Term Variations of the External and Internal Components ... - CiteSeerX

JOURNAL

OF GEOPHYSICAL

RESEARCH, VOL. 91, NO. B5, PAGES 4787-4796, APRIL

10, 1986

Long-Term Variations of the External and Internal Components of the Earth's Magnetic Field J. GAVORET, D. GIBERT, M. MENVIELLE, AND J. L. LE MOUEL Laboratoire de G•omagndtisme,Centre National de la RechercheScientifique, Institut de Physiquedu Globede Paris, France

The present study applies classicaltechniquesof time seriesanalysisto the separation of the external and internal signalsfrom the geomagneticfield. We first differentiatethe data with respectto time in order to get rid of the large secularvariation over the long time span considered(up to 100 years).Next we filter the resulting data to eliminate short-period components of the magnetic signals. We then proceedto identify the external signal by comparingthe long-term variations of the processedcomponents of the geomagneticfield, as measuredat different European observatories,with the long-term variations of geomagneticindices devisedto characterizethe fields from external sources.Finally, we remove the identified external signal from the geomagneticfield seriesand get a satisfactoryestimate of the internal signal. This procedure is facilitated by the different behaviors of the two signalsover the considered time span. The external signal is inherently of recurrent nature linked to solar-terrestrial interaction; it oscillatesaround zero with a maximum amplitude of about 5 nT/yr. The internal signal, on the other hand, displays the characteristicsof a secular trend, combining sustained monotonous behavior over periods of several decadeswith sudden slope variations and reversals; the total range of this internal secularsignalis of the order of 50 nT/yr, far larger than any external contribution. Using the 1883-1983 magnetic seriesat Chambon-la-For•t, the 1890-1983 seriesat Niemegk, and shorter seriesat the United Kingdom observatoriesof Eskdalemuir and Hartland, we have been able to get a coherent overall picture of the secularvariation as measuredin Europe. For instance,the first-order time derivative of the Y (east) component essentiallydisplays an increase in two steps from 1900 to 1925, a monotonousdecreasefrom 1925 to 1969 with a regular steplikesubstructure,and a rapid increasesince 1969, followed by a marked reversal of slope in 1979. These results emphasizethe internal origin of the 1969 jerk and single out, in Europe, a 1979 event of opposite sign, these two features being quite reminiscentof the behavior of the secularvariation during the first quarter of the century.

1.

INTRODUCTION

The time variations of the geomagnetic field are known to

be the result of two primary processes:the so-called secular variation of the main field of internal origin on the one hand and the variation

of the external

field the sources of which

are

located in the ionosphere or further in the magnetosphereon the other hand. The external, or transient, field Bt is itself the sum of a number

of fields from

different

sources

and

with

widely varying geometry, characteristicamplitudes, and time constants.

In the present study we will focus on the long-period variations of the geomagneticfield, say longer than 1 year, using monthly mean values available from magnetic observatories. Now, the elementary signalsin the external field can be, and generally are, of short-scaleduration. Substorm-type variations, for example, have a typical time constant of about 1 hour but, as they also have, at a given station, a preferredsign, averaging processesdo not eliminate them. And if the frequency of occurrenceor/and the amplitude of theseeventsare modulated by a long-period wave (e.g., the annual or the 11year solar variation), they will induce a corresponding longperiod peak in the geomagneticfield spectrum.A similar longperiod signal can be generated by the solar daily variation which has a nonzero mean value on 24 hours at some places and for some components.These considerationsexplain why we shall use in the following both 3-hour activity indices and daily ranges to monitor the long-period variations of the external

field.

The problem of splitting the geomagnetic time series into

their external and internal components, although often addressed,has not yet received a conclusive answer. It had been formerly believed that the longer periods had an internal origin, whereas the shorter ones had an external origin, and that a clear cut existed between the spectra of the two fields. For example, a value of 3.7 years for the boundary frequency was first proposed by Curtie [1966, 1968], then pushed to

longer periods,up to 10 years,by Curtie [1973] and Alldredge [1977], although it was recognized that signals with a clear external origin, such as the 11-year cycle,fell close to the limit [e.g., Yukutake, 1965]. More recently, an internal event of short duration, occurring in 1969, has been singled out and characterized as an impulse of the third-order time derivative of the internal field, i.e., a jerk [Courtillot et al., 1978, 1979; Ducruix et al., 1980; Le Mouk'l et al., 1982; Malin and Hodder,

1982]. This rapid change was claimed by Courtillot and Le Mouk'l [1984] and MacLeod [1985] to be completed within 1 year or so. Thus the time range of interest for the internal field must be pushed toward the short-period side, down to 1 year, and it is most unlikely that any simple spectral analysis of the geomagnetic time serieswill ever lead to a clear separation of the two components. In this paper we addressourselvesanew to the separation of the external and internal signals from the geomagneticfield. We use a method fairly different from the ones used in previous analyses. First, we identify the external signal by comparing the long-term variations of the componentsof the geomagnetic field at different observatories with the long-term variations of some of the various geomagnetic indices devised to characterize

the fields from

the different

external

sources.

Then, after some scaling, we remove the identified external signal from the time seriesof the geomagnetic components in Copyright 1986 by the AmericanGeophysicalUnion.

order to get the internal signal (in particular, we emphasize the internal origin of the 1969 jerk as observed in the European observatories).

Paper number 5B5570. 0148-0227/86/005B-5570505.00 4787

4788

GAVORET ET AL.' LONG-TERM VARIATIONS OF THE GEOMAGNETIC FIELD

In order to get rid of the large secular variation over the long time span considered (up to 100 years), we are led to work with the first- and second-ordertime derivativestit,//t of the time seriesof the element u (u = X, Y, Z; X, north component; Y, east component; Z, vertical component). This requires the use of well-adaptedfilters which will be describedin section 4, after we have carried out a brief analysis of the external field (section 2) and given a description of the data (section3). The resultswe obtain will be discussed in section5. 2.

