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Earth's Magnetic Field and Its Wandering Magnetic Poles

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Earth's Magnetic Field and Its Wandering Magnetic Poles GENERAL ARTICLE Earth’s Magnetic Field and its Wandering Magnetic Poles∗ Nandini Nagarajan The Earth’s magnetic field has been a constant source of cu- riosity and wonder, for its ubiquitous use in navigation, the properties of magnetic attraction and the influence and con- nection to celestial phenomena like aurora, sunspots, etc. Records of magnetic measurements exist going back 400 years. Modern measurements, with the addition of satellite-borne observations, provide accuracy and enables understanding of Nandini Nagarajan is a intriguing characteristics of the geomagnetic field. Some of geophysicist who has spent these are: magnetic polarity reversals, wandering of the mag- over 40 years in studies of netic poles and the most fundamental one: the origin of the geomagnetism covering field in the Earth’s interior and the mechanisms that have commissioning of observatories, low-latitude sustained it for over a billion years. geomagnetic phenomena, magnetotelluric field campaigns and studies of Introduction electromagnetic induction for crustal structure and Surface observations of physical properties and potential fields of resource exploration. She has the Earth, provide different kinds of information about the Earth’s worked at the Indian Institute of Geomagnetism and interior, and even, about the fields themselves. We know the cur- National Geophysical vature, rotation speed and angular velocity, mass and angular mo- Research Institute. mentum of the Earth from these observations. Very little is known about the structure and properties of the Earth’s interior, through direct observation or measurements at the surface, and drilling only provide information up to depths ∼10 km. Deeper infor- Keywords mation has been only been inferred from observations of earth- Magnetic field, polarity reversal, axial dipole, polar wander, dipole quakes, gravity and magnetic measurements and laboratory sim- moment, dip pole. ulations of conditions in the interior. Pressure and temperature inside the Earth increase with depth, leading to changes in the viscosity and composition of matter. It is challenging to simu- ∗Vol.25, No.3, DOI: https://doi.org/10.1007/s12045-020-0951-9 RESONANCE | March 2020 363 GENERAL ARTICLE late these properties under laboratory conditions below a certain depth. Therefore, the understanding of processes in the Earth’s deep interior, the core, progresses cautiously, with several caveats and disclaimers, by collating results from laboratory and compu- tational simulations, repeated and more precise measurements, continuing into the 21st century. The nature, shape and The nature, shape and approximate strength of the ‘Earth’s mag- approximate strength of netic field’ has been known, and used for navigation, for many the ‘Earth’s magnetic centuries; the earliest Chinese records dating back to the 12th field’ has been known, De Magnete and used for navigation, century. Gilbert published the treatise describing for many centuries; the the Earth as a dipole, a giant bar magnet, in 1600 CE (previ- earliest Chinese records ously AD). The geomagnetic field and its variations, both rapid dating back to the 12th (∼hours) and slow (∼years) have been observed and studied for century. nearly 3 centuries, and provide insights into both the external in- fluence of the Sun and internal mechanisms within the Earth pro- ducing magnetic variations. The origin and source of the Earth’s field, and its ‘slow (secular) variation’ over tens of years have been a mystery, testing the boundaries of mathematical techniques and observational accuracy. More rapid and noticeable fluctu- ations on the scale of days also seemed to be at odds with the rigidity of the Earth. Defining the Earth’s Magnetic Field The primary definition of the Earth’s magnetic field as approxi- mated by a dipole, was found to have discrepancies. For example, even early navigation, and charts plotted from ship’s measure- ments of declination showed that the location of the North Mag- netic Pole was not coincident with the Earth’s axial poles. The intensity of the field, estimated from moment experiments, and charts showing lines of equal intensity and declination show more irregularity as in Figure 1. To reproduce such observed fields, the concept of quadrupole arrangements was proposed. The simplest multipole magnet is the dipole, then quadrupole (four poles), oc- tupole (eight poles), etc. Any magnetic field can be described as a dipole and its strength approximated by the dipole moment and 364 RESONANCE | March 2020 GENERAL ARTICLE Figure 1. Contours of magnetic field intensity (top) and declination (below) where the blue contours are east and the red are west. (Image credit: http://www.geomag.bgs.ac.uk/ research/modelling/IGRF.html) additional complexity is simulated by an arrangement of dipoles, that would produce quadrupole/multipole fields. This was an at- Carl Freidrich Gauss, tempt to seek a physical model that would replicate the patterns one of history’s most of field intensity