3 Liverpool Cambridge l-lcrstmonceux Iaeroes *

*2

*3

*3

2,302 104 60 2,426 154 296 98 96 86 130 90 34 104 166 256 2,160 2,625 64 1,233 118 158 32 100 200 60 114 180

1.1946 1.0924 1.1937 1.1942 1.1889 1.2046 1.2092 1.1884 1.2119 1.1934 1.1975 1.2348 1.2119 1.2120 1.1903 1.1835 1.1963 1.2007 1.1931 1.2104 1.1940 1.2041 1.0734 1.1480 1.1961 1.1319 1.6077

=

1

+

h

Phase s

- -

N2

S2

1.182 1.099 1.145 1.185 1.185 1.173 1.186 1.158 1.152 1.162 1.182 1.223 1.160 1.201 1.176 1.171 1.173 1.228 1.167 1.182 1.170 1.179 1.089 1.156 1.136 1.142 1.552

1.225 1.161 1.221 1.202 1.201 1.214 1.232 1.201 1.241 1.202 1.215 1.198 1.221 1.220 1.188 1.186 1.213 1.209 1.202 1.230 1.220 1.196 1.114 1.174 1.119 1.156 1.488

Instrument

M2

N2

S2

2.80 4.31 4.09 2.25 1.59 3.29 3.60 2.13 7.03 2.02 1.35 1.17 0.81 1.12 0.34 1.22 1.90 1.82 1.23 1.83 1.36 0.86 —3.46 0.68 3.99 0.66 0.32

3.00 0.84 2.52 2.70 2.57 4.19 3.53 1.24 7.00 2.01 1.17 0.06 3.02 1.35 1.14 1.62 2.87 3.40 1.93 2.45 1.75 0.64 3.98 0.08 2.69 0.43 5.27

0.84 4.30 4.03 0.37 0.54 1.90 1.96 1.32 4.12 1.23 0.62 5.55 --0.40 0.43 0.22 —-0.07 0.52 1.32 0.46 1.04 --0.41 ---0.43 3.41 0.56 0.45 1.77 --7.55

-

X G G X X S G G G G G G G G A X X A X G X A A G G G G

*2

22 730 730 3 2 I 804 804 804 804 730 730 721 721 220 2 14 130 6 7303 204 210 721 721 721 730

N

= number of days of available tidal registration. G = Geodynansics graviiiieter; A = Askania gravimeter; X = several miscellaneous instruments, in each case number of them follows. These stations are not profile stations (with appropriate authorization they are included for comparison).

functions has been applied independently by Kuo and by Moens. Kuo considers the effects of the North Sea and of the Mediterranean Sea only, using a cotidal map drawn by himself. He obtains effects of about the required amplitude but with a phase which lies between 156°(Paris) and 188°(Bonn, Walferdange). At Bruxelles the phase is found to be 1 78°09.This means that such a contribution of the indirect effect would make the observed amplitude lower than its theoretical value corresponding to an elastic earth model. The correction therefore should consist of the vectorial subtraction of this amount from the observed amplitude which should then give higher

values of the S factors than the observed ones which are already comprised between 1.19 and 1.21 in western Europe. M. Moens made a calculation for us of the global effect of the world oceans using Zahel’s (1970) world cotidal map and the British Admiralty maps for the North Sea, Irish Sea and the Channel with two options: (a) digitization of these maps and direct cornputation without any correction; and (b) the same with a correction for the conservation of the total mass of the oceans. The results are quite different as shown by some typical examples in Table VIII. The procedure (a) is satisfactory for the phases as it re-

193 TABLE VI Trans-world tidal gravity profiles for western Europe

Intrunient Bruxelles Oostende Brugge Witteveen Walferdange Strasbourg Paris Clermont Ferrand Grasse Bordeaux Chur Torino Genova Padova Trieste Graz Tihany Frankfurt am Main Bonn l-lannover Bad Grund Kid Busum Arhus Bornholm Cambridge Liverpool Herstmonceux Helgoland Faeroes *1 *2 *3

X G G G X X S G G G G G A G G G A X X X A X A G A G G G A G

*

22 730 730 74 5 2 1 804 804 804 804 730 97 730 721 721 220 2 14 7 130 3 204 730 204 721 721 721 204 730

N *2

Ratio

A

2,302 104 60 116 2,426 154 296 98 96 86 130 90 702 34 104 166 256 2,160 2,625 1,233 64 158 80 118 32 60 200 114 100 180

