A Model of Virtual Geomagnetic Pole Motion During Reversals

Physics of the Earth and Planetary Interiors 115Ž. 1999 173±179 www.elsevier.comrlocaterpepi

A model of virtual geomagnetic pole motion during reversals

V.V. Kuznetsov ) Institute of Geophysics, Siberian Branch of Russian Academy of Sciences, Geophysical ObserÕatory, Koptyug AÕenue 3, 630090 NoÕosibirsk, Russian Federation Received 23 January 1998; received in revised form 10 August 1998; accepted 14 March 1999

Abstract

A new model of virtual geomagnetic pole motion during a reversal of the Earth's magnetic field is proposed. The model is based on the idea that the geomagnetic field is the summation of the dipole field and the field of global magnetic anomaliesŽ. GMAs . At the time of a reversal, the dipole field changes its sign and the field of the GMAs remains non-zero. The geographic location of the global magnetic anomaliesŽ. Canadian, Brazilian, Siberian and Antarctic are close to the 908W and 908E meridians; this defines the paths of the virtual pole drift at the time of a reversal. q 1999 Elsevier Science B.V. All rights reserved.

Keywords: Virtual geomagnetic pole; Motion; Reversals

1. Introduction ber of suggested models is increasing, which shows that this problem of interest to the scientific commu- During the last 10 years, magneticians have taken nity, and for the present has not been resolved. Let an interest in a phenomenon discovered in palaeo- us consider the problem more closely. magnetism. It has been found that during a reversal, ClementŽ. 1991 has shown that the distribution of the virtual geomagnetic polesŽ. VGP move through VGP paths on the Earth's surface possessed symme- the Central Asia and Australia or through North and try during the Matuyama±Brunhes geomagnetic re- South AmericaŽ. see Fig. 1 . Both paths are close to versal. He found that VGPs were spread over the the 908 meridian in the eastern and western hemi- entire Earth's surface, but that the greatest number of sphere. Some papers are devoted to studying the determinations during the Matuyama±Brunhes geo- VGP drift directionsŽ Koci, 1990; Clement, 1991; magnetic reversal lay within the region 608W"308. Tric et al., 1991; Constable, 1992, 1993; Jackson, At the same time, the antipodal part of VGP occu- 1992; McFadden, 1992; Gubbins, 1993; Gubbins and pied a corridor along 1108E"308. Tric et al.Ž. 1991 Coe, 1993; Hollerbach and Jones, 1993; McFadden have studied the distribution of VGP drift trajectories et al., 1993. ; other papers consider possible drift during the Upper Olduvai reversal and they have models based on the concept of the dynamo mecha- selected two cases: the change of geomagnetic field nism of the geomagnetic field generation. The num- polarity from reverse to normalŽ. R™N and the change from normal to reverseŽ. N™R . The VGPs ) E-mail: [email protected] moved only through the American continents. The

