Gubbins D., Herrero-Bervera E. Encyclopedia of Geomagnetism and Paleomagnetism

Подождите немного. Документ загружается.

help us infer its internal structure similar to the inferences about the

interiors of the icy Galilean satellites made from measurements of their

gravitational fields by the Galileo spacecraft. Titan is distinguished by

its massive atmosphere of nitrogen (95%) and methane (5%). The sur-

face pressure on Titan is about 1.5 times the pressure at Earth’s surface.

Titan is the only moon in the solar system with such a substantial atmo-

sphere whose existence holds clues to the formation and evolution of the

satellite and the nature of its interior.

Pluto, Charon, and Triton

The small minor planet Pluto and its comparably sized moon Charon

are additional examples of icy solar system bodies. Their densities

are somewhat uncertain; Pluto’s density lies between about 1750 and

2150 kg m

3

, and Charon’s density lies in the range 1300

2200 kg m

3

(Table I4). We have little other information about these

bodies, so it is impossible to conclude one way or another about the

separation of ice from rock in their interiors. In addition to ice and

rock, Pluto and Charon may contain organic material in their interiors.

Pluto and Charon are likely to be typical of many other icy objects

orbiting at the edge of the solar system in the so-called Kuiper belt.

Pluto is very similar in size and density and surface composition to

Neptune’s icy moon Triton (Table I4). Nitrogen and methane ices (in

addition to water ice) have been detected on the surfaces of Pluto

and Triton, and both bodies have thin predominantly nitrogen atmo-

spheres. Triton is in an unusual orbit around Neptune; the orbit is

highly inclined and is retrograde (the inclination of the orbit is about

157



). Triton’s orbit suggests that it formed elsewhere in the outer

solar system and was captured from heliocentric orbit by Neptune.

Triton was likely strongly heated during this capture event, and it is

therefore expected to have differentiated into a rock core surrounded

by an ice mantle. Theoretical considerations suggest that Pluto might

also be differentiated, though not by heating during capture.

Giant planets in the outer solar system

Jupiter

The outer planets are large, fluidlike bodies with low densities com-

pared to the densities of the terrestrial planets (Table I4). Jupiter, the

largest planet in the solar system, is composed largely of hydrogen

and helium (Figure I23/Plate 12). Hydrogen and helium are gases in

the outer layers of Jupiter (H

and He are 86.4% and 13.6%, respec-

tively, by number, in Jupiter’s atmosphere), but pressures are so large

in the deep interior of Jupiter that its hydrogen and helium are more

like dense liquids than gases at large depths. Hydrogen transforms to

a metallic, highly electrically conducting phase at a depth perhaps

as shallow as 20% of Jupiter’s radius. The dynamo that produces

Jupiter’s magnetic field could reside in this metallic hydrogen region

of the planet’s interior. The molecular hydrogen envelope could be

electrically conducting enough near the base of the layer to support

dynamo action. There may be a relatively small core at the center of

Jupiter as large as several Earth masses (up to about 10 Earth masses)

and made of rock, metal, and ices (water, ammonia, and methane).

Jupiter is so massive that it is contracting under its own gravitation,

a process that releases gravitational potential energy in the form of

heat. This heat is radiated from Jupiter’s atmosphere; it has been

measured and has been found to be comparable to the amount of heat

Jupiter receives from the Sun and reradiates to space. Models of

Jupiter’s interior are based on theoretical considerations and are

constrained by its density and spacecraft observations of the planet’s

gravitational field described by gravitational coefficients such as

¼J

(and higher degree coefficients like J

and J

Saturn

Saturn is similar to Jupiter in its interior (Figure I23/Plate 12). It is a

smaller planet (Table I4 ) and contains relatively more helium. The

molecular to metallic phase transition in Saturn occurs deeper within

the planet (at a depth of about 0.5 Saturn radius) as compared to Jupi-

ter. This is because the pressure at which the phase change occurs is

found deeper within Saturn as a consequence of the planet’s smaller

size and gravity. Like Jupiter, Saturn also has a magnetic field likely

generated by a dynamo in the metallic hydrogen part of its interior.

Saturn might also have a rock, metal, ice core at its center.

Uranus and Neptune

Uranus and Neptune are known as icy giants (Figure I23/Plate 12).

They are similar to each other in mass and size but smaller than Jupiter

and Saturn (Table I4). Their densities are about the same as that of

Jupiter but about twice as large as that of Saturn. They are believed

to have outer envelopes of hydrogen and helium, but deep interiors

consisting mostly of ices such as water, methane, and ammonia. They

might also have rock, metal, ice cores of about an Earth mass at their

centers. Uranus and Neptune have magnetic fields that must be gener-

ated in highly electrically conducting regions of their icy interiors.

