Modelling the core magnetic field of the Earth

1982 ◽  
Vol 306 (1492) ◽  
pp. 179-191 ◽  
Keyword(s):  
Magnetic Field ◽  
Spherical Harmonics ◽  
Secular Variation ◽  
Long Wavelength ◽  
Core Field ◽  
The Core ◽  
The Earth ◽  
High Degree ◽  
Current Systems ◽  
The Magnetic Field

The magnetic field generated in the core of the Earth is often represented by spherical harmonics of the magnetic potential. It has been found from looking at the equations of spherical harmonics, and from studying the values of the spherical harmonic coefficients derived from data from Magsat, that this is an unsatisfactory way of representing the core field. Harmonics of high degree are characterized by generally shorter wavelength expressions on the surface of the Earth, but also contain very long wavelength features as well. Thus if it is thought that the higher degree harmonics are produced by magnetizations within the crust of the Earth, these magnetizations have to be capable of producing very long wavelength signals. Since it is impossible to produce very long wavelength signals of sufficient amplitude by using crustal magnetizations of reasonable intensity, the separation of core and crustal sources by using spherical harmonics is not ideal. We suggest that a better way is to use radial off-centre dipoles located within the core of the Earth. These have several advantages. Firstly, they can be thought of as modelling real physical current systems within the core of the Earth. Secondly, it can be shown that off-centred dipoles, if located deep within the core, are more effective at removing long wavelength signals of potential or field than can be achieved by using spherical harmonics. The disadvantage is that it is much more difficult to compute the positions and strengths of the off-centred dipole fields, and much less easy to manipulate their effects (such as upward and downward continuation). But we believe, along with Cox and Alldredge & Hurwitz, that the understanding that we might obtain of the Earth’s magnetic field by using physically reasonable models rather than mathematically convenient models is very important. We discuss some of the radial dipole models that have been proposed for the nondipole portion of the Earth’s field to arrive at a model that agrees with observations of secular variation and excursions.

scholarly journals Development of an improved geomagnetic reference field of Antarctica

1999 ◽  
Vol 42 (2) ◽  
Author(s):  
A. De Santis ◽  
M. Chiappini ◽  
J. M. Torta ◽  
R. R. B. von Frese
Keyword(s):  
Magnetic Field ◽  
Secular Variation ◽  
Reference Model ◽  
Reference Field ◽  
Spherical Cap ◽  
Core Field ◽  
The Core ◽  
Spherical Cap Harmonic Analysis ◽  
The Antarctic ◽  
Magnetic Observatories

The properties of the Earth's core magnetic field and its secular variation are poorly known for the Antarctic. The increasing availability of magnetic observations from airborne and satellite surveys, as well as the existence of several magnetic observatories and repeat stations in this region, offer the promise of greatly improving our understanding of the Antarctic core field. We investigate the possible development of a Laplacian reference model of the core field from these observations using spherical cap harmonic analysis. Possible uses and advantages of this approach relative to the implementations of the standard global reference field are also considered.

The westward drift of the Earth's magnetic field

1950 ◽  
Vol 243 (859) ◽  
pp. 67-92 ◽  
Keyword(s):  
Magnetic Field ◽  
Secular Variation ◽  
Outer Part ◽  
Earth’S Magnetic Field ◽  
Dynamo Theory ◽  
The Core ◽  
The Earth ◽  
Earth's Magnetic Field ◽  
Harmonic Analyses ◽  
Westward Drift

The westward drift of the non-dipole part of the earth’s magnetic field and of its secular variation is investigated for the period 1907-45 and the uncertainty of the results discussed. It is found that a real drift exists having an angular velocity which is independent of latitude. For the non-dipole field the rate of drift is 0.18 ± 0-015°/year, that for the secular variation is 0.32 ±0-067°/year. The results are confirmed by a study of harmonic analyses made between 1829 and 1945. The drift is explained as a consequence of the dynamo theory of the origin of the earth’s field. This theory required the outer part of the core to rotate less rapidly than the inner part. As a result of electromagnetic forces the solid mantle of the earth is coupled to the core as a whole, and the outer part of the core therefore travels westward relative to the mantle, carrying the minor features of the field with it.

Magneto-inertial waves and planetary rotation

2021 ◽  
Author(s):  
Jérémy Rekier ◽  
Santiago Triana ◽  
Véronique Dehant
Keyword(s):  
Magnetic Field ◽  
Polar Motion ◽  
Density Stratification ◽  
Length Of Day ◽  
Inertial Waves ◽  
Torsional Oscillations ◽  
The Core ◽  
The Earth ◽  
Planetary Rotation ◽  
The Magnetic Field

