- Email: [email protected]
A geomagnetic jerk for the end of the 20th century?
Earth and Planetary Science Letters 183 (2000) 369^373
Express Letter
www.elsevier.com/locate/epsl
A geomagnetic jerk for the end of the 20th century? Mioara Mandea *, Eric Bellanger, Jean-Louis Le Moue«l Institut de Physique du Globe de Paris, B.P. 89, 4 Place Jussieu, 75252, Paris, cedex 5, France Received 6 July 2000; accepted 26 September 2000
Abstract The series of magnetic measurements at some European observatories give some hint of a new geomagnetic jerk around 1999. The geomagnetic impulses would present the remarkable and intriguing property to occur with a frequency of one per decade, in the last third of the 20th century. The geomagnetic jerks have been proposed to be indicators which anticipate the changes in the Earth's rotation rate. If this statement is of general validity, the 1992 jerk should be followed by an acceleration of the Earth rotation which would take place now. And, along the same lines, we might predict a new deceleration in less than 10 yr. ß 2000 Elsevier Science B.V. All rights reserved. Keywords: secular variations; annual variations; length of day
1. Introduction Some recent studies of the Sun's magnetic ¢eld have suggested that this ¢eld has possibly a memory [1]; how about the geomagnetic ¢eld? On geological time scales, the Earth's magnetic ¢eld, grossly dipolar, presents stable polarity intervals, with duration of the order of a few hundreds of thousands of years, interrupted by sharp reversals from one polarity to the other. Turning to the historical period for which direct accurate measurements are available, it appears that the temporal variations of the geomagnetic ¢eld cover a wide spectrum which may roughly be divided into
* Corresponding author. Tel.: +33-238339500; E-mail: [email protected]
higher frequencies due to external sources located in the ionosphere and above in the magnetosphere, and longer periods due to internal sources (the dynamo in the outer core). The part of the magnetic ¢eld with its origin in the outer core is known as the main ¢eld and its change in time as the secular variation. The boundary between external and internal sources was formerly thought to be located around periods of at least a few years. However, events of internal origin with time scales of the order of or shorter than 1 yr have been shown to exist, as ¢rst noted by Courtillot et al. [2], and Malin and Hodder [3]. Examination of geomagnetic data from worldwide observatories has indeed revealed sudden changes in the trend of the secular variation, which have been called `geomagnetic jerks' or `secular variation impulses' and have been discussed by a number of authors (see for more details [4^7]). In order to make a systematic study of the jerks which occurred since the beginning of
0012-821X / 00 / $ ^ see front matter ß 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 1 2 - 8 2 1 X ( 0 0 ) 0 0 2 8 4 - 3
EPSL 5638 20-11-00
370
M. Mandea et al. / Earth and Planetary Science Letters 183 (2000) 369^373
Fig. 1. The secular variation of the East magnetic component (dY/dt) for Chambon la Foreªt observatory, from 1883 to 2000 (solid circles) and Niemegk observatory, from 1890 to 2000 (opaque diamonds). The new geomagnetic jerk, around 1999, is present on the both series.
the century, without making any a priori assumption on their existence, location or form, a wavelet analysis was applied to the geomagnetic time series from about one hundred observatories [8]. One of the advantages of this analysis is its high sensitivity to localized events referred to as singularities, de¢ned as discontinuities of some Kth derivative of the signal (K is the regularity of the event). Prior to the 20th century the quality of available data is rather poor and the detection of such events is di¤cult because of the external signal and of the noise [9]. During the 20th century eight events have been detected, three being unquestionably of global extent (1969, 1978, and 1992), three being possibly similarly of global extent (1901, 1913, and 1925), while the remaining two are not seen everywhere at the Earth's surface (1932 and 1949). A problem arising when applying wavelet analysis is that the boundary e¡ects are important and prevent detection events close
to the beginning or the end of the time series. In order to reveal them, when they exist, one must make recourse to a more classical method of analysing the trend of the secular variation. In the following, such a method evidences in Chambon la Foreªt and Niemegk series a new change in the trend of the secular variation, a new geomagnetic jerk, which took place only a few months ago. 2. A new geomagnetic impulse? The following study has been performed on the observatory monthly means (de¢ned as being the averages over all days of the month and all times of the day) of the database we recently created (http:+//+www.ipgp.jussieu.fr). We have simply computed the secular variation of the East magç (t) = netic component of the ¢eld, dY/dt = Y Y(t+1)3Y(t31), with t expressed in months. ç (t) values have then been smoothed with a simY
EPSL 5638 20-11-00
M. Mandea et al. / Earth and Planetary Science Letters 183 (2000) 369^373
ple 12-month running average to get rid of most of the annual variation. These data allow us to detect an event which could be a new jerk (in the ç usual form of a sudden change of slope of the Y curve; by sudden, we mean completed in less than 1 yr), although its full characterization is not yet possible. Jerks in the North magnetic (X) and vertical (Z) components are not so easy to detect as those in the Y (the behavior of Y and of declination (D) are similar) ; removing the external ¢eld e¡ects is more di¤cult for X and Z components because of the geometry of the disturbance ¢elds. Fig. 1 shows the secular variation of the East magnetic component (Y) at Chambon la Foreªt (CLF) and Niemegk (NGK) observatories over time spans of respectively 118 and 111 yr. A clear ç graph appears at the end change of trend of the Y of the time span covered by the data. The new impulse seems to be located around 1999. Some other observatories were considered, with the lengths of time series at the end of 1999 or thereafter. A similar event has been detected in the following European series (indicated by their IAGA code): BFE, DOU, ESK, FUR, HAD, LER, NUR.
