Geomagnetism

Speculations on the origin of the geomagnetic field


The earth's magnetic field is a very curious natural phenomenon. Magnetic fields have now been found on other celestial bodies, but many, such as the Moon, have no magnetic field. The origin of the field is deep within the bodies, in the mysterious interior where we have only indirect knowledge of the materials and physical conditions, and where motion was never suspected. The source of the field appears to be currents and magnetic fields mixed in the turbulent motions of hot conducting fluids, or semi-solids, influenced by the rotation of the body. As a point of information, the equatorial radius of the earth is 6378 km, its average density is 5.5 g/cm2, its moment of inertia I = 0.3335MR2, and it rotates at a rate of 7.29211 x 10-5 radian/s. The volume of the earth is about a million million cubic kilometers. In the figures quoted below, precision should not be assumed to be accuracy.

The internal structure of the earth, as revealed by seismology, is sketched at the right, approximately to scale. The solid crust, the only part we experience directly, is represented by the line of the circumference, since it is only about 33 km thick, on the average. It consists of basaltic ocean basins (70% by area) (the "sima"), with piles of granitic detritus on top heaved up by convection from below (the "sial"), which are the continents (30% by area). It represents only 1.5% of the earth's volume, but is the only part we know directly. At its base is the Mohorovicic discontinuity, the "Moho." The large-scale geological events here are all caused by movements in what lies below the Moho. Above it, in addition to the usual Si and O are the lighter elements--Na, K, Al, Ca--and much of the radioactivity, concentrated in granitic rocks. The density of granite is about 2.65, of basalt, 2.87. The terms granite and basalt only indicate rocks of the same general composition here, not the crystalline varieties that give rise to a family of geological names. The ocean basins are all relatively young rock. Old rocks are found only on the continents. The melting of rocks, as at spreading centers and volcanoes, is a local phenomenon.

Below the crust is the mantle, the thick layer composed of magnesian rocks, probably olivine or pyroxene. It represents 82% of the earth's volume, and is almost entirely composed of Mg, Si and O, the oxygen actually taking up most of the room, with Mg and Si in the interstices. Olivine is (Mg,Fe)2SiO4, closer to the Mg end of the series represented by the mineral Forsterite. Its density is 3.27-3.37. The beautiful gem material peridot is olivine, and the rock dunite, found at Dun Mountain, New Zealand, is mainly olivine. Olivine is a semiconductor, like most silicates, and its conductivity may increase greatly under high pressure and temperature. The activity of the mantle, and the fact that the continents float like rafts on it, is only a recent discovery, one that finally gave geology a reasonable mechanism for its deductions on the history of the planet, instead of the ludicrous speculations of the past. It is possible to find out a great deal about the elastic constants and density of material deep in the earth, but temperature is more uncertain. The chemical constitution is inferred from the composition of stars, meteorites and other planets, combined with the assumed history of the earth. The hydrostatic pressure at the base of the mantle is about 1.37 x 10 dyne/cm2, over a million atmospheres, and the density 5.68 gm/cm (increasing from 3.32 at the base of the crust). The stratification of the earth according to density is remarkable.

The core, with a radius of about 3500 km, was discovered by seismology. It makes up 16.5% of the volume of the earth. There is a rapid and large increase of density at the surface of the core, by a factor of about 2, from about 6 to 9 gm/cm3 that shows that this is a very significant boundary. The outer core is liquid (only P waves can penetrate it) while the inner core or "central body," radius 1250 km, is solid. The density at the surface of the central body is 11.5, and at the very center has been estimated as 17. Examining meteorites gives the hint that maybe the core is iron (commonly called "nickel-iron," giving prominence to a minor ingredient), segregated from the silicates because of its density. Incidentally, most meteorites are stony, not metallic. If the core is iron, it is a different iron from that we know at the surface, because it is much denser. However, its density is in line with theoretical estimates.

The temperature in the mantle and core are not known with any confidence, but the core temperature has been estimated at about 2000K. It has been presumed that the temperature gradient in the mantle keeps olivine at close to the melting point, or about 4.7°/km. On the other hand, if there is free convection, the adiabatic rate of 0.4°/km should govern. The difference between these shows ample drive for convection. The temperature gradient in the crust is much larger, between 10°/km and 50°/km, which removes the radioactive heat generated in the crust. An upper limit of about 10,000K has been estimated for the temperature at the base of the mantle, but the probable value is much lower, as has been stated above. The thermal conductivity of the mantle is small, and conduction to the surface cannot have reached a much greater depth than 400 km in the life of the earth. If the earth solidified from a liquid, it must have solidified from the bottom up, since the solidified matter would not have been able to carry off the heat by conduction. Of course, convection is probably by far the dominant heat transfer mechanism in the earth, and arguments based on conduction have little weight.