LONG-TERM

VARIATIONS MAGNETIC

OF THE EXTERNAL

FIELD

The external field is basically linked to the solar activity through two sets of interaction processes:the energy transfer between the solar wind and the earth magnetosphere on the one hand, the ionospheric E layer ionization on the other hand. Although relations exist between these two processes,it is more convenient to study them separately. Only a brief outline of the involved processeswill be given here. 2.1.

Input of Energy From the Solar Wind

The solar wind magnetosphere interaction constitutes a

magnetohydrodynamic (MHD) dynamo, the efficiency of which is regulatedby the geometryof the interplanetarymagnetic field (IMF) and, in particular,by its north-southcomponent B:. When B: is positive(2-4 nT) for an extendedperiod of time (at least a few hours), the efficiencyof the dynamo is usually believed to be minimum [e.g., Baumsohann and FriisChristensen,1984]. In this situation, which may be considered as the "ground state" of the magnetosphere[Akasofu, 1977], the energy of the plasma sheet particles decreases.When such conditions last for a few days, the energy of these particles becomes very low (< 1 keV), even in the central part of the sheet:

this relaxation

time

constitutes

one characteristic

time

constant of the magnetosphericbehavior. When B: becomes negative, i.e., takes a southward direction, the dynamo efficiencyincreasesand the magnetosphere no longer remains in the ground state. The auroral convection electrojetsare greatly enhanced and energy coming from the solar wind is rapidly stored in the magnetotail. The mag-

netospherethen tends to release sporadically,within a few hours [BerthelJer, 1977; Svalgaard, 1978-], the accumulated energyinto the forms of kinetic energyof auroral particlesand Joule heat energyin the ionosphere,as well as into the forms of kinetic energy of particles in the plasma sheet.This release of energy event is named by Akasofu [1977] a "magnetosphericsubstorm." The geomagnetic effects associated with magnetospheric substormsmake up most of the irregular activity and different geomagneticindiceshave been elaborated to characterize this activity, the morphology of which dependsupon the latitude. At auroral latitudes the irregular activity is linked to the auroral electrojets.It is a nighttime activity, and both its morphology and its time constantsare highly dependenton the level of activity. It is monitored by the auroral AE indices.At subauroral latitudes the irregular activity is mainly made up of variations generated by auroral jets, field-aligned currents, and the ring current. Its characteristic time constants are smaller than 3 hours, and it is monitored by the 3-hour am or aa indices. At low latitudes, finally, the observedirregular activity is mainly related to the ring current. It is monitored by the Dst index. (See Mayaud [1980] for a comprehensivedescription of these indices.) All the magnetic variations monitored by the geomagnetic

indicesare ultimately related to the sameenergyinput, i.e., the kinetic energy of the solar wind plasma. The long-term variations of the associatedindices are then expectedto display similar behaviors. This will indeed be verified in section 5.

We will thus be able to characterizethe long-term variations of Bt of magnetosphericorigin by the aa index series, for which a homogeneousand reliable data set from 1868 onward [-Mayaud, 1973; 1980] is available. 2.2. IonosphericIonization Degree

Ionosphericionization degreedependson both electronprecipitations from the magnetosphereand the flux of solar extreme ultraviolet (EUV) and X rays. The electron precipitationsfrom the magnetosphere,basically linked to the auroral activity, occur at auroral latitudes during magnetosphericsubstorms.The long-term variations of the associated magnetic effects can then be monitored by thoseof the aa index (seesection2.1). There is a close relationship between the long-term variations of the ionization degreeof the daytime ionospheredue to the EUV and X ray fluxes and that of the Wolf relative sunspot number R •Reid, 1972]. It follows that such a relationshipdoesalso existbetweenthe sunspotnumber and the intensity of the solar daily variation S. (This variation S indeed resultsfrom the drifting of the ionized particlesby the thermal atmospheric tides across the lines of force of the earth's magnetic field.) This latter relation was early recognized I-Ellis, 1880; Maurain, 1926-]and discussedby Chapman and Barrels [-1940-1. In section5 we will give a new illustration of the close relationship between the long-term variations of S and R.

We will thus be able in fine to characterizethe long-term variations of Bt, due to the modulation of the amplitude of the solar daily variation S, by the Wolf number R seriesfor which an homogeneousand reliable data set is available from 1749 onward.

2.3. Practical Monitoring of the Long-Term Bt Variations

Accordingto the previousdiscussion,we will try to represent the long-term variations of the external field B, by a weighted sum of the aa index and the Wolf number R. Let Xt(Oi), Yt(Oi),and Zt(O•) be respectivelythe north, east, and verticalcomponentof B, as measuredat the ObservatoryO•. Then

2,(o,) = •x(o,)•

+/•x(o,)a

•tt(Oi)= O•y(Oi)•-• -4-l•y(Oi)• 2,(o,) = •z(O,)• + l•z(O,)g where t2 denotes the long-term behavior of u (over time periodslarger than 1 year). O•x(Oi),yr(Oi), O•z(Oi) , flx(Oi), flr(Oi), and flz(Oi) are parameters to be adjusted, y being dimensionlessand fl having the dimensionof a magnetic field. We have adjusted these parameters for the subauroral observatoriesof Niemegk, Eskdalemuir, Hartland, and Chambon-la-Forbt. 2.3.1. Adjustmentof the otparameters. As recalled in sec-

tion 2.1, the B, variations of magnetosphericorigin depend principally on the ring current activity on the one hand and on the field-alignedcurrent and auroral electrojetactivitieson the other hand.