*3

1.0117 1.0253 1.0352 1.0129 1.0178 1.1475 1.0065 1.0119 1.0114 0.9968 1.0134 1.0322 0.9944 0.9931 1.0159 1.0097 1.0106 1.0099 1.0145 1.0133 0.9934 1.0018 1.0015 1.0110 1.0179 1.0007 0.9904 1.0052 0.9908 0.9545

B

C

1.0963 1.2100 1.2653 1.1039 1.1513 1.0875 1.0484 1.0874 1.0900 0.9768 1.1082 1.3041 0.9604 0.9555 1.1166 1.0662 1.0838 1.0826 1.1119 1.1037 0.9520 1.0132 1.0109 1.0798 1.1392 1.0065 0.9261 1.0409 0.9409 0.7185

1.0266 0.9370 1.0003 1.0490 1.0536 1.0330 1.0357 1.0326 1.0267 1.0503 1.0313 1.0374 1.0118 1.0508 1.0298 1.0253 1.0284 1.0319 1.0403 1.0391 1.0422 1.0306 0.9744 1.0324 1.0304 1.0688 1.0086 0.9825 0.9147 1.4122

G = Geodynamics gravimeter; A = Askania gravimeter; X = several miscellaneous instruments, in each case number of them follows. N = number of days of available tidal registration. See text Section 4.

TABLE VII Results at some additional stations according to previously published papers 01

a Darmstadt Genova* Potsdam Witteveen * *

1.156 1.157 1.160 1.157

Calculations made at ICET.

M

2

K

—0.5 —1.6 —0.3

—0.5

Reference

a

K

1.190 1.171 1.180 1.214

0.5 0.0 1.3 2.1

-

Gerstenecker et al. (1973) ICET Dittfeld (1974) Bragard (1974)

194 TABLE VIII Some typical results of indirect effects corrections Station

*

Observed value

a

Corrected value K

(a) without oceanic mass conservation

(b) with oceanic mass conservation

a

K

a

K

Herstmonceux Oostende

1.1319 1.0924

0.66 4.31

1.2253 1.1242

0.40 0.94

1.1859 1.0843

—1.46 —0.73

Bruxelles Walferdange Witteveen

1.1946 1.1910 1.2136

2.80 2.61 2.15

1.2064 1.1962 1.2120

—0.15 --0.06 —0.07

1.1679 1.1593 1.1669

—1.55 —1.23 —1.44

Bordeaux Faeroes

1.2119 1.6077

7.03 —0.32

1.2469 1.1437

3.18 —6.32

1.2184 1.0963

1.93 —12.36

*

Calculated by M. Moens.

duces the observed phase advance to about zero in

England, Belgium, Luxembourg, France, Holland and Switzerland, and to a negative value (lag) of —0.60° to —1.00°in Germany and northern Italy. However all S factors are still slightly increasing up to 1.21 to 1.26 which is not acceptable. The procedure (b) on the contrary is satisfactory for the amplitudes as it diminishes all the S factors by about 0.02 to 0.03 in the western part and by about 0.04 in Germany which would appear a desirable solution if it did not change the phases too much by bringing them to quite strong negative values: —1.5° to —2.2°.The phase may be considered as a very valuable constraint for the evaluation of the indirect effects and as a check of the quality of the cotidal charts. Critical tests are in this respect the coastal stations. (Table VIII) This led to the conclusion that the cotidal maps we have used are imperfect. Other available cotidal maps do not differ significantly from them so that their use would not change this conclusion. Unfortunately indeed, the empirical description of the tides in the open ocean is only just beginning as Munk et al. (1970) pointed out, and the theoretical calculation of the tides in the open ocean from the Laplace’s tidal equations are far from being perfect (e.g., Pekeris and Accad, 1969; Hendershott and Munk,

1970; Zahel, 1970; etc.). The tidal gravity data provided here are therefore of considerable value in solving the inverse problem for the ocean tides by means of land and island based tidal gravity observations as proposed in Jachens and Kuo (1973), as well as in evaluating other geological or geophysical properties of the earth. 5.1. A remark concerning the Faeroes station

It is to be noted that this station, situated in the middle of the North Atlantic Ocean had to be installed on the top of a cliff which is 700 m high. It results that the nearby oceanic tidal masses have a strong influence and should be known in detail to provide a precise correction. This is until now not the case.

