7
KpamKue coo6ulenua Si on fait/t partir des rdsultats de comparaison dans la composante EW une moyenne pond6r6 des valeurs 7, on obtient ?(Mz) = 0,824 4, 0,002, ~,(Sz) = 0,729 E 0,004, 7(N2) ~-- 0,873 ~ 0,012, D'oh suit que 7(Ki) = 0,750 ± 0,006, ;:(O1) = 0,708 4- 0,008. 7(O1) -- ~(Kt) = --0,042 4. 0,010. C'est une valeur qui caract6rise l'effet dynamique du noyau terrestre. Elle est de toutes les valeurs obtenues et pubti6es jusqu'h ce moment la plus proche/t la valeur th6orique Y(Ot) -- -- ?,(K1) = --0,044 calcul6e pour le module de Molodenskij (avec un noyau interne). 6. En ce qui coneerne les diff6rences des phases x il semble qu'il existe dans la composante EW une diff6rence r6elle --9 ° pour les ondes semidiurnes (c'est/t dire le retard 18 minutes). Jusqu'ici on n'a pas encore interprdt6 les valeurs x. I1 semble que la valeur x observde/t Pfibram est li6e ~t la profondeur de la station et aussi aux autres caract6ristiques locales. Dans la composante NS ce sont les tr6s petites valeurs x (1,2 °) pour les pendules en quartz qui sont frappantes. C'est en d6saccord avec les r6sultats du m6me appareil pour la composante EW et aussi avec les valeurs conformes obtenues/t l'aide des autres inclinom6tres. Re~u le 30. 7. 1971 Critique: M. Bur$a SPECTRUM OF THE GEOMAGNETIC FIELD IN CENTRAL EUROPE ALLA D~ODEN~UKOV~ Geophysical Institute, Slovak Acad. Sci., Bratislava*) Pe3 ro Me : Cmarnba nocanutena 6onpoey usyueuu~ cnenmpa eeo:aaeuumuoeo no:ta ua meppumopuu CpeOnegt Eaponb~. B uacmuocmu pacc:aompeua 27-3ueaua~ aapuat/ua c ee ebtCUtU:aU eap~uouutteetcu:au no :aamepua,~aM 7 cpe3neeaponef~cKux ogcepearnopuf¢ a nepuo3 1960---68ee. Cde:taubt neKomop~e abtaoObt omnocume:tbno cnenmpa:tbuoeo cocrnaaa ecex mpex Ko¢~noueumo, eeo~aeuumuoeo no:ta npu pa~ubtx ypoeunx coaneuuofi aKmuauocmu. 1. INTRODUCTION Systematic observations of the geomagnetic field have now been carried out for a long space of time by means of a widespread network of specially equipped stations. One of the important tasks is to process the data obtained from these observations, and to interpret them in treating the fundamental problems in geophysics. The variable geomagnetic field retains certain regularities in the course of its variations. Whereas earlier mostly harmonic analysis was used to discover obscured periodicities [1 ], recently spectral analysis by means of correlation functions is being used more frequently for this purpose [2--4]. There exist the numerous papers treating these problems, which justify one in saying *a Address: D6bravsk/t cesta, Bratislava - Patr6nka. 202 Studia geoph, et geod. 16 (1972)

Spectrum of the geomagnetic field in central Europe

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Page 1: Spectrum of the geomagnetic field in central Europe

KpamKue coo6ulenua

Si on fai t / t part i r des rdsultats de comparaison dans la composante EW une moyenne pond6r6 des valeurs 7, on obtient

?(Mz) = 0,824 4, 0,002,

~,(Sz) = 0,729 E 0,004,

7(N2) ~-- 0,873 ~ 0,012, D ' o h suit que

7(Ki) = 0,750 ± 0,006,

;:(O1) = 0,708 4- 0,008.

7(O1) - - ~(Kt) = --0,042 4. 0,010.

C'est une valeur qui caract6rise l'effet dynamique du noyau terrestre. Elle est de toutes les valeurs obtenues et pubti6es jusqu 'h ce moment la plus p roche / t la valeur th6orique Y(Ot) -- - - ?,(K1) = --0,044 calcul6e pour le module de Molodenskij (avec un noyau interne).

6. En ce qui coneerne les diff6rences des phases x il semble qu'il existe dans la composante EW une diff6rence r6elle - -9 ° pour les ondes semidiurnes (c 'est / t dire le retard 18 minutes).

Jusqu'ici on n 'a pas encore interprdt6 les valeurs x. I1 semble que la valeur x observde/t Pf ibram est li6e ~t la profondeur de la stat ion et aussi aux autres caract6ristiques locales.