The magnetic field BRCrelated to the ring current has

approximatelya p•0 geometry,and thus, at a given latitude L, its componentscan be estimated to (BRccos L, O, --BRCsin L). The time variationsof BRCare monitoredby the Dst index. Furthermore, as argued in section2.1 and shown in

GAVORET ET AL.' LONG-TERM VARIATIONS OF THE GEOMAGNETIC FIELD

section 5, the long-term variations of Dst and those of aa are nearly identical within a scaling factor, which is found experimentally to be -2. Within this approximation, the long-term variations of the north and vertical components of B}tc are

then --2•-• cosL and + 2•-• sin L, respectively. The magnetic field BACrelated to the field-aligned currents and the auroral electrojets does not exhibit such a simple geometry. Simple considerationsbased on the time scale and amplitude of their variations lead us to estimate that BAC contributesto the Xt, Yt,and Zt monthly mean values by an amount containedwithin 50% of the correspondingaa mean value.

FC

/------•

.,oo

I

.•o_

Io36•

.•o.

it/'\ •

,•20

ß

ß• ß

If•x

.,•.

tL/

.,,o_

Thus

•x(Oi) = --2 cos L(Oi) + ax(O•) with --0.5 < ax(O•) < 0.5 %(Oi) = ar(Oi)

with --0.5 < ar(Oi) < 0.5

•z(O•) = + 2 sin L(O•) + az(Oi)

with --0.5 < az(00 < 0.5

ß •,0

The final ax(O0 (respectively,ar or az) values at the different observatories are experimentally adjusted so as to make the variations of the time seriesX - •xaa (respectively,Y - •raa or Z- •zaa) and that of •-• as decorrelatedas possible(see •ection 5 for illustrations). We have, of course, performed this adjustmentfor time periodsexcludingany jerk of secularvarihtion, that is, for 1926-1968. As a first approximation we find

./," / / I

I 'x 'x "..',

I o••-V-• 72

F' , 60

48

, ',

36

24

,

•

12

,

•

0

, 12

;

, 24

,•h 36

••' 48

•

72

MONTHS Fig. 2. Impulse responsefunctions of the composite filter FC of diCerent G•ussi•n filters Gin. The p•mmeter • of the norraM distribution

function

•nd

the hMf

width

m of the G•ussi•n

•lt•

the monthly mean value of u for all hours and the monthly

For all observatories

At Chambon

4789

mean value

of u for that hour

where

S is minimum

in the u

component (Figure 1). The long-term variations of d(X), d(Y), and d(Z) at the different observatories are then found to be

la For•t

identical within a scaling factor and moreover proportional to those of m(X), m(Y), and m(Z). For instance at Chambon la For•t, we find that

0.3

At Hartland and Niemegk

m(X) 0.4

0.3

m(Y) •- 0

d(X)

At Eskdalemuir

0.5 For all observatories

•zz= 1

2.3.2. Adjustmentof the • parameters. As recalled in section 2.2 the Bt variations of ionospheric origin are directly linked to the solar daily variation $. During the night hours, $ is nearly zero, and the night level can be taken as its reference level. Thus, for a given component u (X, Y, or Z) and for a given month, the $ contribution to the monthly mean value of u is equal to the difference re(u) between the monthly mean value of u for all hours and the monthly mean value of u for

nighthours (Figure1). Unfortunately, m(u)is small, and in order to get more accurate results,one is led to compute the differencesd(u) between

4.

4'REFERENCE NIGHT LEVEL4. 4.4..9:__• -,4--- -- 4' Fig. 1. Sketchof the daily variation of componentu of the geomagnetic field, illustratingthe quantitiesm(u)and d(u).

0.2

d(Z)

In order to determine the fi parameters, we have first scaled the long-term variations of d(u) to that of the Wolf number R. Then, using the values of the 0•coefficientsdetermined as described previously, we adjust the fi coefficientsso as to carefully fit the variations of the synthetic signal components Xt(Oi), Yt(00, Zt(O•) with that of the correspondingcomponents of the geomagneticfield. As a first approximation,we find for all observatories'

fix = - 3.10-2 nT 3.

fir = 0

fiz = 1.10-2 nT

THE DATA

We have analyzed the monthly mean values series of the componentsX, Y, Z of the earth's magnetic field, measured at four European observatories, namely, Chambon-la-For•t, Eskdalemuir,Hartland, and Niemegk. 3.1.

HOUR (LT)

m(Z)

Original Data From Magnetic Observatories

In the 1975 issue of Niemegk Jahrbuch, the series of monthly mean values of X, Y, Z are published for all the years 1890-!975 but 1945. From 1976 to 1982 these data are published in the correspondingannual reports. The seriesof monthly mean values of X, Y, Z at the United Kingdom (U.K.) observatories have been calculated from the hourly data for the horizontal component H, declination D, and vertical componentZ (sent to us as magnetic tape recordings by the officersof these observatories).We have thus been able to obtain monthly mean values at Eskdalemuir from 1911 to 1982 and at Abinger and Hartland from 1926 to 1982.

4790

GAVORET ET AL.: LONG-TERM

VARIATIONS OF THE GEOMAGNETIC FIELD

0.9

•L ,---' - o

..--

,

x,• _-

,

,

-•-,•

_, ,.z

T----,•--

.

' --•--"'

,J

' /'% •.

•

.,

//•'"'x".,

' '

'

'

d(Y) ......

•' '

R

....