371
3. Geomagnetic jerks and changes in the Earth's rotation rate Implications of the observation of geomagnetic jerks for core motions, Chandler wobble or lower mantle conductivity have been recently further analysed [10^12]. Geomagnetic jerks result from a sudden acceleration of the £ow at the top of outer core that is supposed to generate the secular variation at short time scales (less than W102 yr). Flows computed from observatory data show a smooth acceleration during time intervals separated by jerk occurrences at the time of which, on the contrary, an acceleration jump is observed [10]; the geometry of these jumps tends to be conserved from a jerk to the following, whereas the sign changes. Maybe more interesting is the possibility of using these events to predict the changes in the length of the day, as argued in several previous studies which showed a correlation between geomagnetic jerks and rapid changes in the trend of the length of the day (LOD) variation. The jerks lead these trend changes by a few years [13]. This is the way how the long series of the declination ç ) at Chambon la (D) and of its secular variation (D
Fig. 2. Filtered monthly mean values of the secular variation of the declination (dD/dt: full line, left scale) and of the excess length of the day (LOD within a change of sign: dotted line, right scale), from 1962 to 2000. The dD/dt curve is correlated with the variations in the LOD curve and leads it by some 6 yr ( þ 2 yr).
EPSL 5638 20-11-00
372
M. Mandea et al. / Earth and Planetary Science Letters 183 (2000) 369^373
Foreªt observatory were used to successfully predict an acceleration of the rotation rate in the early 1980s [14], and then a deceleration some 10 yr later [15], correlated respectively with the 1969 and 1978 geomagnetic jerks. Changes in the rotation were found to lag changes in the secular variation by 9 þ 2 yr [13] (this is too large a value; see below). In the present study the correlation between the geomagnetic jerks dates and the changes in the LOD is investigated for the 1962^2000 time span, over which daily values for LOD are available, which were used to produce monthly means of LOD to be compared with the monthly means ç at Chambon la Foreªt observatory. An expoof D ç ; the nential smoothing ¢lter was applied to D adjustment was done automatically, in a least ç and, in orsquares sense [16]. The two curves, D der to represent the variation of the rotation rate, LOD within a change of sign, are shown on Fig. ç curve, though well correlated with the 2; the D LOD (within a change of sign) curve, leads it by some 6 yr ( þ 2 yr). A simple forward shift of the ç curve by some 6 yr makes indeed the visual ¢t D satisfactory. Our favored physical mechanism to account for this correlation is the topographic core^mantle coupling [17]. According to Jault et al. [18] the surface £ow is for its main part locked in a speci¢c con¢guration with respect to the core^mantle topography ; departures from this standing con¢guration however occur, notably at the jerk time, which give rise to changes in the secular variation (slightly smoothed by the conducting mantle). The £ow change is very e¤cient to exert, after some time (the velocity ¢eld is continuous in time), a topographic torque capable of accelerating or decelerating the mantle. 4. Conclusions We think it already possible, despite the lack of hindsight, to advance that a new geomagnetic jerk is occurring now, around the end of the 90s. It is fortunate that the magnetic satellite Òrsted is still £ying, giving a new opportunity to investigate this phenomenon.
