KPATKHE C O O B I K E H H $ I - SHORTER C O N T R I B U T I O N S

I N V E S T I G A T I O N O F G R A V I M E T R I C R E C O R D S

A T N O N - T I D A L F R E Q U E N C I E S * )

PETER VARGA

The Ro land Edtvds Geophysical Inst i tute, Budapest**)

P e 3 m M e : HccAeOyernca cneKmp epaau~aempu,wcKuxpeeucmpoepaJ~t~t ua uenpunuanbtx ~tacmomax.

Ho~ca3ano, ~tmo 6Jtu3tcaa u auue~uaa CaZ3b u~eemca ~e~tcby cneKmpo~t amMoco~epnoeo Oaaaenun

u npwtuanb~x peeucmpoepaMM. Pacc~umaua caa3b 9mux ~)ayx aaaeuu~ a cayuae pa3auunbtX npudopoa

u cmauquFt. 06uapy~ceua 6au3naa u auue?maa caa3b. Onpe()eJteubt nonpaanu a~mJtumyOubtx xapaK-

mepucmw¢ a cay~tae e~taattbtx npuauaubtx aoau. ~ona3auo, umo a cneKmpe nadJuoc)ennbtx tcpuabtx

u~vteemc.~t neSoabutan attoMa~ma na ttacmome 56°/h, nornopaa odnapyy, ceua o eay*tae pa3auun~x

cmamcu(t. Paec~tampuaatomca pa3autmbte ao3cao~cnbte od~acneuun 9rnoeo aaJtenua.

The purpose of this project was the investigation of the spectrum of gravimetric tidal curves at non-tidal frequencies. The frequency intervals between long-period and diurnal, diurnal and semidiurnal, semi- and terdiurnal waves were investigated and also higher frequencies. The obtained spectra (the Fourier transformation with the Gibbs factor were used) are shown in Fig. I. The general tendency of the spectrum, or, we may say of the noise can be seen clearly after adjusting the spectral curve using the least-squares method. The same tendency is displayed by the spectra of the corresponding pressure records. It appeared expedient to compare these spectra by means of methods of mathematical statistics [1 ], in order to obtain information on the baro- metric effect on gravimetric records. The investigation of this problem by comparing the spectra has certain advantages over comparing the observed series, from which tides have been eliminated. The main advantage is the following: in order to determine the barometric deformations from the barometric curves, it is necessary to consider a considerably large area around the tidal station, the boundary of which is not defined precisely. Drawing on the fact that lhe barometric curves display roughly the same pattern and that they may only be displaced in phase over large areas, we used the amplitude spectra which, as we know, are independent of phase. In the case of Hungary the error in interpolation of the adopted distance of 200 km represents about 1"5 mbar, which is fully accounted for by the difference in phase of the barometric curves.

The spectra were compared in the following manner: First of all, the coefficient of correlation was determined for mutually corresponding curves. Since the correlation coefficient can only be used to investigate linear relations, we then determined the correlation function which could be applied to characterizing relations other than linear. As we know, the correlation function defines the dispersion relation, generated by the argument, and the general dispersion. Clearly, the close- ness of the correlation coefficient and function are evidence of the linear character of the relation of two events. In the case of different instruments we obtain, in our calculations, different cor- relation coefficients, from 0"74 to 0.93, and correlation functions close to them in magnitude. This speaks in favour of a linear relation between gravimetric and barometric spectra, which may then be described by a linear regression equation. It should be mentioned that the relation between adjusted spectra (dotted lines in Fig. 1) was always characterized by a coefficient larger than 0.90.

*) Presented at the meeting of Working Group 3.3. of the K A P G (Prague, November 1975). **) Address: H-1145, Budapest, Columbus 17-23, Hungary.

Studiageoph. etgeod. 21 [1977] ] 9 5

S h o r t e r C o n t r i b u t i o n s

The regression lines obtained (y in pgal, when x is in mbar) read

a) GS-15 No. 220 (instrument of the IFE AS USSR, stat ion Tihany, 115 days): y = 0-045 -}- -I- 0.387 x;

b) BN-07 (station Tihany, series of 42 days): y = 0.157 --}- 0-725 x;

c) GS-15 No. 222 (station Potsdam, series of 71 days) [10]: y = 0.111 -}- 0-719 x,

and allow one to estimate the barometr ic effect on tidal observations. Finally, for this purpose it is initially necessary to estimate the accuracy of the regression curves obtained. For this purpose we used a selected distribution of y-values, corresponding to a fixed value x - - x 0, These selected distributions are related to the Student t-distribution and[ the selected s tandard deviation S~I x

of the observed values Y i relative to the forecast ye, (~c and y are the ari thmetic means of the quan- tities x i and yi) as follows:

n

S,/= = g [ ( Y ' - Ym) z (n - 2) ] ' /z = i=1

= { ( n - 2) ~, (y i -- .#1~-- I f ( x / - .21 (.h -- .~)]z [ f (x, - .2")21-1} '/~ . i=i i=l i=I

In this way the uncertainty at a given interval of confidence, determined (we used a 95% interval) in the case of an actual value of x = xo:

+ (Xo - t=1

~o l GS't~ iV #. 220/25,00797J 7~01. t97(,/

m o 30 40 50 #0 7O pg~

mObar I0 20 30 40 50 60

o t ~ 5o ~o • " ~/h 70

Fig. 1.