Crusts of terrestrial planets

The discussion above has emphasized the deep interiors of planets and

moons. The outer layers of the terrestrial planets all have rocky crusts,

and the outer regions of the giant planets all have gaseous atmo-

spheres. Of course, some terrestrial planets also have atmospheres.

The rocky crusts of Mercury, Venus, Earth, Moon, and Mars are com-

positionally distinct from the rocks of the underlying mantles. The

crusts of the terrestrial planets formed by differentiation from the pri-

mordial mantle rocks, i.e., they are formed by melting of the original

mantle rocks and separation of the melt from the unmelted residuum

(the present mantle rocks). Separation was achieved by the gradual

upward migration of the lighter magma that later solidified to form

the crust. This process is going on today at the mid-ocean ridges on

Earth, the sites of seafloor spreading. We know a great deal about

the Earth’s crust because we have the rocks themselves (at least the

rocks of the upper crust) and data from seismic, magnetic, and gravity

studies that reveal values of crust density and thickness. We also have

rock samples and seismic, magnetic, and gravity data that reveal

the nature of the lunar crust. Meteorites, believed to be from Mars,

the so-called SNC meteorites (Shergotty-Nakhla-Chassigny), provide

information about the composition and mineralogy of the planet. For

Venus, Mars, and the Moon there are considerable data about their

crusts from gravity, topography, and geochemical observations by

orbiting spacecraft. Landers on Venus and Mars have provided in situ

analyses of the surface rocks. The crusts of the terrestrial planets are

essentially basaltic in character, similar to the rocks that form the crust

beneath the Earth’s oceans. On Earth there are actually two distinct

types of crust, oceanic and continental. The rocks of the continents

are compositionally distinct from those of the ocean floor. Continental

rocks are richer in silica and formed from multiple stages of melting

and differentiation in the presence of water. The oceanic crust is about

5 km thick on average while the continental crust is much thicker,

about 40 km thick. Because of the concentration of the crust in

the northern hemisphere beneath Eurasia, there is a hemispheric

dichotomy in the Earth’s crustal thickness.

It is not known if there is crust on the other terrestrial planets similar

to the continental crust of Earth. There are two crustal types on the

Moon, the anorthositic crust of the lunar highlands (the light crystalli-

zation product of the lunar magma ocean) and the basaltic crust of the

lunar maria (the infill of the lunar impact basins). There is a hemi-

spheric dichotomy in crustal thickness on the Moon with the farside

of the Moon having a substantially greater thickness than the nearside.

The lunar crust has also been thinned beneath the South Pole Aitken

basin. There may be two crustal types on Venus, one type forming

the high-standing plateaus like Ishtar Terra, and the other forming

the volcanic rises like Beta Regio. The in situ analyses by the Venera

446 INTERIORS OF PLANETS AND SATELLITES

landers have revealed basaltic compositions in the Venusian lowland

plains. Mars also has a crustal dichotomy. The primordial crust of

the southern hemisphere stands higher and is thicker than the primor-

dial crust of the northern hemisphere which has been mantled with a

thin covering of younger and compositionally distinct crust. (The aver-

age thickness of the crust of Mars is between about 50 and 100 km.)

The crustal dichotomies of the terrestrial planets were likely formed

by internal dynamical processes, although major impacts, particularly

on the Moon (e.g., the large South Pole Aitken basin) could also have

played a role. The crustal dichotomies are probably the cause of

the offsets between the centers of mass and the centers of figure of

the terrestrial planets.

Less is known about the crust of Mercury. Remote sensing observa-

tions indicate that Mercury has a basaltic crust. If the Messenger

spacecraft successfully orbits Mercury and returns anticipated data,

we will know as much about Mercury’ s crust as we do about the

crusts of the other terrestrial planets.

The main source of information about the thicknesses of the crusts

of the terrestrial planets (other than Earth) derives from the topography

and gravity data obtained by orbiting spacecraft. These data have

enabled the construction of global crust thickness maps of the Moon

and Mars. The observed gravity variations are first modified to account

for the effects of topography using the measured topography. The extra

mass associated with elevated regions and the mass deficit associated

with low areas contribute to the measured variations in gravity. The

resulting gravity variations are known as Bouguer gravity anomalies.