0031-9201r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S0031-9201Ž. 99 00075-8 174 V.V. KuznetsoÕrPhysics of the Earth and Planetary Interiors 115() 1999 173±179 authors believe that in this case VGPs ``prefer'' to Our computer model permits us to change the move through the Americas but not through Asia and field source intensitiesŽ within the magnitudes fixed Australia. by the magnetic observatories closest to the pole. KociŽ. 1990 has noted an interesting peculiarity of and to choose the velocity of the magnetic poleŽ. MP VGP drift during the reversal that occurred after the drift to correspond to the velocity determined by Jaramillo epoch. The VGP drifted from the southern Canadian magneticians based on observations in hemisphere northward from 908Sto208S, at which 1974, 1984 and 1994. I have used this model and the point, its path was interrupted; VGP occurred again data of the magnetic observatories closest to the pole only at latitude 408N, moving along the 908E merid- in 1994 to estimate the location of the NMP in 1994. ian. Some authorsŽ Clement, 1991; Gubbins and Subsequent direct observations, made in the region Coe, 1993.Ž. think that at the time of a N™R of NMP by Newitt and BartonŽ. 1996 in May 1994, reversal the VGPs move along the ``Asian path''; have confirmed the correctness of my prediction during aŽ. R™N reversal they move along the Ž.Kuznetsov, 1996 and, thus, the validity of my ``American path''. model. The measured velocity of the recent motion The problem of the VGP-drift during reversals of the poles is 10±15 kmryearŽ Peddie and Zunde, has recently been considered in papers by Gubbins 1987; Newitt and Barton, 1996. which is more than and SarsonŽ. 1994 , McFadden and Merrill Ž. 1995 the drift velocity of the palaeopoles by a factor of and Fuller et al.Ž. 1996 . The authors of these papers 100 000Ž. Courtillot and Besse, 1987 . Note the fact have analysed previous attempts to explain peculiari- that during a reversalŽ which lasts about thousand ties in the VGP drift, which were based on the years. the MP must drift with a velocity on the order magnetic dynamo model. They have concluded that of 10 kmryear. Can the conclusion be made that a at the present time this phenomenon is not well reversal of the Earth magnetic field is happening at understoodŽ. Fuller et al., 1996 . the present time? Can the model of recent pole motion be used to explain the drift trajectories during the time of a reversal? In this paper I will try to 2. Model answer the second question. HopeŽ. 1959 was probably the first to postulate Four global magnetic anomaliesŽ. GMA are dis- that global magnetic anomalies influence the drift of tinguishable on a total intensity map of the geomag- the North Magnetic PoleŽ. NMP . To develop this netic field, namely CanadianŽ. CMA , Brazilian idea further, I decided to simulate the magnetic field Ž.BMA , Siberian Ž. SMA and South Ž Antarctic . in Arctic. It turned out that three magnetic field Ž.ŽAMA Barraclough, 1987 . . As one can see from sources were necessary in order for the calculated Fig. 1, these anomalies are placed on the path of pattern of the magnetic field lines to reproduce the VGP motion during the time of a geomagnetic field real pattern, not two sources as Hope thought. I reversal. Using the ideas put forward in the model of speculated that the two sources were the Canadian the recent motion of MP, we will try to explain this and Siberian anomalies, but where was the third phenomenon. In doing so, we assume that when the source located? It turned out that the third source dipole component changes its sign, and that the determined the dipole field position and was located GMA field exists for a time period longer than the at the pointŽ. 708N, 2708E . In a similar manner, the polarity change period. According to our model, the field in Antarctic was calculated. Here, only two generation of the dipole part of geomagnetic field sources were necessary: the dipole field source and occurs on the inner core boundaryŽ in Bullen's F- the field of the SouthŽ. Antarctic anomaly. Both layer.Ž Kuznetsov, 1990 . . In this layer, a phase sources were on the 1408E meridian at latitudes of transition happens and electric processes arise to approximately 858 and 508S, respectively. Thus, the accompany to it. A radial hydrodynamic stream of longitudes of the sources of the dipoleŽ. main geo- matter can occur. Let us imagine such stream of magnetic fieldŽ. 1408E and 2708E did not coincide matter in the form of a Rossby vortex with good with each other or with the geomagnetic pole longi- electric conductivity. With availability of the dipole tudeŽ. Kuznetsov, 1990 . magnetic field frozen in the stream, the vortex is the V.V. KuznetsoÕrPhysics of the Earth and Planetary Interiors 115() 1999 173±179 175