IqODULAI'ED ENERGY SPECTRA

I0. ~ BONN, BN-07~ 60DAY3

] A (C"O~N:CK:RES:DUAO °°t II o.iI / i

z2 ~s so 56 W ~ ~o rUYANY, GS-15 N o 220,2~0 DAYS

0.#

JO PECNK BNO?, 100 DAYS

. . . . . . . ~ ~ ° 0 72 c,6 60 ~07 54 #

Fig. 2.

] 9 6 Studio geoph, et geod. 21 [1977]

I£pamKue coo6ulenun

where ~ is unity -- the confidence interval, was used to determine the error for given values of x. The errors obtained (1 .5~ for the GS-15 No. 222, 2"0~ for No. 220 and 5-8~ for the BN-07) are sufficiently small and, therefore, the regression curves may be used to estimate the corrections of the amplitude characteristics (6) for the main tidal waves. The results of the computat ions are given in Tab. 1. The computations allow one to conclude that the corrections in respect of the barometr ic effects are appropriate in the case of short series (up to 5 months), but that they decrease rapidly with the increase of the number of observation days.

Table 1.

Wave Barometric pressure Gravity variation ~ correction (mbar) (ligal) (~ )

STATION: T I H A N Y ;

Oa

K1 N~ M2 S2

STATION: T I H A N Y ;

O1 K1 N2 M2 S2

STATION: T I H A N Y ;

O1 K1 N2 u2 s2

I N S T R U M E N T : BN-07; 42 DAYS

0.176 0.128 0-232 0.168 0.118 0.086 0.050 0.036 0-274 0.199

I N S T R U M E N T : GS-15 N ° 220;

0.101 0-039 0.354 0-137 0.013 0.005 O.082 O.032 O.385 0-149

I N S T R U M E N T : GS-15 N ° 220;

0-050 0-019 0.147 0.057 0-010 0-004 0.026 0.010 0-117 0.045

115 DAYS

260 DAYS

0"36 0'35 0"93 0"09 0"99

0'09 0"24 0"04 0"06 0"61

0"05 0"11 0"04 0"02 0'22

The S2-waves and, to a lesser extent, the Kl-waves form an exception, because the decrease of the correction is distinctly slower. The reason for this is evidently that there exist regular barometr ic variations, described by Haurwitz [2], at S z frequencies and close to K 1 frequencies. The presented corrections also include the instrumental and external par t of the barometr ic effect. As a result of the computations, carried out by Ivanova and Pertsev [3], it is thought tha t tha t GS-15 instrument No. 220 appears to be nearly ideally pressure compensated and tha t the other two instruments being investigated have a small instrumental constant.

In the process of investigating the noise of the recorded curves, we observed in particular, apar t f rom the part of the spectrum, monotonous ly decreasing with frequency (dotted line in Fig. 1), also an oscillating component. In the frequency interval of frequencies higher than the terdiurnal with the results of the GS-15 gravitymeter No. 220 we found that the maximum ampli- tude was close to the frequency of 56°/hr in all the partial series. The ampli tude amounted to several hundreds ~tgal. In order to determine whether the observed maximum is r andom or not , we proceeded in the following way: we collected the data f rom various instruments, recording at various times and stations, computed their spectra and then their power spectra.

Studia geooh, et geod. 21 [1977] 197

Shorter Contributions

The power spectra calculation caused an amplitude filtration: the large spectral peaks were enhanced the small diminished. Figure 2 shows the normed power spectra. We introduced norming, in order to be able to Unify the curves into one (Fig. 3) and also to amplify the peaks which appeared regularly and damp the r andom ones.

14E,~ (5~0 o~rs)

::I A

7) 6i . . . . . r g0 ~ - - ---;W . . . . . . . i i~ ,*= " 6~.47 F607

Fig. 3.

In the initial spectra from Bonn the amplitude amounted to 0.03 lagal, in Potsdam to 0.06 lagal, in Pecn~ to 0.06 ggal and in Tihany to 0.02 ~tgal. The ampli tude was determined in this case as the difference between the frequency peak and the mean noise. In the individual series the noise amounted to ½ - - ½ of the maximum peak. This fact also indicated that the data from just one stat ion or one instrument are insufficient to substantiate the peak at the frequency of 56°/hr. As a result of these investigations it should be pointed out that in the case of anomalies which are small compared to the mean noise, there is an uncertainty in the posit ion of the spectral peak. Since no mathematical estimate of this feature exists, we investigated it experimentally using models and found that the frequency of the anomaly was determined with an accuracy of 0 .5--1 .0°/hr and in some cases even reached 1.5°/hr.