<p>Magnetic fields inside planetary objects can influence their rotation. This is true, in particular, of terrestrial objects with a metallic liquid core and a self-sustained dynamo such as the Earth, Mercury, Ganymede, etc. and also, to a lesser extent, of objects that don’t have a dynamo but are embedded in the magnetic field of their parent body like Jupiter’s moon, Io.<br>In these objects, angular momentum is transfered through the electromagnetic torques at the Core-Mantle Boundary (CMB) [1]. In the Earth, these have the potential to produce a strong modulation in the length of day at the decadal and interannual timescales [2]. They also affect the periods and amplitudes of nutation [3] and polar motion [4]. <br>The intensity of these torques depends primarily on the value of the electric conductivity at the base of the mantle, a close study and detailed modelling of their role in planetary rotation can thus teach us a lot about the physical processes taking place near the CMB.</p><p>In the study of the Earth’s length of day variations, the interplay between rotation and the internal magnetic field arrises from the excitation of torsional oscillations inside the Earth’s core [5]. These oscillations are traditionally modelled based on a series of assumptions such as that of Quasi-Geostrophicity (QG) of the flow inside the core [6]. On the other hand, the effect of the magnetic field on nutations and polar motion is traditionally treated as an additional coupling at the CMB [1]. In such model, the core flow is assumed to have a uniform vorticity and its pattern is kept unaffected by the magnetic field. </p><p>In the present work, we follow a different approach based on the study of magneto-inertial waves. When coupled to gravity through the effect of density stratification, these waves are known to play a crucial role in the oscillations of stars known as magneto-gravito-inertial modes [7]. The same kind of coupling inside the Earth’s core gives rise to the so-called MAC waves which are directly and conceptually related to the aforementioned torsional oscillations [8]. </p><p>We present our preliminary results on the computation of magneto-inertial waves in a freely rotating planetary model with a partially conducting mantle. We show how these waves can alter the frequencies of the free rotational modes identified as the Free Core Nutation (FCN) and Chandler Wobble (CW). We analyse how these results compare to those based on the QG hypothesis and how these are modified when viscosity and density stratification are taken into account. </p><p>[1] Dehant, V. et al. Geodesy and Geodynamics 8, 389–395 (2017). doi:10.1016/j.geog.2017.04.005<br>[2] Holme, R. et al. Nature 499, 202–204 (2013). doi:10.1038/nature12282<br>[3] Dumberry, M. et al. Geophys. J. Int. 191, 530–544 (2012). doi:10.1111/j.1365-246X.2012.05625.x<br>[4] Kuang, W. et al. Geod. Geodyn. 10, 356–362 (2019). doi:10.1016/j.geog.2019.06.003<br>[5] Jault, D. et al. Nature 333, 353–356 (1988). doi:10.1038/333353a0<br>[6] Gerick, F. et al. Geophys. Res. Lett. (2020). doi:10.1029/2020gl090803<br>[7] Mathis, S. et al. EAS Publications Series 62 323-362 (2013). doi: 10.1051/eas/1362010<br>[8] Buffett, B. et al. Geophys. J. Int. 204, 1789–1800 (2016). doi:10.1093/gji/ggv552</p>

On the determination of the size of the Earth’s core from observations of the geomagnetic secular variation

1981 ◽  
Vol 374 (1756) ◽  
pp. 15-33 ◽  
Keyword(s):  
Magnetic Field ◽  
Secular Variation ◽  
Magnetic Data ◽  
Time Interval ◽  
Perfect Conductor ◽  
Geomagnetic Secular Variation ◽  
The Core ◽  
First Case ◽  
Fractional Error ◽  
The Magnetic Field

When the magnetic field of a planet is due to self-exciting hydromagnetic dynamo action in an electrically conducting fluid core surrounded by a poorly-conducting ‘mantle', a recently proposed method (Hide 1978,1979) can in principle be used to find the radius r c of the core from determinations of secular changes in the magnetic field B in the accessible region above the surface of the planet, mean radius r s , with a fractional error in r c of the order of, but somewhat larger than, the reciprocal of the magnetic Reynolds number of the core. It will be possible in due course to apply the method to Jupiter and other planets if and when magnetic measurements of sufficient accuracy and detail become available, and a preliminary analysis of Jovian data (Hide & Malin 1979) has already given encouraging results. The ‘magnetic radius’ ̄r̄ c of the Earth’s molten iron core has been calculated by using one of the best secular variation models available (which is based on magnetic data for the period 1955-75), and compared with the ‘seismological’ value of the mean core radius, r c = 3486 ± 5 km. Physically plausible values of r̄ c are obtained when terms beyond the centred dipole ( n = 1) and quadrupole ( n = 2) in the series expansion in spherical harmonics of degree n = 1,..., ^ n ,..., n * are included in the analysis (where 2 ≼ ^ n ≼ n *≼ ∞). Typical values of the fractional error ( r̄ c - r c ) / r c amount to between 0.10 and 0.15. Somewhat surprisingly, this error apparently depends significantly on the value of the small time interval considered; the error of 2% found in the first case considered, for which ^ n — n * = 8 and for the time interval 1965-75, is untypically low. These results provide observational support for theoretical models of the geomagnetic secular variation that treat the core as an almost perfect conductor to a first approximation except within a boundary layer of typical thickness much less than 1 km at the core-mantle interface.

The Magnetic Field of the Earth: Paleomagnetism, the Core, and the Deep Mantle

Physics Today ◽  
1997 ◽  
Vol 50 (9) ◽  
pp. 70-70 ◽  
Author(s):  
Ronald T. Merrill ◽  
Michael W. McElhinny ◽  
Phillip L. McFadden ◽  
Subir K. Banerjee
Keyword(s):  
Magnetic Field ◽  
The Core ◽  
The Earth ◽  
Deep Mantle ◽  
The Magnetic Field
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