One thing that is certain is that the pressure increases to extraordiary values deep in the earth. This produces changes in materials that give them unfamiliar properties. Laboratory experiments can hint at the properties of materials under extreme pressures, up to about 10,000 atmospheres, but not at the higher pressures within the earth. Theoretical studies of atoms under great pressure give valuable insights, especially for simpler materials like iron. In addition, the material composition is not known definitely, so the properties of the materials of the earth are matter for doubt. However, the earth is more than 90% composed of the four elements oxygen, iron, silicon and magnesium.

Antineutrino detectors in Japan have recently (2005) succeeded in detecting antineutrios from radioactive decay in the earth. This is the first direct probe other than seismic waves that can be used to study the composition of the earth. It must be remembered that all our hypothesizing about terrestrial magnetism and conditions near the core rests on very little information.

The earth probably formed at a rather high temperature, as the gravitational energy of the particles that accumulated was dissipated, but this may not have been enough to cause the earth to be molten, as was once assumed. Volcanoes are not holes to the molten rock below, but result from local deep heating and the presence of active gases. There would actually have been no way to get rid of the excess heat from the release of gravitational energy on coalescence, even through geological time. Without a molten state, the segregation of materials according to specific gravity would be difficult, but somehow it got done. Since then, radioactive decay has heated the earth, especially the lighter materials segregated at the surface by mantle convection, and perhaps an equilibrium has been reached there. Radioactivity is confined mainly to the crust, so that the core is either cooling very slowly or is at a temperature maintained by contact with the mantle, unless it contains radioactive sources of its own, as has been conjectured (without evidence). If there is no source of energy in the core, there is no energy to drive convection there. Convection in the mantle transfers heat to the surface, where it is dissipated into space. Only a small concentration of radioactivity is required to supply the necessary heat. If there were a lot of radioactivity in the mantle, the earth would melt. Details of the convection are unknown, since they depend on obscure viscous properties of matter under the conditions there. The heat conductivity of the mantle is very low, and the temperature gradient probably far from adiabatic, so there is ample drive for convection. The observations of continental drift and deep-focus earthquakes (up to 700 km deep, well in the mantle) seem to establish the reality of convection in a seemingly solid medium beyond doubt, though how it occurs is not known.

In reading geologist's speculations on earth heat, it is difficult to escape the impression that some believe a region of matter can spontaneously rise in temperature because of heat flowing in from elsewhere (usually below), and cause melting or whatever. This not only violates the Second Law of Thermodynamics, it also abuses good sense. Also, the concepts of viscosity and flow, and the distinction between "liquid" and "solid," depend on the time scale of the stresses. What is rigid to an earthquake wave may flow readily in the space of mere years, a short time in geology. Arthur Holmes dissipated a lot of absurdities along these lines, but work still remains to be done.

The geomagnetic field is approximately a dipole field at the surface of the earth and outwards. This shows only that the sources of the field are within the earth at some depth, and predominantly currents that circle the axis. The case of multiple current loops adding to the axial dipole is very unlikely. A dipole field is the lowest order in a multipole expansion of the field, and as such is no surprise. The field gives no detailed information on the currents that produce it. A dipole field is shown in the diagram, with the characteristic variations of the radial and tangential components with polar angle θ. The quantity m is the magnetic moment. For the earth, its magnitude is about 8 x 1025 cgs units (abamp-cm2). With m in these units, and r in cm, the magnetic field B is in gauss. The axis of the dipole cuts the surface of the earth at 79°N, 110°W (in far northern Canada, in the Arctic Ocean near the Queen Elizabeth Islands). The usual North Magnetic Pole, the dip pole where the magnetic field is vertical, is somewhat farther south, and not exactly antipodeal to the South Magnetic Pole. Note that the south end of the dipole is at the north, and the north at the south. This is a result of calling the end of the compass needle that points north the north pole. Opposite polarities attract. These poles have moved rather steadily, the North Magnetic Pole now heading northwards out into the Arctic Ocean.

The observed field varies more irregularly over the surface than a pure dipole field, because of the effects of different magnetic permeabilities of the materials of the crust. However, if you calculate the field at the equator from the magnetic moment, 0.308 G is obtained, which is about right. The field varies slowly with time, the secular change. These changes slowly move westward, and are perhaps cyclical. At one time, this was thought to be the only significant variation, and that the field was approximately constant with time. Now it is known that this is not true, and the field sometimes reverses suddenly. It seems, however, to retain the same general axis. The moment has been decreasing slowly, to us, but rather rapidly on a geologic scale, and my be getting ready to reverse again in a thousand years or so. Although alarmists are worried, such reversals in the past seem to have had no biological effects. Taking the moment as 1.000 in 1937, it had decreased from 1.053 in 1836. At this linear rate, it would decrease to zero in about 2000 years. Incidentally, changes are sometimes measured in gammas, with 1 gamma = 10-5 gauss = 1 nT. The nanotesla is usually found on recent maps.