Dans la composante NS ce sont les tr6s petites valeurs x (1,2 °) pour les pendules en quartz qui sont frappantes. C'est en d6saccord avec les r6sultats du m6me appareil pour la composante EW et aussi avec les valeurs conformes obtenues / t l 'aide des autres inclinom6tres.

Re~u le 30. 7. 1971 Critique: M . Bur$a

S P E C T R U M O F T H E G E O M A G N E T I C F I E L D I N C E N T R A L E U R O P E

ALLA D~ODEN~UKOV~

Geophysical Insti tute, S lovak Acad. Sci. , Bratislava*)

Pe3 ro Me : Cmarnba nocanutena 6onpoey usyueuu~ cnenmpa eeo:aaeuumuoeo no:ta ua meppumopuu

CpeOnegt Eaponb~. B uacmuocmu pacc:aompeua 27-3ueaua~ aapuat/ua c ee ebtCUtU:aU eap~uouutteetcu:au

no :aamepua,~aM 7 cpe3neeaponef~cKux ogcepearnopuf¢ a nepuo3 1960---68ee. Cde:taubt neKomop~e

abtaoObt omnocume:tbno cnenmpa:tbuoeo cocrnaaa ecex mpex Ko¢~noueumo, eeo~aeuumuoeo no:ta

npu pa~ubtx ypoeunx coaneuuofi aKmuauocmu.

1. I N T R O D U C T I O N

Systematic observations of the geomagnetic field have now been carried out for a long space of t ime by means of a widespread network of specially equipped stations. One of the impor tan t tasks is to process the data obtained from these observations, and to interpret them in treat ing the fundamental problems in geophysics.

The variable geomagnetic field retains certain regularities in the course of its variations. Whereas earlier mostly harmonic analysis was used to discover obscured periodicities [1 ], recently spectral analysis by means of correlation functions is being used more frequently for this purpose [2--4]. There exist the numerous papers treating these problems, which justify one in saying

*a Address: D6bravsk/t cesta, Bratislava - Patr6nka.

202 Studia geoph, et geod. 16 (1972)

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S h o r t e r Con t r ibu t i ons

that the fluctuations of the geomagnetic field form a continuous spectrum, in which peaks occur at certain frequencies. Some parts of the spectrum are due to hydromagnetic processes in the Ear th 's core [5], on the one hand, and a broad range of frequencies is represented by external sources (from several milliseconds to the l 1-year cyclic variation), on the other. However, the distribution of the energy in the spectrum of the geomagnetic field is not quite clear yet,

The spectral analysis of the components of the geomagnetic field, using the data of the Central European observatories, is the purpose of this paper.

The spectral characteristic includes the information on the physical properties of the Ear th 's interior [6]. Therefore, the spectral analysis is the prerequisite for further investigation of the distri- bution of the electrical conductivity of the Earth. Whereas short-period variations of the geo- magnetic field are used to study the properties of the Earth 's crust and upper mantle, long-period variations are used to study the distribution of the electrical conductivity at larger depths.

2. THE M E T H O D

In the present paper the 27-day variation and its harmonics are investigated with the help of the records of the components of the geomagnetic field made in the years 1960--1968 at the fol- lowing observatories:

~0N 2E ~0N 2E

Hurbanovo 47°09 , 18002 , Wien-Kobenzl 48°15 , 16°19 ,

Prfihonice 49°59.3 ' 14°32.5 , Ffirstenfeldbruck 48°09-9 , 11°16-6 '

Swider 52006-9 ' 21°15.2 , Tihany 46054 , 17°54 ,

Wingst 53°44.6 , 09o04.4 '

Three components of the geomagnetic field were investigated: the magnetic declination D, the horizontal intensity of the field H, and the vertical intensity Z, the diurnal mean values of which were considered over intervals corresponding to the different levels of solar activity, in a similar way as it is done for English and Australian observatories [8]. I f a sufficiently long time interval is considered, all r andom effects cancel out or their influence is minimum, so that the signal will be less disturbed and more marked [7], which will guarantee that the computed power spectrum will approximate the real spectrum.

Under the condition that the record will be used from a certain time onwards, the corresponding time series can be expressed as follows [9]: U n = U( t o + nh), where n = 1, 2 . . . . . N; h = 1 day. In order to simplify the subsequent calculations, the values U n are transformed to so-called centred quantities Xn, which have a zero mathematical expectation.

The accuracy of the final results and their resolution form the criteria for the choice of the length of series N, as well as of the number of correlation lag values m to be computed. O n t h e other hand, the quantiti tes N and m determine the number of degrees of freedom k ~ 2 N / m . The quant i tyk is indirectly proport ional to the normalized standard error and it defines the signal-to-noise ratio, i.e., N and m should be chosen so that k is larger. Usually k = 9--" 22.

In the present case time series of three years were analysed in dependence on the level of the solar activity: the periods of decreasing activity, minimum activity and of the activity increasing to maximum. If m = 108, k = 20.