While the Bouger gravity map accounts for topography effects, it does

not take account of the fact that variations in topography are generally

isostatically compensated by variations in crust thickness. According

to a geophysical principle known as Airy compensation, the masses

of material columns above a certain depth of compensation are

balanced; the crust is thicker beneath elevated topography compared

to average crust so that the extra mass of the topography is balanced

by an equal mass deficit associated with the replacement of heavy

mantle rock by lighter thickened crust. Similarly, the crust is thinned

beneath topographic depressions, so that the mass deficit of negative

topography is balanced by an equal mass excess associated with the

replacement of thinned crust by heavier mantle rock. By attributing

the Bouguer gravity anomalies to crustal thickness variations, those

variations can be determined. However, the depth of compensation

or average crustal thickness must be assumed or constrained by some

other observations. In this way, the crustal thickness map of Mars

shown in Figure I26/Plate 13b has been derived from topography

and gravity measurements obtained by the Mars Global Surveyor

spacecraft. The map assumes that the average crust thickness on Mars

is 50 km. The crustal dichotomy between the northern lowlands and

southern highlands is immediately apparent. The strongly magnetized

region of the Martian crust lies in the southern highlands (see Mag-

netic field of Mars, chapter and figure), but not all of the southern

hemisphere crust is magnetized. The principle of Airy compensation

is well established for Earth where it can be tested against seismic

measurements of crustal thickness. The thickest crust on Earth lies

below its most mountainous regions.

Concluding remarks

Seismic measurements directly probe a planet’s interior, determining

structure and providing constraints on composition and mineralogy.

We have such observations for Earth, but the only other planet that

has been seismically studied is the Moon. Nevertheless, we have learned

a good deal about the interiors of other planets and moons in our solar

system by observing how some of them respond dynamically to tidal

torques and by measuring their densities and external gravitational and

magnetic fields. Still other observations of the geology and composition

of their surfaces provide additional clues about what lies inside them.

Though we only have observed most of the bodies shown in Figure

I23/Plate 12 from the Earth, or from orbiting and flyby spacecraft, it is

rather remarkable that we can draw the cutaway views shown in the

figure to reveal what these planets and moons are like inside.

Sources

The data and models on which this article is based are discussed in

the following papers: Mercury (Schubert et al., 1988; Spohn et al.,

2001; van Hoolst and Jacobs, 2003; Solomon, 2003), Venus (Schubert

et al., 1997), Earth (Schubert and Walterscheid, 2000), Moon (Hood,

1986; Khan et al., 2004), Mars (Schubert et al., 1992; Spohn et al.,

1998; Yoder et al., 2003; Neumann et al., 2004), Jupiter (Guillot

et al., 2004), Galilean satellites (Schubert et al., 2004), Saturn (Hubbard

and Stevenson, 1984; Guillot, 1999), Titan (Hunten et al., 1984; Grasset

et al., 2000; Stevenson, 1992; Sohl et al., 2003). Uranus (Hubbard and

Marley, 1989; Hubbard et al., 1991; Podolak et al., 1991), Neptune

(Hubbard et al., 1995), Triton (McKinnon et al., 1995), Pluto and

Charon (Stern, 1992; McKinnon et al., 1997).

Gerald Schubert

Figure I26/Plate 13b Map of crust thickness of Mars based largely on gravitational and topographic data from the Mars Global

Surveyor spacecraft (Neumann et al., 2004).

INTERIORS OF PLANETS AND SATELLITES 447

Bibliography

Grasset, O., Sotin, C., and Deschamps, F., 2000. On the internal struc-

ture and dynamics of Titan. Planetary and Space Science, 48:

617–636.

Guillot, T., 1999. A comparison of the interiors of Jupiter and Saturn.

Planetary and Space Science, 47: 1183–1200.

Guillot, T., Stevenson, D.J., Hubbard, W.B., and Saumon, D.,

2004. The interior of Jupiter. In Bagenal, F., Dowling, T.E., and

McKinnon, W.B. (eds.), Jupiter: The Planet, Satellites, and Magneto-

sphere. Cambridge: Cambridge University Press, pp. 35–57.

Hood, L.L., 1986. Geophysical constraints on the lunar interior.

In Hartmann, W.K.R., Phillips, J., and Taylor, G.J. (eds.), Origin

of the Moon. Houston, TX: Lunar and Planetary Institute, pp.

361–410.

Hubbard, W.B., and Marley, M.S., 1989. Optimized Jupiter, Saturn,

and Uranus interior models. Icarus, 78: 102–118.

Hubbard, W.B., and Stevenson, D.J., 1984. Interior structure of Saturn.