Dr William Gilbert, Queen Elizabeth's physician, made a terrella of magnetized iron in 1600 to illustrate his concept of terrestrial magnetism. When it was deduced in the 20th century that the core was probably nickel-iron, some thought that permanent magnetism in the core made Gilbert's illustration close to the fact. There was no idea how the core ever became magnetized in the first place, however, and the temperature seems too high anyway, above the Curie point where permanent magnetism disappears. Later, an ingenious theory, most recently supported by P. M. S. Blackett, supposed that the rotation of the earth (and other celestial bodies) somehow created a magnetic field that was proportional to the angular momentum. The only thing left out of this theory of the origin of the geomagnetic field was an explanation of the origin of the geomagnetic field. The fact that the field reverses, and that some rotating bodies have magnetism, and some do not, rule out these two theories rather conclusively.

The conclusion that the outer core was liquid, and a metal, gave rise to the idea that currents in this region could be the cause of the field. The discovery of the solid inner core helped the theory considerably. It is quite conceivable that the liquid conductor could produce a self-exciting homopolar generator, but I do not believe this was worked out in detail, only in principle. However, there is no apparent energy source in the core to support the convection that drives the generator. Since the magnetic field itself requires no additional energy once it is established, the only energy that is necessary to maintain the field is that compensating the resistive dissipation of the currents. The theory of currents at the surface of the core was developed by Elsasser and Bullard, and is rather unsatisfyingly explained in the Reference. It is a theory of the terrestrial dynamo without any dynamo. We note that any currents or fields deep in the core would be entirely shielded from the outside, even on a geologic time scale.

Another possibility is shown at the right. The convective cell shown rises at the equator near the mantle-core boundary. We must presume that the temperature and pressure at this depth produce a conducting material that takes part in the convection at a rate sufficient to produce the observed current (this would have to be faster than the generally very slow movements in the upper mantle). The convection could reverse, and then the field would reverse with it. This convection may be confined to the neighborhood of the boundary, and not penetrate to as shallow depths as shown in the diagram for clarity. No convection in the upper mantle is anywhere near fast enough for the purpose. If there were many cells from equator to pole, the resultant field would be the algebraic sum of the individual fields produced by the cells, which would alternate in polarity. In fact, the field could then reverse with only changes in one or two cells. This is like the Elsasser-Bullard theory, but on the other side of the mantle-core boundary.

About how much current is necessary? Let's assume the observed magnetic moment is produced by a total current I moving in a circle at the mantle-core boundary, at about half the earth's radius. The area of the disc bounded by the current is then about 3.2 x 1017 cm2. The magnetic moment is the product of the current and the area, and 10 A equals 1 abamp, so the required current to produce the earth's field is 250 x 106 A. This seems like quite a large amount, until we make a comparison with ordinary currents in wires. A current density of 1 A per mm2 is quite reasonable, so our conductor would need an area of 250 x 102 mm2. This would be a conductor only 15.8 m in diameter, hardly noticeable at a depth of 3000 km! The actual current density required would be much less, a million times less for a conducting diameter of 15.8 km. Rather small convective velocities would then be required, but an exact estimate would depend on the resistivity of the conducting matter, which is unknown. The conductivity at the base of the mantle has been estimated at a million times greater than the conductivity of surface rocks, about 0.5 S/cm. There is so much area available that an appeal to some unsuspected superconductivity is not required.

This idea also shows why the field is roughly, but not exactly, aligned with the rotational axis, since convection in polar regions will be parallel to the field and not induce much current. We assume here that the rotation does control the convection to keep it chiefly meridional, though at the top of the mantle the directions are random. This surface convection is not related to the magnetic field in any case. There will also be interaction between current loops to cause them to become parallel and coalesce if possible. This is only an alternative to currents only in the core, and the presence of a large poloidal field there, neither of which is certain. Its main idea is that mantle convection has some connection with the geomagnetic field. In the mantle, the conductivity would be low enough that the magnetic field would not be frozen in the slowly convecting material, and a low velocity would be sufficient to produce the necessary current.