It is remarkable and intriguing that the geomagnetic impulses occur with a frequency of one per decade in the last third of the 20th century (not before, nor apparently in the 19th century, [9]). These appear to be markers which anticipate the changes in the Earth's rotation rate. If, as we believe, this statement is of general validity, the 1992 jerk should be followed by an acceleration of the Earth rotation which would be taking place now. And, along the same lines, we predict a new deceleration in less than 10 yr, following the new (possible) magnetic event. Finally let us, not to be timid, risk a third prediction. A correlation between geomagnetic jerks and phase changes in the Chandler wobble series was proposed and discussed in [11]. We are also led to predict that a phase change in the Chandler wobble is now taking place or will take place in a close future (say, in a few years at most). Acknowledgements We thank Richard Holme, Susan Macmilan and an anonymous referee for careful, constructive reviews. This is IPGP contribution 1711.[AC]
References [1] R. Olivier, J.L. Ballester, Is there memory in solar activity?, Phys. Rev. E 58 (1998) 5650^5654. [2] V. Courtillot, J. Ducruix, J.-L. Le Moue«l, Sur une acce¨le¨ration re¨cente de la variation se¨culaire du champ magne¨tique terrestre, C.R. Acad. Sci. D 287 (1978) 1095^1098. [3] S.R.C. Malin, B.M. Hodder, D.R. Barraclough, Geomagnetic secular variation: A jerk in 1970, in: J.O. Cardus (Ed.), 75th Anniversary Volume of Ebro Observatory, Roquetes, Tarragona, 1983, pp. 239^256. [4] D.N. Stewart, K.A. Whaler, Geomagnetic disturbance ¢elds: An analysis of observatory monthly means, Geophys. J. Int. 108 (1992) 215^223. [5] M. Alexandrescu, D. Gibert, G. Hulot, J.-L. Le Moue«l, G. Saracco, Detection of geomagnetic jerks using wavelet analysis, J. Geophys. Res. 100 (1995) 12557^12572. [6] S. Macmillan, A geomagnetic jerk for the early 1990's, Earth Planet. Sci. Lett. 137 (1996) 189^192. [7] P. De Michelis, L. Cafarella, A. Meloni, Worldwide character of the 1991 jerk, Geophys. Res. Lett. 25 (1998) 377^ 380.
EPSL 5638 20-11-00
M. Mandea et al. / Earth and Planetary Science Letters 183 (2000) 369^373 [8] M. Alexandrescu, D. Gibert, G. Hulot, J.-L. Le Moue«l, G. Saracco, Worldwide wavelet analysis of geomagnetic jerks, J. Geophys. Res. 101 (1996) 21975^21994. [9] M. Alexandrescu, V. Courtillot, J.-L. Le Moue«l, Highresolution secular variation of the geomagnetic ¢eld in Western Europe over the last 4 centuries: Comparison and integration of historical data from Paris and London, J. Geophys. Res. 102 (1997) 20245^20258. [10] M. Le Huy, M. Mandea, J.-L. Le Moue«l, A. Pais, Time evolution of the £uid £ow at the top of the core. Geomagnetic jerks, Earth Planets Space 52 (2000) 163^173. [11] D. Gibert, M. Holschneider, J.-L. Le Moue«l, Wavelet analysis of the Chandler wobble, J. Geophys. Res. 103 (1998) 27069^27089. [12] M. Mandea, M. Alexandrescu, D. Gibert, J.-L. Le Moue«l, G. Hulot, G. Saracco, An estimate of average lower mantle conductivity by wavelet analysis of geomagnetic jerks, J. Geophys. Res. 104 (1999) 17735^17746.
373
[13] J.-L. Le Moue«l, V. Courtillot, D. Jault, Changes in Earth rotation rate, Nature 355 (1992) 26^27. [14] V. Courtillot, J.-L. Le Moue«l, Geomagnetic secular variation impulses: a review of observational evidence and geophysical consequences, Nature 311 (1984) 709^716. [15] C. Gire, J.-L. Le Moue«l, T. Madden, Motions at the core surface derived from secular variation data, Geophys. J.R. Astron. Soc. 84 (1986) 1^29. [16] E.S. Gardner Jr., Exponential smoothing: the state of the art, J. Forecast. 4 (1985) 1^28. [17] R. Hide, The topographic torque on a bounding surface of a rotating gravitating £uid and the excitation by core motions of decadal £uctuations in the Earth's rotation, Geophys. Res. Lett. 22 (1995) 961^964. [18] D. Jault, G. Hulot, J.-L. Le Moue«l, Mechanical coremantle coupling and dynamo modelling, Phys. Earth Planet. Int. 98 (1996) 187^191.