Fig. 1. Tracks of the VGP drift during a reversal and the locations of the global magnetic anomalies:Ž. 1 Canadian, Ž. 2 Brazilian, Ž. 3 Siberian andŽ. 4 Antarctic. source of a magnetic field which increaseŽ or de- geomagnetic field is equal to zero. Let us use some crease. the vertical component of geomagnetic field. simple examples to illustrate this. Imagine that there On a magnetic field map the vortex shows itself as a are two magnetic field sources, A and B. As a first GMA. The dipole part of geomagnetic field during approximation, assume that both sources have the the reversal period turns out to be equal to zero, after same polarity and their intensities have a spatial which the magnetic field generated by the Rossby distribution. Let us symbolise the distance between vortexŽ. the GMA field will be non-zero for some themŽ. in geographic degrees as k. Our task is to time. The time during which the generation of the determine the segment y Ž.which is the part of k , GMA field will continue is influenced by the electric where the value Hs0. The necessary equation is: conductivity of the F-layer matter. A sin yyB sin kyy s0. 2 To estimate the distribution of the H component Ž. Ž. on the Earth's surface, it is necessary to know the The solution of this equation is: depth at which the generation of GMA fields takes s r q r place, which is the stream location. According to ctg y Ž.A B cos k sin k. different estimatesŽ Alldridge and Stearns, 1969; If AsB, then yskr2, if As0, then ysk,if s Alldridge, 1980; Kuznetsov, 1990. , the depth x Bs0, then ys0. In a similar manner it is possible 0.2 R, where R is the Earth's radius. The distribution to define the MP location for sources with polarities of the horizontal Ž.H component of the geomagnetic of different signs: field at the Earth's surface is: A sin yyB sin kqy s0. s y r 5 Ž. HA A sin a Ž.1 x cos a r , 1r2 The solution of this equation is: and rs Ž.1qx 2 y2 x cos a Ž.1 ctg ys Ž.ArBycos k rsin k. here, A is the intensity of GMA at its epicentre. Let us define the concept of a MP. We suppose If AsB, then yspykr2, if As0, then ysyk, that it is a point at which the H component of the if Bs0, then ys0. 176 V.V. KuznetsoÕrPhysics of the Earth and Planetary Interiors 115() 1999 173±179

To a first approximation, the Earth's magnetic However, this is not so; therefore, the ``magnetic'' field is a dipole; its magnetic lines ``leave'' the SMP sinusoidal is shifted by 208. The real field differs and ``enter'' the NMP. Let us assume in our two-di- from the idealised one. Fig. 2a shows the distribution mensional model that the magnitude of field along a of geomagnetic field H component intensity along magnetic line is positive if this line is oriented 908E and 908W meridians and the shifted sinusoid clockwise and the magnitude is negative if the line is which denotes the dipole part of the geomagnetic directed anticlockwise. Let us take the SMP as the field. Fig. 2b shows the non-dipole part of geomag- origin of readingsŽ. 08 for two-dimensional fields; netic field. As is clear from our model, the non-di- then the NMP is equal to 1808. If the geographic and pole part of the field is influenced by the sources of MPs were to coincide, then the geomagnetic field GMA field. Therefore, we arrive at the notion that would be sinusoidal with the origin at the SMP. the non-dipole part of geomagnetic field is the sum