Wha t are the causes of this anomaly?

1) The quarter-day waves are concentrated at the frequency 57"5°/hr and their theoretical ampli tude is smaller by one order of magnitude than the observed (0.003 lagaI).

2) There exists a regular component of the atmospheric tide [21, the period of which is appro- ximately quarter-day. Moreover, the ampli tude of these variations is too small to generate a gravi- metric wave of the order of 0-01 ~tgal.

3) The higher harmonics of ocean tides [4] which are generated i n the shallow parts of the seas and which can strongly influence the form of the tide al though not its character, could also in principle be sources of the observed anomaly. Moreover, the quarter day higher harmonics (according to our investigations among them the most significant Me, MS¢, $4 and M N 4) as shown in Fig. 3, have slightly different frequencies and, therefore, cannot be the immediate source of the observed anomaly.

4) It seems impor tant to investigate tile relation wilh the oscillations of the inner Earth 's core [5, 6]. By comparing the results of theoretical papers with ours, we found that there was a jump in density of 0"3 g/cm 3 at the boundary of the inner and outer core. In the case of free oscillations of the inner core one should observe the same split t ing of the spectral lines as in the case of the free oscillations of the Ear th [7]. The splitting, a l though not very distinct, can also be seen in Fig. 3. What is problematic with regard to this explanation is that the American geo- physicists, who carried out observations at the South Pole [8] with instruments more accurate than we had, were not successful in establishing the effect of the eigen oscillations of the inner core.

5) As is known, the frequency characteristic of the Fourier t ransformation with lhe G i b b s factor contains expressions with integral sines [9]. The resulting curves of the frequency charac- t eristic than display secondary maxima, lhe positions of which depend on the le~gIh of the series

] 98 Studia geoph, et geod. 21 ,[1977]

Kpamnue coo6uleuun

and on the frequency difference. Our investigations have shown that in this case that there is no penetrat ion of large tidal waves via the secondary maxima, which are very small as a result of applying the Gibbs factor.

Appendix: After this paper had been prepared for publication, the computat ions of the barometr ic effect based on observations at Pecn3 ~, made with the instruments BN-07 and GS-15 No. 222, were concluded. The obtained results are very similar to those obtained at Tihany and Potsdam.

The regression equations (after smoothing by means of the least-squares method) read as follows:

BN-07 ... y ~ I '110 ~ 0"731x ;

the error is about 3 ~ considering a confidence interval of 0-95. The correlation coefficient is equal to 0'987.

GS-15 No. 222 ... y = 0-141 + 0,720x ;

the error is about 2 ~ considering a confidence interval of 0"95. The correlation coefficient is equal to 0-976.

Received 17. 11, 1975 Reviewers: J. Pieha, Z. ~irnon

References

[1] J. S. B e n d a t , A. G. P i e r s o l : Random Data. Wiley-Intersci., New-York 1972. [2] S. C h a p m a n , R. S, L i n d z e n : Atmospheric Tides. D. Reidel Publ. Co., Dordrecht 1970. [3] M. B. HBaHoBa, ]3. H. FIep~eB: O~en~a Bnnnnna aTMoc~epnoro Bo3,~yxa Ha npHnnBn~,Ie

H3MeHeHH~ CFIYlbt T~x'gecrH. MeTo,~nl~a n3Meper~n~ 3eMH/~IX npH~qHBOB~ Hay•a, M. 1970. [4] J. J. D r o n k e r s : Tidal Computations. Nor th-Hol land Publ. Co., Amsterdam 1964. [5] I. J. W o n , J, T. K u o : Oscillation of the Ear th 's Inner C o r e . . . J. Geoph. Res., 78 (1973),

905. [6] F. H. B u s s e : On the Free Oscillation of the Ear th 's Inner Core. J. Geoph. Res., 79(1974),

753. [7] Z. S. A l t e r m a n , Y. Eya l , A. M. M e r z e r : On Free Oscillations of the Earth. Geoph.

Surveys, 1 (1974), 409. [8] B. V. J a c k s o n , L. B. S l i c h t e r : The Residual Daily Ear th Tides at the South Pole. J.

Geoph. Res., 79 (1974), 1711. [9] C. L a n c z o s : Applied Analysis. Prentice-Hall, Inc., Englewood Cliffs, N. J., 1956.

[i0] H.-J. D i t t f e l d : One Year Ear th Tide Registrations with the Gravimeter GS-15 No. 222 in Potsdam. XVI. Gen. Ass. I U G G , lAG, Grenoble 1975 (not published).

Studia geoph, et geod. 2t [~977~ 199