EPSL 5638 20-11-00
Express Letter
www.elsevier.com/locate/epsl
A geomagnetic jerk for the end of the 20th century? Mioara Mandea *, Eric Bellanger, Jean-Louis Le Moue«l Institut de Physique du Globe de Paris, B.P. 89, 4 Place Jussieu, 75252, Paris, cedex 5, France Received 6 July 2000; accepted 26 September 2000
Abstract The series of magnetic measurements at some European observatories give some hint of a new geomagnetic jerk around 1999. The geomagnetic impulses would present the remarkable and intriguing property to occur with a frequency of one per decade, in the last third of the 20th century. The geomagnetic jerks have been proposed to be indicators which anticipate the changes in the Earth's rotation rate. If this statement is of general validity, the 1992 jerk should be followed by an acceleration of the Earth rotation which would take place now. And, along the same lines, we might predict a new deceleration in less than 10 yr. ß 2000 Elsevier Science B.V. All rights reserved. Keywords: secular variations; annual variations; length of day
1. Introduction Some recent studies of the Sun's magnetic ¢eld have suggested that this ¢eld has possibly a memory [1]; how about the geomagnetic ¢eld? On geological time scales, the Earth's magnetic ¢eld, grossly dipolar, presents stable polarity intervals, with duration of the order of a few hundreds of thousands of years, interrupted by sharp reversals from one polarity to the other. Turning to the historical period for which direct accurate measurements are available, it appears that the temporal variations of the geomagnetic ¢eld cover a wide spectrum which may roughly be divided into
* Corresponding author. Tel.: +33-238339500; E-mail: [email protected]
higher frequencies due to external sources located in the ionosphere and above in the magnetosphere, and longer periods due to internal sources (the dynamo in the outer core). The part of the magnetic ¢eld with its origin in the outer core is known as the main ¢eld and its change in time as the secular variation. The boundary between external and internal sources was formerly thought to be located around periods of at least a few years. However, events of internal origin with time scales of the order of or shorter than 1 yr have been shown to exist, as ¢rst noted by Courtillot et al. [2], and Malin and Hodder [3]. Examination of geomagnetic data from worldwide observatories has indeed revealed sudden changes in the trend of the secular variation, which have been called `geomagnetic jerks' or `secular variation impulses' and have been discussed by a number of authors (see for more details [4^7]). In order to make a systematic study of the jerks which occurred since the beginning of
0012-821X / 00 / $ ^ see front matter ß 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 1 2 - 8 2 1 X ( 0 0 ) 0 0 2 8 4 - 3
EPSL 5638 20-11-00
370
M. Mandea et al. / Earth and Planetary Science Letters 183 (2000) 369^373
Fig. 1. The secular variation of the East magnetic component (dY/dt) for Chambon la Foreªt observatory, from 1883 to 2000 (solid circles) and Niemegk observatory, from 1890 to 2000 (opaque diamonds). The new geomagnetic jerk, around 1999, is present on the both series.
the century, without making any a priori assumption on their existence, location or form, a wavelet analysis was applied to the geomagnetic time series from about one hundred observatories [8]. One of the advantages of this analysis is its high sensitivity to localized events referred to as singularities, de¢ned as discontinuities of some Kth derivative of the signal (K is the regularity of the event). Prior to the 20th century the quality of available data is rather poor and the detection of such events is di¤cult because of the external signal and of the noise [9]. During the 20th century eight events have been detected, three being unquestionably of global extent (1969, 1978, and 1992), three being possibly similarly of global extent (1901, 1913, and 1925), while the remaining two are not seen everywhere at the Earth's surface (1932 and 1949). A problem arising when applying wavelet analysis is that the boundary e¡ects are important and prevent detection events close
to the beginning or the end of the time series. In order to reveal them, when they exist, one must make recourse to a more classical method of analysing the trend of the secular variation. In the following, such a method evidences in Chambon la Foreªt and Niemegk series a new change in the trend of the secular variation, a new geomagnetic jerk, which took place only a few months ago. 2. A new geomagnetic impulse? The following study has been performed on the observatory monthly means (de¢ned as being the averages over all days of the month and all times of the day) of the database we recently created (http:+//+www.ipgp.jussieu.fr). We have simply computed the secular variation of the East magç (t) = netic component of the ¢eld, dY/dt = Y Y(t+1)3Y(t31), with t expressed in months. ç (t) values have then been smoothed with a simY
EPSL 5638 20-11-00
M. Mandea et al. / Earth and Planetary Science Letters 183 (2000) 369^373
ple 12-month running average to get rid of most of the annual variation. These data allow us to detect an event which could be a new jerk (in the ç usual form of a sudden change of slope of the Y curve; by sudden, we mean completed in less than 1 yr), although its full characterization is not yet possible. Jerks in the North magnetic (X) and vertical (Z) components are not so easy to detect as those in the Y (the behavior of Y and of declination (D) are similar) ; removing the external ¢eld e¡ects is more di¤cult for X and Z components because of the geometry of the disturbance ¢elds. Fig. 1 shows the secular variation of the East magnetic component (Y) at Chambon la Foreªt (CLF) and Niemegk (NGK) observatories over time spans of respectively 118 and 111 yr. A clear ç graph appears at the end change of trend of the Y of the time span covered by the data. The new impulse seems to be located around 1999. Some other observatories were considered, with the lengths of time series at the end of 1999 or thereafter. A similar event has been detected in the following European series (indicated by their IAGA code): BFE, DOU, ESK, FUR, HAD, LER, NUR.