19•1,5 1929,5 1939,,$1949,5 'I 19595 o.?_

// ',,•

o •0o,

/-'"\.

a./ ',

• - ß ."""•'1ß . /9525

0.6

196•5

. • . - - i•9725

Fig. 5. First-order time derivative, FC filtered, of the Wolf number R series (arbitrary units) compared with that of the daily range d(Y) at Chambon-la-For•t (1920-1961) and at Niemegk (1951]950).

o.5

0.4

0.3

Niemegk: By comparison with the other observatoriesand after having taken account of the secular variations, we have been able to reconstruct the missing data for 1945 and we have been led to shift downwards by 207 the data prior to

O.2

0.1

1945. 0

12 2•

36 •8

f•o 72 8& 96

•

•

•

•

•56 •

•

•92 •

•6

228 2• •

•

2• 2•

•

T (months)

Fig. 3. Transferfunctionsof the composite filterFC and of different Gaussian

filters Gm.

3.2.2. The Y component. Niemegk: Using the sameprocedure as for the X component,we have been able to reconstruct the missing data for 1945. We have brought no other further modification to the original data. 3.2.3. The Z component. Difficulties in getting accurate

The series of monthly mean values for X,

Y, Z at

Chambon-la-For•t(previouslyParc St Maur and Val Joyeux) have beencalculatedfrom H, D, Z data for the period 18831982. For all theseobservatories,provisionaldata were used for the year 1983.

valuesof Z before the advent of the proton magnetometerby the end of the years 1950 are indicatedby the large scattering of the correspondingseriesfrom the different observatories. Consequently,we have not been able to make use of the data prior to 1957 except for a comparison between the observatories of Eskdalemuir and Nicmegk for which we went back to 1951.

3.2.

Corrected

Data

A major difficulty one often encountersin magneticobservatories is to define and keep accurate baselines as time evolves.Fortunately enough (from one point of view), the time series analysis which we perform on the data is extremely sensitive to sudden variations in the baseline. This is due to the fact that we calculate first-order time differences of the

previouslysmootheddata. A few nanoteslasstep in the baseline will thus superimposethe characteristicbell shapeof the

3.3. GeomagneticIndices The monthly mean values of the Dst and AE indices have been calculated from hourly values of these indices available at the Word Data Center A (WDC-A) of Boulder (sent to us as magnetic tape recordings);those of the aa indices are published in the IAGA bulletins 32 series.Let us point out that except for the Dst, these indices are free from the difficulties associatedto absolutemeasurements(seesection5).

impulse responseof the filter on the otherwise smooth derived series.As we use noncausal symmetric filters of finite width,

we can easilytrace the observedperturbationto its midpoint and thus locate with a very high precision the time of occurrenceof a steplikevariation in the baseline.A comparison with the behavior at neighbor observatoriesthen providesus with a good estimateof both the sign and amplitude of the step. The major corrections to the data from the different observatories will now be describedfor eachcomponentof the magneticfield. 3.2.1. The X component. Eskdalemuir: We have located right at the end of the year 1933 a jump in the baselinewhich we estimate

to about

-15

nT.

We

have thus been led to

correctthe seriesand subtract157 from all data prior to Janu-

4.

PROCESSING OF THE TIME SERIES

Over a long time span,the evolutionof the differentcomponents of the earth's magnetic field can be fairly accurately representedby a successionof parabolic branches [Courtillot and Le Mou#l, 1976]. Consequently,one method to remove the trend is to use a subtrac.tionprocedure after fitting the data with secondor,derparabolic moving averages. An alternative and softer procedure to get rid of the trend, and which we use in the present study, consists in differentiating the origin•altime series.Moreover, as we are mainly interested in studying long-period variations, the highfrequency component of the signal is eliminated by suitable filtering of the data.

ary 1934.

10-2nT/month • ..'-..' '..•

-'ø o.

//'

....

-

.:',•--.•

. :......

.

:.'".-.

....._

/

-

.

c••,o Iœ\/• / -'•:L_•-•__'•_-•--4-'•'•--'-. •'_•_•_•i_:.__• • _•:• _ , o•--•-•,•-•-•-•

l/

1873

1960,5

Fig. 4.

1965,5

1970,5

1975,5

19•0,,•

First-order time derivative FC filtered, of the geomagnetic indices:aa (solid line), Dst (dotted line), AE (dashedline).

I • •J

1893

J • / •JI •I 1913

•

I

1933

• • . L__ •

1953

I

1973

l_

1981

Fig. 6. First-order time derivative, G60 filtered, of the aa index series(dashedline) comparedwith the Wolf relative sunspotnumber R seriessmoothedwith a 12-month moving average(solid line).

GAVORETET AL.' LONG-TERM VARIATIONSOF THE GEOMAGNETICFIELD

I

....

I

•929,5

....

•939,5

I

'•

•9¾9/5

'

'

I

....

•959,5

4791

•

I

•969,5

•979/,5

Fig. 7. First-ordertimederivative, FC filtered,of the Y component of the geomagnetic fieldat the differentobserva-

tories compared withthatof •raa.C•, Chambon la Forest •z(CLF);C2,Hartland•z(HAD);C3,Eskdalemuir ? (ESK)' C4,Niemegk •z(NIE);A 8ytia = 0.4tia.Notethatin all subsequent figures, curves relating to thedifferent observatories will be represented by the samelinesas in this figure.

4.1.

Differentiation

Successivederivatives of the discrete time series u, are com-

puted by simplefirst differences:

l•t = ldt+ 1 • Idt 4.2.

iit -- ldt+2 -- 2Ut+ 1 -[- ldt

simple moving averagecenteredfilters, 12- and 24-months wide, respectively.This composedfilter (hereafterreferredto as FC) the impulseresponsefunction of which is represented on Figure 2, eliminates most of the periods shorter than 30 months (Figure 3). This filter, which has a rather low smoothing power, will be usedthroughoutfor studyingthe first-order time derivatives of the magnetic series.