Analysis of the origin of the field must be based on the principles of magnetohydrodynamics. The fundamental considerations are found in Elsasser's review, and in the text by Jackson, but the environment at the surface of the core is considerably different from that of both the laboratory and the sun, and quite hidden from view, so that the movements cannot be observed, only their results. If the mantle is conducting, and in motion, it must be treated satisfactorily. Fields will be able to penetrate the mantle with more ease than a fluid, metallic core, but still will be dragged along by convection, though they may not be able to affect it dynamically to the same degree. The theory must include feedback to explain the secular changes of the field and reversals, and some relation between the earth's rotation and the field which causes the dipole to be roughly, but not exactly, axial. It takes no energy to maintain the field, only a little to supply the losses in the current system, but there is still a large amount of field energy present. More energy is required to drive the convection that provides the necessary motion. The dynamo cannot be static, and must rely on motion, since it is essentially a self-excited homopolar dynamo. Appeals to relative motion between the core and mantle, or within the mantle, must explain how this relative motion occurs and is maintained. Dynamical causes can only be traced back to Coriolis forces in any case. Then, of course, the field reversals would not necessarily imply a reversal of relative motions, only a reversal of the currents. In any case, there is every reason to believe that the interesting area is within a few hundred kilometers radius from the surface of the core.

I have assumed above that the core is iron, as was universally believed up to about 1950. This is a reasonable assumption, but of course there is no direct evidence of this, only inference. It has been suggested that the core is actually a high-pressure modification of olivine, and that the central body may either be iron or yet another modification of typical mantle material. I would much prefer this state of things to an iron core, because then there would be no sorting of the earth by density to explain. It would all have been of about the same composition, and the observed density distribution would be a result of the pressure distribution, not of sorting that put iron below the silicates. Indeed, the moon has a density of 3.34, as if it were a solid sphere of green olivine, with insufficient central pressure to produce a core, and so, no magnetic field (actually, there is probably no mantle convection, either).

Planetary probes have produced some very interesting results on the magnetic fields of the other planets. Mercury has a weak field, in spite of its moonlike nature. Mercury is rich in iron, though. Venus shows no cypromagnetic field at all, something of a surprise. However, there is no evidence of plate tectonics and so of mantle convection on Venus, either. Mars possesses an areomagnetic field, but a feeble one. If it has a core, it is a small one, so this is not unexpected. Jupiter has a very strong field, which some attribute to a metallic form of hydrogen that occurs under high pressure, but whose source is simply unguessed. My source did not mention the Saturnian field, but it would be a surprise if it were not also strong. Uranus and Neptune present strange results. They have considerable fields, but they are not aligned with the rotational axis (Uranus: 58.6° away; Neptune: 46.9° away). In both cases, the dipole is quite eccentric, by 1/2 and 1/3 the planetary radii, respectively. This information shows the problem is not a simple nor uniform one.

References

W. M. Elsasser, Rev. Mod. Phys. 22, 1-35 (1950). This is an excellent review of knowledge about the interior of the earth and how it was obtained. It is remarkable how little has been added since its publication. The most important news was the discovery of the reversals of the earth's field in the course of establishing the reality of continental drift and mantle convection. We also now have the inevitable computer programs that provide detailed magnetohydrodynamic results that can probably be massaged into any desired form, making up for the lack of real information. The information on the Elsasser-Bullard theory of geomagnetism is very unsatisfying. In essence, no theory is actually presented, only some general results of magnetohydrodynamics and some mention of the effects of turbulence. There is no discussion of why the field is approximately aligned with the earth's rotation, what limits its magnitude, how it can reverse, and other interesting questions. The only feasible power source found was radioactivity in the core, producing heat that had to be convected out. There are interesting comments on mantle convection and the strange behavior of matter under these extreme conditions, however.

Scientific American, 287(5), p. 24 (November, 2002). Possibility of a field flip.

P. M. S. Blackett, Nature 159, 658 (1947). Rotational theory of general celestial magnetism.

J. D. Jackson, Classical Electrodynamics, 2nd ed. (New York: John Wiley & Sons, 1975), Chapter 10.

T. G. Cowling, Magnetohydrodynamics (New York: Interscience, 1957), Chapter 5. The state of dynamo theories in 1957. At this time, field reversals were not recognized, and the fields of other planets were not known. Explains more about Elsasser's and Bullard's theories, and presents some general observations.

Magnetic field maps are available from USGS. Select "Magnetic Charts" from the menu. The latest US maps for declination (D), inclination (I) and total field (F) available for download are 1995. There are some excellent world maps for 2000. The PDF files are all right, but take a long time to load. I'll have to see if maps are not also available from the UK or Canada. Programs are also available that calculate the field from a model, but I have not examined them yet. There is also some miscellaneous information on the site.


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Composed by J. B. Calvert
Created 2 September 2002
Last revised 30 July 2005