371
3. Geomagnetic jerks and changes in the Earth's rotation rate Implications of the observation of geomagnetic jerks for core motions, Chandler wobble or lower mantle conductivity have been recently further analysed [10^12]. Geomagnetic jerks result from a sudden acceleration of the £ow at the top of outer core that is supposed to generate the secular variation at short time scales (less than W102 yr). Flows computed from observatory data show a smooth acceleration during time intervals separated by jerk occurrences at the time of which, on the contrary, an acceleration jump is observed [10]; the geometry of these jumps tends to be conserved from a jerk to the following, whereas the sign changes. Maybe more interesting is the possibility of using these events to predict the changes in the length of the day, as argued in several previous studies which showed a correlation between geomagnetic jerks and rapid changes in the trend of the length of the day (LOD) variation. The jerks lead these trend changes by a few years [13]. This is the way how the long series of the declination ç ) at Chambon la (D) and of its secular variation (D
Fig. 2. Filtered monthly mean values of the secular variation of the declination (dD/dt: full line, left scale) and of the excess length of the day (LOD within a change of sign: dotted line, right scale), from 1962 to 2000. The dD/dt curve is correlated with the variations in the LOD curve and leads it by some 6 yr ( þ 2 yr).
EPSL 5638 20-11-00
372
M. Mandea et al. / Earth and Planetary Science Letters 183 (2000) 369^373
Foreªt observatory were used to successfully predict an acceleration of the rotation rate in the early 1980s [14], and then a deceleration some 10 yr later [15], correlated respectively with the 1969 and 1978 geomagnetic jerks. Changes in the rotation were found to lag changes in the secular variation by 9 þ 2 yr [13] (this is too large a value; see below). In the present study the correlation between the geomagnetic jerks dates and the changes in the LOD is investigated for the 1962^2000 time span, over which daily values for LOD are available, which were used to produce monthly means of LOD to be compared with the monthly means ç at Chambon la Foreªt observatory. An expoof D ç ; the nential smoothing ¢lter was applied to D adjustment was done automatically, in a least ç and, in orsquares sense [16]. The two curves, D der to represent the variation of the rotation rate, LOD within a change of sign, are shown on Fig. ç curve, though well correlated with the 2; the D LOD (within a change of sign) curve, leads it by some 6 yr ( þ 2 yr). A simple forward shift of the ç curve by some 6 yr makes indeed the visual ¢t D satisfactory. Our favored physical mechanism to account for this correlation is the topographic core^mantle coupling [17]. According to Jault et al. [18] the surface £ow is for its main part locked in a speci¢c con¢guration with respect to the core^mantle topography ; departures from this standing con¢guration however occur, notably at the jerk time, which give rise to changes in the secular variation (slightly smoothed by the conducting mantle). The £ow change is very e¤cient to exert, after some time (the velocity ¢eld is continuous in time), a topographic torque capable of accelerating or decelerating the mantle. 4. Conclusions We think it already possible, despite the lack of hindsight, to advance that a new geomagnetic jerk is occurring now, around the end of the 90s. It is fortunate that the magnetic satellite Òrsted is still £ying, giving a new opportunity to investigate this phenomenon.