Filtering

The secondgroup of filters is obtained by a discretesam-

Two typesof low passfiltersare currentlybeingusedin this study. They differ one from the other by their cutoff frequenciesand by their smoothingefficiencies. The first filter is obtained through the composition of two

1929,5

pling of the normal distributionfunction [(2rr)•/2rr] -• exp (--t2/2o'2). The specificationof these filters requires explicit values of both the variance a 2 and the width (2rn + 1) of the sampling.In order to approximate a continuousfilter, we set

' ' I ' ' ' ' ' I '"""'i•'' 1939,5 •94 9/.5 1959,5

' I ' ' •969,5

'

Fig. 8. First-order timederivative, FC filtered, oftheY component oftheprincipal fieldYv(O•) = Y(00 - •r(O•)aaat the differentobservatories comparedwith that of •raa. SeeFigure 7 for the captionof the differentlines.

4792

GAVORET ET AL.' LONG-TERM VARIATIONS OF THE GEOMAGNETIC FIELD

eliminatemost variationsof period shorterthan about 3 years (Figure 3). Then we are left essentiallywith the l 1-year solar variation and its first harmonic on the one hand, and the filtered eventscoming from the earth's core on the other hand. We first present the results concerningthe magnetic indices, then illustrate the practical way of eliminating the external field variations, and finally turn to the internal field variations themselves.

5.1. Activity Indices and the Wolf Number 1931

Fig. 9.

Second-order time derivative, G60 filtered, of the Y com-

ponentof the principalfield Y,(Oi) = Y(Oi) - •r(Oi)aa at the different observatories compared with that of Eraa. See Figure 7 for the caption of the different

lines.

From the discussionof section2.1 it is to be expectedthat the IAGA magneticactivityindices,aa, am, AE, Dst, display similar behaviorson the long term. This similarity is illustrated by Figure 4 which displaysthe first-ordertime derivatives of these indices, FC filtered. The anomalous behavior of the Dst index in the post "jerk era," from 1973 to 1976 is to be

noticed(on Figure 4 the discrepancyin behavioris spreadby the half width of sampling m equal to 3.4a so that the surface under the normal distribution

curve be covered over 99.93%.

1.5 years beyond each of theselimits by the filtering process). This anomalous behavior was pointed out by Ducruix et al. [1980], who attributed it to a contamination

of the external

This very large width endowstheseGaussianfilters (hereafter signal by the rapid internal variation correspondingto the referred tO as Gm) with a high smoothing efficiency.Their impulse responsefunctionsare given on Figure 2 (a = m/3.4). 1969 jerk. Unlike the other indices, the Dst index actually depends on the absolute values of the X component of the Their transferfunctionsare displayedon Figure 3' they reach earth's magnetic field at the five low-latitude observatories

their asymptoticcontinuous limit exp(-620)2/2) as soonas

2rc/0)= T';>t 2a, which correspondsto the drawn portions of the curves on Figure 3' below T = 2a, the values of the transfer functionsare actually too small to appear on the chosen

used to elaborate it, and its computation involves the elimination of a parabolic shaped secular variation.

The observedsimilarity of the long-periodvariations of the different geomagneticindices, albeit each of them is dedicated to the monitoring of a specific source of the external field,

scale.Th½se;filters, andmostfrequently the 10yearswideG60 version,will be usedthroughoutfor studyingthe second-order appearsto be strongerthan foreseen(P. N. Mayaud, personal

::timederivativesof the magneticseries. 5.

communication, 1984) and deservesfurther consideration. As stated above (section 2.1), this characteristicshould be related

RESULTS

to the fact that all thesevariations are ultimately related to

As stated in the introduction, the purpose of the present study is to characterizethe long-term magneticvariations of external origin by a clear and reproduciblesignaturein order to remove them from the differenttime seriesof the earth's

the same energy input from the solar wind.

The degreeof ionizationof the ionosphereis monitoredby the Wolf number(section2.2).Figure5 displaysthe variations of the Wolf numbertogetherwith the variationsof the daily

magnet!cfield and get a good estimateof the internalorigin

range d(Y) at Chambon la For•t and Niemegk observatories,

(secular) variation. The filterings we use (see section above)

as defined in section 2.3.2. The three time series have been

/\

o-

"

\

/'•1

\

I

-2-

\ \,/ j

/ •

• ....

I ' ' ' '

I ....

I ....

{

INo: ' ' ' • ' '

10. First-order timederivative, FC filtered,of the (-X) component of the principalfieldat thedifferentobservatoriescomparedwith that of (-fx), wherefx = •x aa + •x R. SeeFigure7 for the captionof the differentlines.

GAVORETET AL.' LONG-TERM VARIATIONSOF THE GEOMAGNETICFIELD

4793

I

/'\

0 / '•

'-'"'v L"

-'"'", /'•,,-"

I

'

",,-,,-' \, ; "",i

"Av. ---,

I-

\ •.--.

O-

\

,,

"% /.

{\

r ß

\" /\j r"J

-,.

\

/-".•/•% \•"x• ....,

\

-1-

-2-

-3-

I

i

i

i

929,$

i

I

!

i

i

?939,5

Fig. 11. First-ordertimederivative,FC filtered,of the (-X) componentof the principalfieldXt,(O3 = X(00 -fx at the differentobservatories comparedwith that of (-fx), wherefx = gxaa + fixR. See Figure 7 for the caption of the different

lines.

processed with the FC filter and appearidenticalbut for a few unimportant details.