observed on the Earth’s surface. The features influential mathematicians, in a noted could be represented as a superposition of multiple dipoles breakthrough in 1838, oriented in the Earth’s core, in addition to the main axial dipole. showed that almost the This is the physical representation of the Earth’s magnetic field. entire magnetic field has to be of internal origin (90%) and could be Carl Freidrich Gauss, one of history’s most influential mathemati- expressed cians, in a breakthrough in 1838, showed that almost the entire mathematically, in terms of spherical harmonics. RESONANCE | March 2020 365 GENERAL ARTICLE Box 1. Superposition of Dipoles and Multipoles It is seen, from the older and even the latest contours of surface field intensity that there are large scale irregularities in the field that could not be modelled by a dipole. A physical representation of the magnetic fields that are not typical dipole fields, is created by superposing additional pairs of dipoles, of varying intensity and orientation. A configuration of such dipoles, oriented at certain angles to each other, is defined as a quadrupole or multipole, The ensuing configuration of field lines and potential surfaces could then describe a more complex field. The significant contributions of the non-dipole, or higher-order terms of spherical harmonic terms, required an equally complex mechanism or model of the Earth magnetic field, within the core. In the absence of an observable mechanism, while theories for the origin of the field were still debated, the physical complexity of the field could be described with a configuration of quadrupoles at certain locations within the Earth. Again, these are representations which help us understand the complexity but do not define the mechanism. Figure A. Field line configurations of a dipole (left) and a multipole (right). magnetic field has to be of internal origin (90%) and could be ex- pressed mathematically, in terms of spherical harmonics, where the coefficients of the sine and cosine terms had physical sig- nificance. This was a mathematical expression of the magnetic field that was validated by fitting it to actual observations. Gauss used spherical harmonics to express the magnetic potential and obtained coefficients in the form of a series – Legendre polyno- mials – by fitting the surface harmonics to the available magnetic data at that time (obtained from limited magnetic observatories and surveys). There are two solutions to the potential expression 366 RESONANCE | March 2020 GENERAL ARTICLE separating that due to internal and external sources: – potential Vi due to sources internal to the Earth (r< RE) – potential Ve due to sources external to the Earth (r> RE), such that V = Vi + Ve. The solutions are given as multipoles or spherical harmonic ex- n −n pansions where Ve varies as r and Vi varies as r . From this, it was deduced that the contributions of the external fields are con- siderably smaller and most of the field intensity is from internal sources. The potential from internal sources is defined as: N n a n+1 V r,θ,φ,t = a gm t mφ + hm t mφ Pm θ , ( ) r n ( )cos( ) n ( )sin( ) n (cos ) n=1 m=0 Where • ϕ = longitude • θ = colatitude • r = radial distance • a = radius of the Earth • n is the degree of the term • m is the order of the term • V is the scalar potential m m • gn , hn are the Gauss coefficients m • Pn cos θ are Legendre polynomials He then demonstrated that these coefficients were close to the coefficients for a field due to a magnetized sphere or a dipole. These Gauss coefficients also delineated the physical form of the field, viz.; the first-order coefficients represent an axial, symmet- ric dipole. Higher-order coefficients represent the deviations from RESONANCE | March 2020 367 GENERAL ARTICLE Figure 2. Representation of the Earth’s magnetic field as a axial, tilted, eccen- tric dipole. (Image source: www.ase.tufts.edu) this, which could also be represented by a configuration of multi- poles, in the form of tilt of the axis, eccentricity, and displacement from the centre of the Earth. This further established an equiva- lence between the patterns of multipole configurations and the coefficient terms. Further, using spectral analysis, Gauss showed that the best fit to the observed field was obtained if the dipole was not purely axial but made an angle of about 11o with the The Earth’s magnetic Earth’s rotation axis. The Earth’s magnetic field is thus defined field is defined as a as a ‘tilted eccentric dipole’, (Figure 2) with a nearly spherical ‘tilted eccentric dipole’, equipotential surface, tilted and offset from the axis of rotation. with a nearly spherical equipotential surface, tilted and offset from the These spherical harmonic coefficients were determined periodi- axis of rotation. cally, providing estimates of the changes in the Earth’s magnetic field over a century (1850–1950). These models with limited ac- curacy needed revision, with more surface measurements, as the need arose for more precise base values for more detailed map- ping of magnetic variations for magnetic surveys, resource ex- 368 RESONANCE | March 2020 GENERAL ARTICLE Box 2.
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