Acknowledgements Such an extended program could not have been realized without the generous hospitality of many European scientific institutions and the efficient help in the maintenance from distinguished geophysicists or astronomers. In this respect we are pleased to thank the following host institutions and colleagues:

195 TABLE IX List of the stations Station

Country

Longitude (°E’)

Latitude (°N’)

No.

Liverpool Cambridge Herstmonccux

Great Britain Great Britain Great Britain

356 56 0 12 359 40

53 24 52 10 50 52

0101 0105 0110

Oostende Brugge Bruxelles

Belgium Belgium Belgium

2 56 3 13 4 21

51 14 51 12 50 48

0219 0220 0201

Witteveen

The Netherlands

6 40

52 49

0271

Walferdange

Luxembourg

6 10

Paris-Sèvres Strasbourg Clermont Ferrand Bordeaux ~,rasse

France France France France France

~ieI -lelgoland usum -lannover BadGrund Bonn Frankfurt am Main Darnistadt

49 40

0256

2 7 3 359 6

13 46 6 28 56

48 48 45 44 43

50 35 45 50 45

0315 0306 0310 0312 0311

FR. of Germany FR. of Germany FR. of Germany FR. of Germany F.R.ofGermany F.R. of Germany FR. of Germany FR. of Germany

10 7 8 9 10 7 8 8

7 53 52 42 15 5 19 42

54 54 54 52 51 50 50 49

20 11 08 23 48 44 03 54

0715 0713 0714 0709 0710 0702 0706 0733

Potsdam

DR. of Germany

13

4

52 23

0764

Faeroes Arhus Bornholm

Denmark Denmark Denmark

62 0 5-6 10 55 10

0821 0822 0823

Graz

Austria

15 26

47

4

0695

Tihany

Hungary

17 52

46 54

0954

9 32

46 51

0610

45 42 45 24 45 4 44 25

0509 0508 0516 0505

Chur

Switzerland

Trieste Padova Torino Genova

Italy Italy Italy Italy

333 3 10 12 14 49

13 11 7 8

46 53 33 55

The stations are grouped by country and listed in order of decreasing latitude; No. is their code number in the worldlist of stations established by the International Center for Earth Tides.

Laboratoire de Geodynamique, Walferdange

Osservatorio Geofisico di Trieste (Italy): I. Marson

(Luxembourg): J. Flick Institut de Physique du Globe, Strasbourg (France): R. Lecolazet Cerga, Grasse/Nice (France): G. Vigouroux Institut de Physique du Globe, Clermont Ferrand (France): M. Fourvel

Istituto di Geodesia e Geofisica, Padova (Italy): A. Norinelli Royal Greenwich Observatory at Herstmonceux (U.K.): N.P. O’Hora Institute of Oceanographic Sciences, Liverpool (U.K.): G.W. Lennon

Observatoire de Bordeaux (France): Rousseau

Laboratoriet for Geofysik, Arhus (Denmark): N.

Politecnico di Torino (Italy): Philippe Melchior

Breiner

196

Morkedal Radar Station, Faeroe Islands: Prit. Jakobsen Magnetisch Station, Witteveen (The Netherlands): M. i ipping Lehreseminaar, Chur (Switzerland): R. Florin lnstitut für theoretische Geodäsie, Hannover (F.R. of Germany): HG. Wenzel Technische Hochschule in Graz (Austria): H Lichtenegger. Special thanks are also due to the Belgian Royal Navy for the transportation of one piece of equipment

to the Faeroe Islands as well as for its cooperation in the maintenance of Oostende and Brugge stations, to M. Van Ruymbeke who was responsible for the installation at Oostende, Brugge and Clermont Ferrand, to N. Breiner for the installations at Arhus and Godhavn

(Grønland), to R. Brein who made his excellent resuits from Frankfurt am Main available at the Inter-

national Centre for Earth Tides. Finally, we thank Professors G. Ingliilleri, J. Kovalevsky, R. Meissner, K. Rinner, S. Saxov and W. Torge for their interest and efficient help in that project.