Finally, some kind of correlation is to be expectedbetween the Wolf number R, characteristicof the solar activity, and the

component at the different observatories,together with the 0.4da serieswhich representsthe first-order time derivative of the averageof 0•r(O•)aa, estimateof the Y componentof Bt taken at the different observatories(cfi section 2). We consider

geomagneticactivity indiceslinked to the solar wind and notably the aa index [Legrandand Simon,1981]. Figure 6 displaysthe first-ordertime derivative(variation)of the aa series, G60 filtered, and its correlation with the Wolf relative sunspot

[• -- %(O3da]as a reasonable estimator ofthefirst-order time derivative •p(O3oftheY component oftheinternal principal

number series. This correlation is indeed spectacular: the da curve crossesthe zero axis with an increasingtrend every time the Wolf number is minimum. Furthermore, the da curve of

displaysclearcut features:a monotonousdecreasingtrend

Figure6 clearlydisplaysa 22-yearperiodicity:a simple"single bump" l 1-year cycle is followed by a more complex "two bumps" cycle. The 22-year magneticcycle of the sun modulates the irregular magnetic activity of the earth's magnetic

fieldBeatobservatory O•.Figure 8represents the•(O•)series, FC filtered. Overthe1926-1983 timespan,thevariation of •,

from 1926 to 1969, followed by a rapid linear increase up to

1979; the slopethen reversessharplyuntil at least 1981.This latter behavioris quite reminiscentof the one at the beginning

!

field.

5.2. GeomagneticField Seriesat the Different Magnetic Observatories

I

5.2.1. Y component1926-1983. Figure 7 showsthe longterm variations of the first-order time derivative •r of the Y

[

•, ,[ ',. ,I

•.-;';

•k-/ '--'

•k •' •,• t't'•'• ,'/ "-'L,.. ,-'"' .... '/" \, t •

' •,\•\.

o r

s.!

x

rct'

'q',.-'."-'/

•

'•,/"

/

,,',,,, •,, k

V, ,,-,xj,F'"

/

't•

•

'*

x4,'-"'2, L/

/i

/-

.;

[';','/ /

1•

'93'

,

,--

• 9 58,5

'939

Fig. 12. Se•ond-ordertime derivative,060 filtered,of the (-X)

component of the prin•ipalfieldXp(03 = X(03-fx

at the different

observatoriescomparedwith that of (-fx), wherefx = SeeFigure 7 for the •aption of the differentlines.

19.68•

19 78,5

Fig. 13. First-order time derivative,FC filtered, of the Z component of the geomagneticfield at the differentobservatories compared with that of fz = •z aa + flzR. See Figure 7 for the caption of the different

lines.

4794

GAVORET ET AL.' LONG-TERM

VARIATIONS OF THE GEOMAGNETIC FIELD

'1 o-

-[' I '" I'

k/-

-!

•

/"

•.,,f/ \ •

ß .•

' 1884,5

f.-.\

• [\..,, ."'.•'-., 1l.,,,._, IE•J.,L,.,,•x .5/• x?,,-', ,,, xx\ • -, k. ,F, z• ,

Fig. 16.

o

\ -.-'

/..,'

i

I

1924,5

1944,5

19 64,5

1984,5

First-order time derivative, FC filtered, of the Y component

of the principalfield Ye= Y -- •raa at Chambon-la-ForEt.

t..-4,. '-/", I /./•.• / 'x ', , I-- IlK .\ ', •_,r' //' "\ .,--/r'--• '-. -", r '"-,:•', ,----'? ,o' ','•./ k, '-, /

1904,5

Z components, X is negatively correlated to aa at the Euro-

pean observatories.Thus, in order to keep similar representations of these correlations we have analyzed the (-X) series,sign which will be implicitly meant henceforth in this

\\ ,..,.,:

paper.

Figure 10 showsthe variations of the first order time deriva-

ø.1 ....

, ....

,

tive 3• of the X componentat the differentobservatories, togetherwith the variationsof the quantityfx, FC filtered. (fx-

•x aa + fixR represents an estimation of the external

Fig. 14. First-order time derivative,FC filtered,of the Z compo-

componentXt (section2). The correlationbetweenthe 3• and

tories comparedwith that of fz = Czzaa + l•zR. See Figure 7 for the caption of the different lines.

good estimate of the secular variation of the internal X com-

is spectacular, apart,of course, fromtheseculartrend nentof theprincipalfieldZ•,(Oi)= Z(Oi) -fz at thedifferentobserva- fx series

of the3• variation. We consider 3•t,= 3•-fx a reasonably

ponent. Figure11displays the3?vseries at thedifferent observatories.Again,for the whole 1926-1983time span,the 3?

of the century (see section 5.3 for a further discussionof this similarity). The 1969 jerk is by now well documented [e.g., Courtillot and Le Moub'l, 1984; Malin and Hodder, 1982; MacLeod, 1985], but its sharpnessis particularly spectacularon the pres-

variation is essentiallymade up of a monotonous decreasing trend up to 1971 followed by a rapid increaseup to now. The changeof slopeis lesssharpthan on the Y component'in fact, a 2-year-long "plateau" (1970-1972)separates thesetwo trends

entcurves. Comparing the0.4daseries to the•, one(Figure8) leaves no doubt about the internal origin of the 1969 jerk. As

of the variation. The jerk time could be considered as the time when the monotonous decreasestops (1970). The comparison

forthe1979slopereversal ofthe?, series whichisobserved in

between the3?•,series andthefx one(Figure11)againclearly

Western Europe, we do not know yet what its spatial extension is and what

will be the duration

of the new trend.