It is remarkable and intriguing that the geomagnetic impulses occur with a frequency of one per decade in the last third of the 20th century (not before, nor apparently in the 19th century, [9]). These appear to be markers which anticipate the changes in the Earth's rotation rate. If, as we believe, this statement is of general validity, the 1992 jerk should be followed by an acceleration of the Earth rotation which would be taking place now. And, along the same lines, we predict a new deceleration in less than 10 yr, following the new (possible) magnetic event. Finally let us, not to be timid, risk a third prediction. A correlation between geomagnetic jerks and phase changes in the Chandler wobble series was proposed and discussed in [11]. We are also led to predict that a phase change in the Chandler wobble is now taking place or will take place in a close future (say, in a few years at most). Acknowledgements We thank Richard Holme, Susan Macmilan and an anonymous referee for careful, constructive reviews. This is IPGP contribution 1711.[AC]
References [1] R. Olivier, J.L. Ballester, Is there memory in solar activity?, Phys. Rev. E 58 (1998) 5650^5654. [2] V. Courtillot, J. Ducruix, J.-L. Le Moue«l, Sur une acce¨le¨ration re¨cente de la variation se¨culaire du champ magne¨tique terrestre, C.R. Acad. Sci. D 287 (1978) 1095^1098. [3] S.R.C. Malin, B.M. Hodder, D.R. Barraclough, Geomagnetic secular variation: A jerk in 1970, in: J.O. Cardus (Ed.), 75th Anniversary Volume of Ebro Observatory, Roquetes, Tarragona, 1983, pp. 239^256. [4] D.N. Stewart, K.A. Whaler, Geomagnetic disturbance ¢elds: An analysis of observatory monthly means, Geophys. J. Int. 108 (1992) 215^223. [5] M. Alexandrescu, D. Gibert, G. Hulot, J.-L. Le Moue«l, G. Saracco, Detection of geomagnetic jerks using wavelet analysis, J. Geophys. Res. 100 (1995) 12557^12572. [6] S. Macmillan, A geomagnetic jerk for the early 1990's, Earth Planet. Sci. Lett. 137 (1996) 189^192. [7] P. De Michelis, L. Cafarella, A. Meloni, Worldwide character of the 1991 jerk, Geophys. Res. Lett. 25 (1998) 377^ 380.
EPSL 5638 20-11-00
M. Mandea et al. / Earth and Planetary Science Letters 183 (2000) 369^373 [8] M. Alexandrescu, D. Gibert, G. Hulot, J.-L. Le Moue«l, G. Saracco, Worldwide wavelet analysis of geomagnetic jerks, J. Geophys. Res. 101 (1996) 21975^21994. [9] M. Alexandrescu, V. Courtillot, J.-L. Le Moue«l, Highresolution secular variation of the geomagnetic ¢eld in Western Europe over the last 4 centuries: Comparison and integration of historical data from Paris and London, J. Geophys. Res. 102 (1997) 20245^20258. [10] M. Le Huy, M. Mandea, J.-L. Le Moue«l, A. Pais, Time evolution of the £uid £ow at the top of the core. Geomagnetic jerks, Earth Planets Space 52 (2000) 163^173. [11] D. Gibert, M. Holschneider, J.-L. Le Moue«l, Wavelet analysis of the Chandler wobble, J. Geophys. Res. 103 (1998) 27069^27089. [12] M. Mandea, M. Alexandrescu, D. Gibert, J.-L. Le Moue«l, G. Hulot, G. Saracco, An estimate of average lower mantle conductivity by wavelet analysis of geomagnetic jerks, J. Geophys. Res. 104 (1999) 17735^17746.
373
[13] J.-L. Le Moue«l, V. Courtillot, D. Jault, Changes in Earth rotation rate, Nature 355 (1992) 26^27. [14] V. Courtillot, J.-L. Le Moue«l, Geomagnetic secular variation impulses: a review of observational evidence and geophysical consequences, Nature 311 (1984) 709^716. [15] C. Gire, J.-L. Le Moue«l, T. Madden, Motions at the core surface derived from secular variation data, Geophys. J.R. Astron. Soc. 84 (1986) 1^29. [16] E.S. Gardner Jr., Exponential smoothing: the state of the art, J. Forecast. 4 (1985) 1^28. [17] R. Hide, The topographic torque on a bounding surface of a rotating gravitating £uid and the excitation by core motions of decadal £uctuations in the Earth's rotation, Geophys. Res. Lett. 22 (1995) 961^964. [18] D. Jault, G. Hulot, J.-L. Le Moue«l, Mechanical coremantle coupling and dynamo modelling, Phys. Earth Planet. Int. 98 (1996) 187^191.
EPSL 5638 20-11-00