In Gehrels, T., and Matthews, M.S. (eds.), Saturn. Tucson, AZ:

The University of Arizona Press, pp. 47–87.

Hubbard, W.B., Nellis, W.J., Mitchell, A.C., Holmes, N.C., Limaye,

S.S., and McCandless, P.C., 1991. Interior structure of Neptune:

comparison with Uranus. Science, 253: 648–651.

Hubbard, W.B., Podolak, M., and Stevenson, D.J., 1995. The interior

of Neptune. In Cruikshank, D.P., (ed.), Neptune and Triton. Tuc-

son, AZ: The University of Arizona Press, pp. 109 –138.

Hunten, D.M., Tomasko, M.G., Flasar, F.M., Samuelson, R.E., Strobel,

D.F., and Stevenson, D.J., 1984. Titan. In Gehrels, T., and Matthews,

M.S., (eds.), Saturn. Tucson, AZ: The University of Arizona Press,

pp. 671–759.

Khan, A., Mosegaard, K., Williams, J.G., and Lognonné, P., 2004.

Does the Moon possess a molten core? Probing the deep lunar

interior using results from LLR and Lunar Prospector. Journal of

Geophysical Research, 109: E09,007, doi:10.1029/2004JE002,294.

McKinnon, W.B., Lunine, J.I., and Banfield, D., 1995. Origin and evo-

lution of Triton, In Cruikshank, D.P., (ed.), Neptune and Triton.

Tucson, AZ: The University of Arizona Press, pp. 807–877.

McKinnon, W.B., Simonelli, D.P., and Schubert, G., 1997. Composi-

tion, internal structure, and thermal evolution of Pluto and Charon.

In Stern, S.A., and Tholen, D.J., (eds.), Pluto and Charon. Tucson,

AZ: The University of Arizona Press, pp. 295–343.

Neumann, G.A., Zuber, M.T., Wieczorek, M.A., McGovern, P.J.,

Lemoine, F.G., and Smith, D.E., 2004. Crustal structure of Mars

from gravity and topography. Journal of Geophysical Research,

109: E08,002, doi:10.1029/2004JE002,262.

Podolak, M., Hubbard, W.B., and Stevenson, D.J., 1991. Model of

Uranus’ interior and magnetic field. In Bergstralh, J.T., Miner,

E.D., and Matthews, M.S., (eds.), Uranus.

Tucson, AZ: The

University of Arizona Press, pp. 29–61.

Schubert, G., and Walterscheid, R.L., 2000. Earth. In Cox, A.N. (ed.),

Allen’s Astrophysical Quantities, 4th edn. New York: Springer-

Verlag, pp. 239–292.

Schubert, G., Ross M.N., Stevenson D.J., and Spohn, T., 1988. Mer-

cury’s thermal history and the generation of its magnetic field. In

Vilas, F., Chapman, C.R., and Matthews, M.S. (eds.), Mercury.

Tucson, AZ: The University of Arizona Press, pp. 429–460.

Schubert, G., Solomon, S.C., Turcotte, D.L., Drake, M.J., and Sleep,

N.H., 1992. Origin and thermal evolution of Mars. In Kieffer,

H.H., Jakosky, B.M., Snyder, C.W., and Matthews, M.S. (eds.),

Mars. Tucson, AZ: The University of Arizona Press, pp. 147–183.

Schubert, G., Solomatov, V.S., Tackley, P.J., and Turcotte, D.L., 1997.

Mantle convection and the thermal evolution of Venus. In Bougher,

S.W., Hunten, D.M., and Phillips, R.J. (eds.), Venus II: Geology,

Geophysics, Atmosphere, and Solar Wind Environment. Tucson,

AZ: The University of Arizona Press, pp. 1245–1287.

Schubert, G., Anderson, J.D., Spohn, T., and McKinnon, W.B., 2004.

Interior composition, structure and dynamics of the Galilean

satellites. In Bagenal, F., Dowling, T.E., and McKinnon, W.B.,

(eds.), Jupiter: The Planet, Satellites, and Magnetosphere. Cam-

bridge, UK: Cambridge University Press, pp. 281–306.

Sohl, F., Hussmann, H., Schwentker, B., and Spohn, T., 2003. Interior

structure models and tidal Love numbers of Titan. Journal of Geo-

physical Research, 108: 5130, doi:10.1029/2003JE002,044.

Solomon, S.C., 2003. Mercury: the enigmatic innermost planet. Earth

and Planetary Science Letters, 216: 441–455.