This

1979 feature has also been noticed by the Edinburgh team (personalcommunication, 1984) and by Nevanlina [1984]. There is undoubtedly some observational noise and residual

p

demonstratesthe internal origin of the jerk. As in the caseof

theY component, the37•,series present somedepartures from a simple linear decreasingtrend which are coherent from one observatoryto the other and shouldbe consideredas physical. In particular, the 1926-1970 decreasedisplays some steplike

external signalleftonthecurves•r.(Oi)'nevertheless, changes structuresanalogous to that of the Y component. Figure12 presents thevariations of X',, timederivative of 3?v,andthoseoffx.Themostsignificant feature isa change of coherently displayed on thedifferent $/,(Oi)series alongthe level, smoothed by the G60 filtering process,with negative in trend with time constantsof the order of 10-15 years are

1926-1969 decrease,showingsome regular steplikestructures, values till 1971 and positive values after 1971, although this and shouldbe consideredas physicalsignals. simple picture is lessclear than in the Y case. TheG60filtered12,series, timederivative ofthe•, compo- 5.2.3. Z component. It is well known that the Z baselines nents at the different observatories,are shown on Figure 9 were rather poorly defined in magnetic observatoriesprior to together with the second-ordertime derivative 0.4dd of the aa the introduction of proton and optical pumping magnetome-

index.On the 12,curveoneessentially notices a stepfunction centered on 1969.5 and followed by a second step centered on 1978.5 and of opposite sign, smoothed by the filtering process. A more detailed analysis of this phenomenon is given in section 5.4 below.

5.2.2. X component1926-1983.

Conversely to the Y and

ters,by theendof the fifties.ThusFigure13 showsthe 22and da curves(FC filtered) for the 1957-1982 time span only and

Figure14•-

-Jl .... •9s2,s

7•8,.s

7v 6 8,.s

• • 7•,s

Fig. 15. First-order time derivative, FC filtered, of the difference NIE(Z)-ESK(Z).

fz, wherefz = •zaa + l•zR(seesection 2.3).The

1969 jerk can again be observed,but not very clearly. The reason is that the amplitude of the 1969 jerk is quite weak on Z in Western Europe' the zero curve of the Z jerk amplitude crossesFrance and Germany [Le Moub'l et al., 1982, Figure 7]. In fact, if the jerk is interpreted as due to a suddenchange in the accelerationof the fluid at the core mantle boundary(in

84,5

i 19 04, 5

1924, ,.5

!

!

1944, 5

7964,5

Fig. 17. First-order time derivative, FC filtered, of the (-X)

i

1984,,5

compo-

nentof theprincipalfieldX v = X -fx at Chambon-la-For•t.

GAVORET ET AL.' LONG-TERM

VARIATIONS OF THE GEOMAGNETIC FIELD

4795

the frame of the frozen flux approximation), it can then be shown that the secular variation signal is the sum of two terms.

Consideringthe Z component,one can write •½(t)= •½•(t) q-•2(t). •l(t) presents a discontinuity in slopeat thejerk time and its graph is essentiallythe V-shaped curve many examples of which have been given [e.g., Le Mouiil et al., 1982]. On the

contrary,•2(t) hasa continuous first-order derivative. In most placesat theearth'ssurface •l(t) is predominant compared to •2(t), butof course not where•(t) is zeroor weak.Then,like everymagnetic fieldat the surface of a sphere,•(t) haszero lines,whichare not •2(t) zerolines.In the vicinityof these lines(in WesternEuropefor instance) •2(t) masksthe simple •(t) signature. But in sucha place,the gradientof •½•(t)can be expectedto be large {again a general property of magnetic

fieldsat the surfaceof a sphere)anddominatethe •2(t) gradient. It is then worthwhileto computethe differencesin 2(t) between two observatories in order to get an estimate of this gradient.

Figure15 illustrates the FC filtered(•a- •½b) variations(a, Niemegk; b, Eskdalemuir, 16ø of longitude apart) over the period 1951-1982. The similarity of this curve with the corre-

sponding • series (Figure 8)isstriking, withtheapexoftheV again in 1969.5. 5.3. The 1883-1983 Magnetic Seriesof Chambon-la-Fordt Observatory We have measured in the preceding sections the excellent coherence of the X and Y component magnetic series corresponding to the different observatories of Western Europe. Then, in order to get an overall picture of the behavior of the

magnetic field in this area, one may consider the one which has the longest records. We have at our disposal the monthly mean values of X, Y, Z at the French magnetic observatory from 1883 up to now. Three siteswere successively occupied:Saint Maur des Fosses, 7 km east of Paris, from 1883 to 1900; Val Joyeux, 25 km southwest of Paris, from 1900 to 1936; and Chambon-la-ForC•t, 100 km south of Paris, since 1936. An

homogeneousserieshas been built over the whole time span 1883-1983 using the usual site corrections. This series has been checkedand improved using the technique describedin section 3.2.

Figure16 represents the • series, FC filtered. Thecurve displaysthe following clearcut features:it starts with a quiet decreasefrom 1884 to 1902 followed by a rapid increaseuntil 1913; the slope then reversesuntil 1918 when it resumes an increasingtrend up to 1925. From 1925 to 1969 one observes the monotonous decreasingtrend already depicted in section 5.2, followed by the 1969 jerk and the 1979 trend reversal.

All the abovefeaturesare alsofoundon the • seriesat Niemegk for the 1890-1983 time span. Gire et al. [1984] put forward that the 1925 event, which concerns the Western European area, is not a worldwide one; conversely, they propose that a planetary jerk occurred in 1913, which is marked on the

• curveofFigure16bytheprominent 1913-1918 shoulder.

Fig. 19. Second-order time derivative, G48 filtered, of the Y com-

ponentof the principalfield Yp(00= Y(Oi) - •r(OOaaat the different observatories compared with a G48-filtered 12-month-wide step function centered

on 1969.5.

Figure17 represents the J•, series,FC filtered.The curve essentiallydisplays an increasefrom 1900 to around 1915 (the first jerk), a decrease from 1915 to 1970 and finally a new increase,lessrapid than on the Y component.

