How Can Earthʼs Magnetic Field be Used to Give Evidence for Continental Drift?

A2 Research Brief (2015) Wilfrid Somogyi - 8112

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Table of Contents

Magnetic Rocks ! 3

1.1 The Origin of Magnetic Properties! 3

1.2 Magnetic Domains! 3

Earthʼs Magnetic Field! 4

2.1 Origin of the Main Field! 4

2.2 Periodic Reversal of the Main Field! 5

2.3 Secular Variation! 7

Paleomagnetic Evidence for Plate Tectonics ! 8

3.1 Measuring the Magnetic Field in Rocks! 8

3.2 Apparent Polar Wander (APW)! 8

3.3 Effects of Polar Reversal, Secular Change and Westward Drift! 9

Glossary! 10

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Magnetic Rocks1.1 The Origin of Magnetic PropertiesMany minerals throughout the Earthʼs crust contain Iron, which is well know for itʼs magnetic properties. Ferromagnetic minerals such as magnetite, Fe3O4, are given magnetic properties by the magnetic dipole moment of an electron. The magnetic dipole moment of an electron comes from the fundamental property an electron has, called spin, it causes the electron to act like a small bar magnet12 .

The arrangement of electrons in the orbitals surrounding the nucleus will be in such a way as to produce the lowest possible energy state. What this means is that one electron will occupy each d-orbital before electrons are paired in the same d-orbital3. Iron ions have partially filled d-orbitals4, which accounts for many characteristics including ferromagnetism. The unpaired electrons have the same spin and so many of these electrons across the d-orbitals results in a strong total dipole moment. If the electrons were to pair in the orbitals the opposite spins would cancel each other out and there would be no net dipole moment from the atom.

Fig 1.1! ! On the left, the actual arrangement of electrons in the 3d orbitals. On the right, if the ! ! electrons were to be paired in the 3d orbitals it would raise the energy of the orbitals as a ! ! result of electron repulsion.

1.2 Magnetic DomainsMinerals are composed of multiple domains, each of which exhibits a crystalline structure. The domains vary in size but are generally on the nanometre scale. Within each of the domains the magnetic moments are aligned, however in an unmagnetised mineral the domains are randomly arranged so that their magnetic moments tend to cancel out and the mineral has no net magnetic field. However the magnetic moments can be aligned when a magnetic field is applied to the rock as it is heated above itʼs Curie temperature. Under these conditions the domains which are aligned with the field expand at the expense of surrounding, un-aligned domains. The magnetisation of rocks occurs naturally during their formation due to the Earthʼs magnetic field.

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1 Nave, R. Magnetic Dipole Moment, (2004), HyperPhysics, accessed: http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magmom.html ,28.01.2015.

2 Wolfson, R., Essential University Physics, vol. 1, (2007), Pearson Education Inc., Addison Wesley.

3 Lister, T., Renshaw, J., AS Chemistry, 14-19, (2008), Nelson Thornes.

4 Lister, T., Renshaw, J., A2 Chemistry, 214, (2009), Nelson Thornes.

Earthʼs Magnetic Field2.1 Origin of the Main FieldAlthough the exact processes which produce the Earthʼs magnetic field are still not completely understood, it has been known since the 1950s that it arrises from the dynamo effect within the core. The dynamo effect within the Earth is produced by electromagnetic induction within the outer core56. Electromagnetic induction occures as convection currents cause the electrically conducting molten material of the Earthʼs outer core to circulate, a charge is built up by friction between the various layers. As the core rotates relative to the Earthʼs surface, these outward convection currents are organised into loops by the Coriolis effect78 . The circulating charge forms several current loops. This is why the magnetic field generated by the Earth looks very similar to that of a current loop.

Fig. 2.1"" The circulating electric currents caused by the Coriolis effect produce a magnetic field " " around the Earth.

To understand how the current loops in the Earth are produced we first have to look at convection currents within the outer core. As material close to the core is heated it rises upwards toward the surface where it spreads out, cools and then sinks back down. This produces loops of moving charge. However, if we consider the entire Earth we can see that each convection current has a partner current moving in the opposite direction. This would produce a magnetic field with opposite polarisation and so the Earth would have no net magnetic field. The current loops described initially are produced by the Coriolis effect.

The Coriolis effect can be observed when we consider different reference frames. If we consider the Earthʼs reference frame then we observe the traditional convection currents as described above. However if we consider a reference frame in which the Earth rotates, for example that of the Earthʼs axis, then we see that the currents raditating outwards and dropping inwards are organised into spirals.

To better understand the Coriolis effect we can imagine a spinning disc, with a marble that moves in a straight line along the disk from the centre to the edge. Relative to the spinning disc the marble moves in a straight line, however to an observer watching the spinning disc the marble moves with a curved path. Try to picture the path of the marble through the observers reference frame as both the disc spins away from the

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5 Bott, Martin H. P., The Interior of the Earth, 169-174, (1971), Edward Arnold.