Fig. 2.Ž. a Development of the H component of the geomagnetic field along the 908 meridian, and sine curve with the maximum displaced 208 to the west.Ž. b The difference between the curves in Fig. 2a. Ž. c Curves of the source±field source intensity: Ž. 1 H component of the geomagnetic field;Ž. 2 the dipole component of the field; Ž. 3 Brazilian GMA; Ž. 4 Canadian; Ž. 5 Siberian; Ž. 6 Antarctic and Ž. 7 The sum of the source anomalies from 2 to 6. V.V. KuznetsoÕrPhysics of the Earth and Planetary Interiors 115() 1999 173±179 177 of fields of anomalies sources. Fig. 2c shows such a sum of the fields of GMAs and the MP has to scenario. indicate on the epicentre of the closest GMA. It has Let us symbolise the intensities of the sources as been shown by PetrovaŽ. 1990 that the virtual poles follows: A for the dipoleŽ. main field, B for the recorded in Siberia during the Matuama±Brunhes field of BMA, C for the CMA, D for the SMA field reversal are oriented to towards the SMA. This fact and E for the field of the AMA. Assume that in our confirms the validity of our model, from which it model all of the sources are placed along one merid- follows that when As0, the NMP could be at point ian. We take the South Pole as the origin of the Ž.1608 , which is the CMA, or at point Ž. 2108 , which reading. Then in our system of coordinates the loca- is the SMAŽ. see Fig. 2b . At the same time the SMP tion of BMA will be 758 relative to the origin of would be at pointŽ. 3308 , which is in the region s readingŽ. the angle of displacement y1 758 ; the influenced by the AMA. Fig. 2b shows that when s s location of CMA will correspond to the angle y2 A 0, the geomagnetic field can have two MPs in s 1458, for SMA the angle y3 2038, and for AMA the region of the northern GMAs. s y4 3308. The dipole source of the field will be The period during which A remains equal to zero sy ™ displaced in angle by 3408 Ž.y0 208 . The angles is not large, and the previous period, when A 0, a, for which the H component of the magnetic field does not influence the MP drift. The change in pole is equal to zero Ž.Hs0 , correspond to the location position begins when A begins to increase with of the MPs. In our system of coordinates the real inverse sign Ž.yA . Fig. 3 shows the pattern of the s MPs correspond to the following angles a: a1 pole drift that follows from our model. Here the s y y 1688 for the North Magnetic Pole and a2 3358 for magnitude of A increases from 10 to 30 mT. the South Magnetic Pole. Let us write the expression The appearance of the dipole part of geomagnetic for the H component as the sum of the dipole field with inverse sign, even if its magnitude is small component and the sources of the anomalies fields: Ž.about 10 mT , pre-determines the existence of only two MPsŽ. Fig. 3a . The position of the NMP Ž on our HsA sinŽ.aq y yB sin Ž.ay yk 011 scale. is 1808 and that of the SMP is 3308. With a y y y y C sinŽ.a yk22D sin Ž.a yk 33 further increase in A the MPs begin to move in Ž sy m yE sinŽ.ayyk,3 Ž.space, and new MPs also appear A 15 T, Fig. 44 3b. . This figure notes the ``birth'' of two ``new'' sw y y xwr y y here, k1 1 0.2 cosŽ.a ki 1 0.4 cosŽa polesŽ. the angle is about 908 . With a further increase x5r2 s ki. , Ž.i 1,2,3,4 . If this expression is set equal to in A, the new poles begin to move apart while the zero, the solution of this equation will determine the former MPs draw togetherŽ. Fig. 3c, Asy20 mT. locations of the MPs a12and a . In this case, the magnetic field becomes quadrapolar The optimum solution is obtained for: As20 Žattention is drawn to the fact that the quadrapole mT, Bs4 mT, Cs6 mT, Ds9 mT and Es4 mT. character of the Earth's magnetic field during rever- These values give the best agreement between the sal was noted in a paper by Fuller et al.Ž. 1996 ; calculated H component and the observed H com- however, the authors did not explain how such a ponent. In the process, the angles y and the coeffi- field structure could arise. . The two former poles cients k were not changed. This situation is pre- continue to draw together and are eventually annihi- sented in Fig. 2c. The largest discrepancies in the latedŽ see Fig. 3d, where Asy23 mT, the annihila- curves occur between the angles 308±908 and 1808± tion anglef2408.. In Fig. 3e, the dipole component 2408. For other angles, there is good agreement reaches a magnitude Asy20 mT, and the magnetic between the curves. field assumes a pronounced dipole character, with the MPs occupying the positions: the SMP Ž.f08 and NMP Ž.f1508 . 3. Discussion In our model, VGPs move in both hemispheres. The existence of such a phenomenon as the annihila- The key idea of our model is this: at the time tion of poles explains the ``mysterious'' disappear- when As0, the geomagnetic field is equal to the ance of VGP during their drift. Here only one type of 178 V.V. KuznetsoÕrPhysics of the Earth and Planetary Interiors 115() 1999 173±179

Fig. 3. The change in form of the geomagnetic field curves and the MP positions due to increasing the intensity of the H component of the geomagnetic field with the inverse sign for the different magnitudes A: y10 mTa;Ž.y15 mTb; Ž.y20 mTc; Ž.y23 mT Ž. d and y30 mT Ž.e. reversal is considered, namely N™R. The model is It is necessary to note that with this model the based on the ``residual'' field characteristics of summary field of the GMAs does not fit satisfacto- GMA. We cannot verify what the field of the anoma- rily the real Earth's field at angles 308±908 and lies will be when the dipole part of geomagnetic 1808±2408 Ž.Fig. 2c . The first region is influenced by field has inverse polarity. Therefore, in the context the BMA; the second region is influenced by the of this model we cannot consider the VGP drift in SMA. Perhaps this can be explained by the fact that the opposite direction. Thus, we cannot answer the we used in our model the notion of a GMA as a question: Does the pole drift always take place in radial dipole. If we had represented the anomaly as both hemispheres or are there situation when the an inclined dipole, the fit may have been better. poles change their position along a path in one However, this does not change in principle our model hemisphere only? and the results mentioned above. V.V. KuznetsoÕrPhysics of the Earth and Planetary Interiors 115() 1999 173±179 179

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