Figure18 represents thesecond ordertimederivative •, G96 filtered over the same 100-year time span. The curve essentially displays a double bump at the beginning of the century, centered around 1907 and 1920, respectively,with a 20-year duration, then a flat behavior till the 1969 jerk. These results confirm the statements of Gire et al. [1984] based on annual mean values from observatories

distributed

worldwide'

two periods of intense activity, one just after the beginning of the century, the other one after 1969, are separated by a much quieter period. It is then quite understandablethat upon applying a spectral analysistechnique like MESA to the European magnetic seriessincethe beginningof the century, something like a 60-year peak results [Rotanova, 1985]. In our opinion, this does not demonstrate the existence of a true 60-year signal coming from the core [see Malin, 1984] but is merely a consequenceof the approximate 60-year interval separating two periods of similar internal activity. 5.4. Estimation of the Simultaneity of Occurrence of the 1969 Jerk in European Observatories

In former papers [e.g., Courtillot and Le Mou#l, 1984' Malin, 1984' MacLeod, 1985], it has been stated that the jerk occurred "simultaneously" in observatories that are widely apart. Here we will give a further illustration of this statement (but with the limitation of consideringonly European observatories). The jerk is defined as a sudden change of slope of the firstorder time derivative of the geomagnetic field components or as a step in the second-order time derivative [e.g., Ducruix et al., 1980]. This is indeed quite clear on Figure 19 which shows

furthermore thatall the i?,(Oi) curves, G48filtered, crossthe zero line in 1969 within 6 months. Of course,the zero crossing time can depend on the filtering process but to the same extent for all the observatories.

It can then be assessed that the

jerk reaches the different European observatories within a time interval smaller than 6 months. The largest distance between our observatories being 2000 km (EskdalemuirNiemegk), the "phase velocity" of the jerk signal is greater

10-2nT/ ( month?

than 4000 km/yr and can, of course, be much larger. Figure 19 also displays the already quoted feature of the f891

1911

1931

f 9,51

19 71

Fig. 18. Second-ordertime derivative, G96 filtered of the Y compo-

nentof theprincipalfield Yp= Y - •raa at Chambon-la-For•t.

rapiddecrease of the second-order time derivativeof Yewhich crossesthe zero line in 1979 (with the same degree of simultaneity of occurrenceas in 1969). The overall resulting feature, a

4796

GAVORET ET AL.: LONG-TERM VARIATIONS OF THE GEOMAGNETIC FIELD

10-year-wide bump on the acceleration curve could be called a "percussion" of secular variation and is quite reminiscent of the features observed during the first quarter of the century. 6.

differentiating and filtering, actually enables one to simultaneously eliminate short-period signals and one order in the trend. We are left (see Figures 7, 10, and 13) with the neat

picture of regular segmentsof trend modulated by an external signal representingthe signaturesof the magnetic effects associated with magnetospheric substorms and of the solar daily variations.

Magnetospheric substorms can be monitored by the aa index which has been devised by P. N. Mayaud and calculated from 1868 onward, whereas the solar daily variation is closely related to the Wolf number R, the monthly mean value series has existed since 1749. We have then been able to

construct,by simple adjustment of scalingparameters,a fairly good approximation of the external or transient field B,, at Chambon-la-For•t, Eskdalemuir, Hartland, and Niemegk observatories.

We have then simply subtracted Bt from B to obtain a

satisf•!ctory estimateof the internalor principalfield Bv and its secular variation.

This secular variation

as observed at the

European observatories displays, notably for the Y component, a remarkably simple structure: a steady monotonous decreasefollows the two-bump peak of secular variation of the first quarter of the century, up to 1969. Then, since 1969, a new peak is observed which strongly resembles the former one. The approximately 60-year interval separating these two events explains why a 60-year signal is to be found in spectral analysesof the European geomagnetic time series. Furthermore, two other results obtained during the course of this study are worth emphasizing. First, we find new evidence concerning the striking correlation between the longterm variations of the aa index series and the solar activity as measured by the Wolf number R, including a clear echo of the 22-year solar magnetic cycle (Figure 6). The second result is the close similarity presentedby the long-term variations of the various geomagneticactivity indices.A common behavior is, of course,to be expectedsince the ultimate primary source of the irregular activity is the solar wind magnetosphereinteraction. But the close similarity of the corresponding series, albeit each of these indices is devoted to the monitoring of a specific source of the external field, deservesfurther consideration.

Acknowledgments. We are indebted to P. N. Mayaud, B. Picinbono, and D. Gilbert for some fruitful discussions; to C. Mazaudier

and M. Mareschal for critical reading of section 2, and to R. Scheib for compiling the whole 1883-1983 series of Chambon la For•t. This work was supported by Institut National d'Astronomie et de G•ophysique (ATP Noyau grant 1612). Institut de Physique du Globe

de Paris contribution

magnbtiqueterrestre,particulibrementaux hauteslatitudes,Doctorat d'Etat, Univ. Pierre et Marie Curie, Paris, 1977.

Chapman, S., and J. Bartels, Geomagnetism, vol. 1, Oxford University Press, New York, 1940.

CONCLUSION

In order to study the long-term behavior of the earth's magnetic field measured at the European observatories,we have been led to analyze the filtered first-order time derivatives of its three components.The product of the two operators,time

of which

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Courtillot, V., J. Ducruix, and J. L. Le Mou61, Rbponsesaux commentaires de L. R. Alldredge, C. R. Hebd. S•ancesAcad. Sci. Paris, Skr. B, 289, 173-175, 1979.

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(Received March 28, 1985; revisedSeptember 17, 1985; acceptedDecember 12, 1985.)