6 Garland, George D., Introduction to Geophysics, 229-233, (1971), W. B. Saunders Company.

7 Nave, R., The Dynamo Effect, (2006), HyperPhysics, accessed: http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magearth.html 18.01.2015.

8 Vandenbrouck, F., Berthier, L., Gheusi, F., Coriolis Force in Geophysics: an Elementray Introduction and Examples, 359, (2000), European Journal of Physics 21.4.

observer and the marble moves towards the edge of the disc. The line traced on the disc by the marble moves away from the observer and so at the start of the cycle when the marble is at the centre, it is closer to the observer than at the end of the cycle when it is furthest from the observer.

Fig 2.2! ! The Coriolis effect shown on a spinning disc. On the left - the system from the reference ! ! frame of the viewer. On the right - the system from the reference frame of the disc.

Fig. 2.3"" Without the Coriolis effect the magnetic field would cancel each other out, and the earth ! ! would have no net magnetic field.

2.2 Periodic Reversal of the Main FieldAt constructive plate boundaries on the ocean floor, tectonic plates pull apart and molten material from the mantle rises to the surface. Initially this molten rock is above the Curie temperature, allowing it to be magnetised by the Earthʼs magnetic field. After rising to the surface it solidfies to form a new sea bed. The solidifed rock is permanetly magnetised in accordance with the prevailent magnetic field surrounding the Earth.

By measuring the magnetisation of the rock surrounding these plate margins we find that the ocean floor is composed of bands with alternating magnetic polarisation, that is to say there are some bands of rock with a magnetic polarisation opposite to the current field surrounding the Earth. We can discount local anomalies in the Earthʼs magnetic field as the source for this reversed polarisation because this reversed polarisation is present along the entire length of the plate bounary.

The real proof of alternating polarisation in the Earthʼs magnetic field lies in the radioactive dating of reversely polarised mineral samples. Some rocks are capable of self-reversal, and so in order to ammount substantial proof we must find several examples of reverse polarity which can be dated to the same period. Fortunately this evidence is available for rocks as old as 360 million years. The time between reversals is extremely varied, with some periods lasting just 106 years and others lasting up to 107 years910.

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9 Garland, George D., Introduction to Geophysics, 296, (1971), W. B. Saunders Company.

10 Bott, Martin H. P., The Interior of the Earth, 165-168, (1971), Edward Arnold.

Fig 2.4! ! A time-scale of magnetic field reversion based on a uniform spreading rate in the South Atlantic Ocean. Periods of polarity in the same direction as the current field are shown in black. Local magnetic anomalies are shown by dotted lines on the left, the numbers assigned to prominent anomalies are also shown on the left11.

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11 Heirtzler, J. R., others, Marine Magnetic Anomalies, Geomagnetic Field Reversals and Motions of Ocean Floor and Continents, 2123, (1968), Journal of Geophysical Research, vol. 73, AMER Geophysical Union.

2.3 Secular VariationSecular variation describes the changes to the Earthʼs magnetic fields on the time-scale of years. The changes were first noted when plotting a graph of the declination in major cities, for example London in 154012. The changes occur in the direction, declination and magnitude of the field. In order to measure secular change, readings must be taken over a period of many days; the greatest change in the field is that which occurs on a daily basis. An average can then be taken from all these readings so establish how the magnetic field changes over 10 or more years1314.

Fig 2.5! ! Mapping of the changes in the Earthʼs magnetic field in London over 430 years15.

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12 Garland, George D., Introduction to Geophysics, 237, (1971), W. B. Saunders Company.

13 Gass, I. G., Smith, P. J., Wilson, R. C. L., Understanding the Earth, 72-75, (1972), The Artemis Press.

14 Bullard, E. C., The Secular Change in the Earthʼs Magnetic Field, 248-257, (1948), Geophysical Supplements to the Monthly Notices of the Royal Astronomical Society 5.7.

15 Gass, I. G., Smith, P. J., Wilson, R. C. L., Understanding the Earth, 74, (1972), The Artemis Press.

Paleomagnetic Evidence for Plate Tectonics3.1 Measuring the Magnetic Field in RocksThe field around a sample of magnetised rock, is the same as that of a bar magnet. In fact, the first magnets to be discovered were sample of magnetite rock. We know from A-level physics that a changing magnetic field will produce an EMF in a coil of wire. Thus, by spinning a sample of rock near a coil we can measure the magnetic field.

A spinner magnetometer works by spinning a magnet between two ends of an iron core, around which a coil of wire is wound. The iron core is magnetised by the spinning magnet, and the field is directed through the core, linking the turns in the coil. As the magnet spins and itʼs orientation changes, the direction of the magnetic field through the core changes producing a change in the magnetic flux, which according to Faradayʼs law produces an EMF in the coil. By placing a voltmeter across the coil we can measure the EMF produced.