References Baker, TI. and Lennon, G.W., 1973. ‘fhe investigation of marine loading by graviiy variation profiles in U.K. In: 7th mt. Symp. Earth Tides, Sopron. Akademiai Kiado, Budapest, pp. 463-478. Bonatz, M. and Chojnicki, T., 1972. Europèisches Frdgezeiten. Protii. Mitt. Inst Theor. Geod. Bonn, 8: ~ Bragard, F., 1974. West-I.uropean tidal gravity profile, Pap. Meet., Int. Gravim. Comm., Paris, 4 ~ Broz, i. amid Simon, Z., 1974. Die Registrierung der Gezeitenvariationen der Schwerebeschleunigung auf der Station Ceske Budejovice. Sb. Vyzkum. Praci Svazek, 9: 33 44. Dittfeld, [Ii.. 1974. l-rste I- rgebnisse mit deni Gezeiiengravirneter GS 15 an der Station Potsdam. Bull. Inf. Marées Terr., 69: 3850-3853. Ducarmne, B., I 975a. Coniputatinn procedures at the ICIT. Bull. Inform. Marées Terr., 72: 4I56--4 189. I)ucarme, B., 1975h. A fundamental station for trans-world tidal gravity profiles. Phys. Farth Planet. Inter., 11(2): 119 --127: and Coniniun. Ohs. R. BeIg., Sér A (Sér Géopys), 32: 126 (abstract).

Gerstenecker, C.. Groten, F. and Rummel, R., 1973. Report Ofl tidal gravity and tilt measurements during 1969—1973. In: 7th Budapest, Int. Symp.pp. on 687 l-~arth Tides, Sopron. Akadeniiai Kiado, 705. Uendershott. M. and Munk, W., 1970. Tides. Annu. Rev. Fluid Mech.. 2: 205 - 224. Jachens, R.C. and Kuo, iT., 1973. The 01 tide in the North Atlantic Ocean as derived from land-based tidal gravity measurements. In: 7th Int. Sym on Earth Akademniai Kiado. Budapest, pp.1i.165---176. Tides, Sopron. Kuo, iT., Jachens, R.C., Melchior, P. and Ewing, M., 1972. A link of the trans-U.S. and Trans-Europe tidal gravity profiles. I-OS (Trans. Am. Geophys. Union), 53(4): 343 hst ict). Luhirnova, 1967. of Theory of thermal time Larth’s mantle: l.A., Time effect tidal friction. In: state -T.F. of Gaskell (Editor), The Earth’s Mantle. Academic Press, New York, N.Y., p. 248. Meichior, P., 1971. Preccssion-nutations and tidal potential. Celestial Mccii., 4(2): 190 212. Melchior. p., 1973. Physique et dynaniique Géodynamir1ue. Vander, Brussels, p. 29. planétaires, 4. Melchior, P. and Ducarmnc, B., 1976. Tidal gravity profiles in Western Europe. Ohs. R. Beig., Bull. Ohs. Marées Terr. (in press). Melchior. P. and Georis, B., 1968. Earth tides, precessionnotations and the secular retardaiion of Earth’s rotation. Phys. Earth Planet. Inter., 1(4): 267—287. Munk, W., Snodgrass. F. and Wimbush, M., 1970. Tides off shore: Transition from California coastal to deep-sea waters. Geophys. l:luid Dyn., 1: 161. I’ekeris, CI.. and Accad. Y., 1969. Solution of Laplace’s equation for the M2 tide in the world oceans. Philos. Trans. R. Soc. London, Ser. A, 265: 413 --436. Sluckenbroker, B., 1973a. Observations of loading deformation by ,a gravimnetrie tidal profile across northern Germany. In: 7th Ini. Symp. on Earth Tides, Sopron. Akadennai Kiado, Budapest, pp. 137- ISO. Stuckenbroker, B., 1 973b. Ergebnisse von Erdgezeiten-ParalleIregistrmerungen mit drem Askanma-gravmnietern. Z. Geophys., 39. 1 --20. Torge, W. and Wenzel, HG., 1974. Verglemch von Erdgezemtenregistrierungen mit sechs verschmcdenen Gravimetern. Mitt. Inst. Theor. Geod., Tech. Univ. Hannover. Usandivaras, iC. and Ducarme, B., 1976. Etude de Ia structure du spectre dmurne par Ia méthode des ‘noindres carrés. Bull. Géod., 50: 2. Zahel, W., 1970. Die Reproduktion gezeitenbedingter Be\vegungsvorgange im Weltozean inittels des hydrodynamisch-numerisehen Verfahrens. Mitt. lnst. Meeresk., Univ. Hamburg No. XVII.