For purposes of characterizing the solar activity the records of the daily intensity of solar radio noise at 10.7 cm, 2800 Mc/s, were used. [10]. T he series of diurnal values of the components of the geomagnetic field used were smoothed in advance with a weight of 0.6 (pre-whitening)~ The

Studia geoph, et geod. 16 (1972) 203

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Kpamtcue co06uleltus1

value of the weighting coefficient is chosen empirically and a suitable degree of smoothing is adopted. Thanks to pre-whitening the high-frequency harmonics are strengthened, and this is advantageous since the energy increases towards the lower frequencies. After computing the autocorrelat ion function

N - r

c (O = (N - X i=0

the distribution of energy in the chosen frequency range was determined using the Fourier t rans- form [11]. Thus, the spectral curves were computed by means of a G I E R computer according to the following formula;

m - 1

v, = V (rZ,4m) = *[Co + 2 X + ( - i ) " c , , ] . q = l

The values obtained were smoothed by applying the relations U o = 0 .5(V o + V1), U r = = 0 - 2 5 ( V r _ 1 + 2 V r + Vr+l) , b ~ = 0 . 5 ( V , n _ l + Vm), l ~ r < _ m - - 1. A correction for the pre-whitening of the initial series was also effected.

3. N U M E R I C A L RESULTS

The graphs show the spectra of the geomagnetic field at frequencies of f = q/2mT, where q = 0, 1 . . . . . m; (2z) -~ is the Nyquist frequency fN, in the case considered fN = 0.5 d a y - 1 . All graphs show the 27-day variation, which agrees well with the periodicity of the solar rota t ion (not always agreeing accurately with the appropriate frequency) and its harmonics.

The spectral curve of solar flux (not given) shows a predominant concentrat ion of energy at a frequency corresponding to T = 27 days and its harmonics are wide and much weaker, during increased activity merging with the overall noise level. The behaviour of the individual com- ponents of the geomagnetic field for the given time interval differs.

I

~ ~ i "'''~ ~ t ~ ~ ~ ~c, gi~

Fig. 1. Power spectrum of the horizontal intensity on a scale of e o ---- 10022/day - 1 for the ob- servatories of T i h a n y - 1, P r ~ h o n i c e - 2, H u r b a n o v o - 3, S w i d e r - 4, W i e n - - K o b e n z l - 5.

904 Studia geoph, et geod. 16 (1972)

Page 4: Spectrum of the geomagnetic field in central Europe

Shorter Contributions

't J ~

i), " , . / \ \ ".. / \ . , / x . / " \ . . o

\ ,

z

27 115 9 T ( ~oy )

Fig. 2. Power spect rum o f the componen t s o f the geomagnet ic field for H u r b a n o v o at the t ime when the solar activity is increasing to maximum.

3 /"~ \ :

, \ ~

"

\x I / ~\\ . / " \ . . ~__~"'-'~'L~.

I I I r (eaV) 27 "t2L5 9

Fig. 3. Power spec t rum o f the H - c o m p o n e n t for Fi j rs tenfeldbruck t - - at the t ime o f decreasing solar activity,

. , , 2 - - m in imum activity (e 2 = 0.5eo), 3 at the t ime of increasing solar activity.

I.5

ae "v'-., \ l ~ f\

z7 ~ 5 g ~ r(e*v)

Fig. 4. Power spec t rum o f the geomagnet ic field for W i e n - - K o b e n z l dur ing mi n i mum solar activ- ity: 1 - - H - c o m p o n e n t , 2 - - D-componen t , 3 - - Z - c o m p o n e n t (e s = 0.4eo).

studia geoph, et geod. 16 (1972) 2 0 5

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Kpam~cue cooSulenua

The H-component of the geomagnetic field systematically displays a marked peak of the 13.5-day harmonic and also peaks of the 9-day and 6.75-day harmonics (Figs 1, 4). These har- monics disappear in the overall noise level at the time when the activity of the Sun increases to maximum (Figs 2, 3). Figure 3 illustrates the difference of the spectral composition of the variable geomagnetic field at different phases of solar activity. The 9-day harmonic of the H-component has a quite wide peak, which shows that it is not formed by a single frequency component but by a whole range of neighbouring frequencies.

At the time of increased solar activity the spectrum of the Z-component is most disturbed (Fig. 2). In the D-component spectrum the most disturbed is the 13.5-day harmonic and the 9-day is more expressive than the others (Figs 4, 5), but also the 54-day harmonic can be observed (Figs 4, 6). A peculiarity is that at the time of increased solar activity the D-component is more regular than at the time of minimum activity (Figs 2, 5). The Z-component spectrum, apart from traditional harmonics (Fig. 7), also shows a 54-day harmonic (Fig. 4) although the overall degree of noise is larger. The most expressive is the 27-day variation during minimum of solar

\

5

',,, /a A

i i r(o~,) ~.z 15 9

Fig. 5. Power spectrum of the D-component for the observatories of 1 -- Wien-Kobenzl , 2 -- Ffirstenfeldbruck, 3 -- Prflhonice (e3 = 2e0), 4 -- Tihany (84 = 2e0), 5 -- Hurbanovo.