As the magnet spins with an angular velocity ω, the angle between the field and the core at time t is given by (1), and so the flux through the coil is then given by (2)

(1)

(2)

According to Faradayʼs law, the EMF is given by the negative rate of change of flux. For a coil with multiple turns this is (3). So in the case of a magnet spinning in a coil, this is expressed as (4).

(3)

(4)

We then solve the differential, to give the equation (5) which describes a cosinusoidal graph, where the maximum EMF is (6).

(5)

(6)

By solving equation (6) for the three perpendicular axis of the magnetic sample, we can describe the magnetic field using three vectors and hence find its direction and magnitude.

3.2 Apparent Polar Wander (APW)By analysing rock samples and determining the direction of their magnetic field, we can know the postion of the poles relative to that land mass. To know the latitude we look at the declination of the magnetic field, that is, the angle at which the field point into or out of the Earthʼs surface. In the Northern Hemishpere rocks have a negative angle of declination, in the Southern Hemisphere, the reverse. Closer to the poles the magnitude of the angle is greater than that at the Equator, and at the Equator it is 0°. To know the orientation of the land mass, we simply align the field lines of the sample with those of the Earth, so that the south pole of the sample points towards magnetic north1617 .

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16 Nield, T., Supercontinent, 197-198, (2007), Granta Publications.

17 Besse, J., Courtillot, V., Revised and synthetic apparent polar wander paths of the African, Eurasian, North American and Indian plates, and true polar wander since 200 Ma, 4029-4050 (1991) Journal of Geophysical Research: Solid Earth (1978–2012) 96.B3

When we take these measurements for samples from the same land mass but with age differences of millions of years, we find that the magnetic poles appear to wander. Intially it was though that this was due to secular change or perhaps an effect, visible only on million year time-scales, linked to pole reversal. However, when we try to combine the APW maps of different continents, we find that they donʼt fit together. It appears as though the poles have wandered differently for different land masses. The explanation for this is that the land masses themselves move. When we overlay the APW maps for now seperate land masses which are believed to have once been joined as part of the same land mass, we find that the overlap perfectly. Giving us evidence for continental migration.

Fig 3.1! ! APW curves for samples from different continents since the Precambrian period. Solid curves show where palaeomagnetic data from three or more levels in geological time follow a fairly consistent sequence. Pole positions are relative to: ■ China; ● Greenland; ▲ Madagascar. Letters refer to PE, Precambrian; E, Cambrian; O, Ordovician; S, Silurian; D, Devonian; C, Carboniferous; P, Permian; Tr, Triassic; J, Jurassic; K, Cretaceous; LT, MT, UT, Lower, Middle and Upper Tertiary18.

3.3 Effects of Polar Reversal, Secular Change and Westward DriftClearly when trying to map the APW, the effects of Polar Reversal and Secular Change must be taken into account. Polar reversal is simple to correct for as it is clear when the poles have suddenly switched. Polar reversal takes just thousands of years, which is a short time in comparison to the hundreds of millions of years over which the continents drift. The direction of the magnetic field in the samples can simply be reversed for according to the direction of the magnetic field at the time.

Secular Change is slightly more difficult to correct for, as some of the samples that are used will have come from rock samples which have cooled past their Curie point over the space of a few years. However, as Secular Change is largely localised, it is possible to average out the magnetic field over a suitable area to obtain the average direction of the field.

Westward drift is a fairly simple phenomenon, in which the magnetic field appears to drift Westward over time. It is explained simply by the fact that the outer core, which produces the Earthʼs magnetic field, rotates around the Earthʼs axis with a slower angular velocity than the crust, and hence the magnetic field appears to drift westward relative to the surface. The average rate of drift over all latitudes is 0.18°. This can be accounted for by simply subtracting the apparent addtional westward drift of the continents and assuming that the rate of westward drift has remained fairly constant over the time-scale of millions of years1920 .

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18 Deutsch, Ernst, The Rock Magnetic Evidence for Continental Drift, In Continental Drift, ed. Garland, G. D., (1966), University of Toronto Press.

19 Garland, George D., Introduction to Geophysics, 240, (1971), W. B. Saunders Company.

20 Livermore, P. W., Hollerbach, R., Jackson, A., Electromagnetically driven westward drift and inner-core superrotation in Earthʼs core, 15914-15918, (2013), Proceedings of the National Academy of Sciences, 110.40.

GlossaryCurie Point or Temperature the temperature at which the permanent magnetism of a material becomes induced magnetism.

Declination the angle between magnetic north and true north.

Dipole Moment see Magnetic Dipole.

Electron Spin the term used to describe the intrinsic angular momentum of an electron.

Ferromagnetism the manner in which certain materials, such as iron, form permanent magnets.

Inclination the angle into or out from the Earth at which the field points.

Magnetic Dipole a north and south pole which create a magnetic field traditionally flowing from north to south.

Magnetometer a device for measuring the magnitude and/or direction of a magnetic field.

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