/ " k \ :\

o.~ im~ o~ I '~' ' ~ I ~ .... ~ ~ 'la~'~

Fig. 6. Power spectrum of the D-component for Ffirstenfetdbruck 1 -- at the time of decreasing solar activity, 2 -- minimum activity (e2 = 0"4eo), 3 -- solar actiVity increasing to, maximum

(~3 = 0"4~0)"

206 studia geoph, et geod. 16 (1972)

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Shorter Contribution

activity. The spectral differences of the components of the geomagnetic field at various levels of solar activity require more thorough investigation using data from a larger number of stations.

Figures 1, 5 and 7 also confirm the dependence of the spectra of the geomagnetic field on the latitude, although the latitudes of the observatories considered differ only little. This dependence can best be seen with the horizontal component of the geomagnetic field.

It should be interesting to investigate in what way the relative amplitude of the harmonics mentioned changes in relation to the amplitude of the 27-day variat ion in dependence on geo- graphic latitude, using suitably chosen stations.

| I I r ( ~ ) 27 ~ 9

Fig. 7. Power spectrum of the vertical component for the observatories of 1 -- Wien--Kobenzl ( q = 0.8eo) , 2 - Ffirstenfeldbruck, 3 -- Hurbanovo (e3 = 2e0), 4 - Tihany (e4 = 28o), 5 --

Prfihonice, 6 - - Wingst.

4. CONCLUSION

The study of auto-spectra will be extended to the analysis of cross-spectra and the coherence between the components of the geomagnetic field for close and distant observatories. In the first case it will help to investigate the possibility of using the continuous part of the spectrum [12], in the second case to clarify the theory of generation of the fluctuations considered.

The investigation of the coherence of the vertical component for close stations will give a pos- sibility of assessing the conductivity (possible anomalies) at various depths according to the harmonic considered, since at small distances the effect of the magnetospheric and ionospheric parameters is negligible and, therefore, the effects of internal sources come forward. This problem will be treated in another paper.

The author wishes to thank Dr. M. H v o 2 d a r a for valuable consultations and Dr. A. E. Co v i n g t on (Canada) for providing the data on solar radiation.

Received 29. 4. 1971 Reviewer: O. Praus

Studia geoph, et geod. 16 (I972) 207

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Kpamnue coo6utenua

References

[1] S. Chapman , J. Bar te ls : Geomagnetism, v. II. Univ. Press, Oxford 1951, 545. [21 R. B. Blackman, J. W. Tuckey: The Measurement of Power Spectra. Dover Publ.,

New York 1958, 50. [31 R. G. Curr ie : The Geomagnetic Spectrum -- 40 Days to 5.5 Years. J. Geoph. Res., 71

(1966), 4579. [4] D. Eckhard t , K. L a m e r , T. Madden : Long-Period Magnetic Fluctuations and Mantle

Electrical Conductivity Estimates. J. Geoph. Res., 68 (1963), 6279. [5] R. G. Curr ie : Magnetic Shielding Properties of the Earth's Mantle. J. Geoph. Res., 72

(1967), 2623. [6] A. D~oden6ukov~i: K ot~zke riegenia probl6mov elektromagnetickej indukcie pre sf6rickfi

Zem. GO SAV, Bratislava 1969 (not published). [7] IO. 13. IIIay6: IlprIMeneaHe roppeamlVIOHnoro ananJa3a ~si~ o6pa6oTra reoqbH3~'~ecrHx

Aamti, ix. H3B. AH CCCP, cep., reodpa3., No 4 (1963), 578. [8] R. J. Banks : Geomagnetic Variations and the Electrical Conductivity of the Upper Mantle.

Geoph. J. R. Astr. Soc., 17 (1969), 457. [9] E. Parzen : Mathematical Considerations in the Estimation of Spectra. Technometrics, 3

(1961), 167. [10] A. E. C o v i n g t o n : Solar Radio Emission at 10.7 cm, 1947--68. R.A.S.C. Jour., 63 (1969),

10775. [11] J. S. Bendat , A. G. P i e r soh Measurement and Analysis of Random Data. J. Wiley,

New York 1966, 292. [12] R. J. Banks, E. C. Bul la rd : The Annual and 27-Day Magnetic Variations. Earth Planet.

Sci. Lett., 1 (1966), 118.

208 Studia geoph, et geod. 16 (1972)