Spohn, T., Sohl, F., and Breuer, D., 1998. Mars. Astronomy and Astro-

physics Review, 8: 181–236.

Spohn, T., Sohl, F., Wieczerkowski, K., and Conzelmann, V., 2001.

The interior structure of Mercury: what we know, what we expect

from BepiColombo. Planetary and Space Science, 49: 1561–1570.

Stern, S.A., 1992. The Pluto-Charon system. Annual Review on

Astronomy and Astrophysics, 30: 185–233.

Stevenson, D.J., 1992. Interior of Titan. In ESA SP-338, Proceedings

Symposium on Titan, Noordwijk, Netherlands: European Space

Agency, pp. 29–33.

Van Hoolst, T., and Jacobs, C., 2003. Mercury’s tides and interior

structure. Journal of Geophysical Research, 108:7–(1

–16),

doi:10.1029/2003JE002,126.

Yoder, C.F., Konopliv, A.S., Yuan, D.N., Standish, E.M., and Folkner,

W.M., 2003. Fluid core size of Mars from detection of the solar

tide. Science, 300: 299–303.

Cross-references

Harmonics, Spherical

Magnetic Field of Mars

INTERNAL EXTERNAL FIELD SEPARATION

Introduction

The process of separation of the magnetic field can be applied to the

main magnetic field or to the daily variation fields of solar and lunar

origin, or to disturbance fields or disturbance daily variation fields.

Each application has a different purpose. The results of the separation

show that the Earth’s main magnetic field is dominantly of internal ori-

gin, while the daily variation and disturbance fields have external

fields that are greater than the internal fields and therefore originate

above the Earth.

The results of the analyses provide the information needed for stu-

dies of dynamo processes in the Earth’s interior, in the ionosphere,

in the deep oceans, and for distributions of electrical conductivity

within those regions. In studies of magnetic daily variations of solar

and lunar origin, the amplitude ratio and phase angle differences of

the internal and external fields are used as the electrical response func-

tion of the Earth.

The internal and external fields correspond to two independent vec-

tor spherical harmonics that are orthogonal under integration over the

surface of a sphere. However, there is a third, independent vector sphe-

rical harmonic, orthogonal to the internal and external fields, referred

to as the “nonpotential” field, which can be used to resolve the residual

differences between horizontal components of the field that cannot be

represented by “potential” fields, meaning internal and external fields.

Coefficients of the nonpotential field determined from observatory

data are not statistically significant, indicating that the electrical cur-

rent system associated with the maintenance of the Earth’s electrostatic

charge, called the “global electrical circuit,” cannot be determined

from magnetic observatory data. With the availability of satellite mag-

netic data, and the possibility of field-aligned currents at low-Earth

orbit altitudes, it is quite likely that satellite magnetic data will provide

significant nonpotential field coefficients.

448 INTERNAL EXTERNAL FIELD SEPARATION

Field separations can be done globally or regionally. Global ana-

lyses are usually done using spherical harmonics, but some analyses

have been done using surface integral method s, (Price and Wilkins,

1963). A variety of methods are available for regional analyses, includ-

ing spherical cap harmonic analysis (see Harmonics, spherical cap )

and spectral methods. Global analyses using spherical harmonics and

the method of least-squares are the simplest and most easily under-

stood. Spherical cap harmonic analyses are useful for interpolation of

field values, but do not separate the field accurately. Other methods

have problems of implementation, as well as problems with aliasing

or poor choice of spectral cut-off. In the study of magnetic daily varia-

tions, an estimate of the local direction and strength of the overhead

current system is easily obtained by rotating the horizontal magnetic

field variation components clockwise through 90



Spheri cal ha rmonic analys is

The first spherical harmonic analysis on a global scale was that of

the Earth ’ s main magnetic field by Gauss (1838). He assumed that

the Earth was a sphere, and that all measurements of the field were

made on the surface of the sphere. There is an implied assumption that

there are no surface electrical currents on the surface of the sphere and

that there are no electrical currents flowing with a radial component,

e.g., Earth-air, or field-aligned. Thus, the electrical current density will

be zero, J ¼ 0. With all these assumptions, together with the absence

of displacement currents, Ampere ’ s law for the magnetic field strength

H reduces to rH ¼ 0. In regions of constant magnetic susceptibil-

ity, the equation for the magnetic flux density B is therefore

rB ¼ 0 ; so that the magnetic flux density is the gradient of a

scalar potential, that is, B ¼rV ; where the scalar potential function

V is a function of the radius r of the sphere, the colatitude y , and the

east longitude f.

The magnetic flux density has no divergence, because there are no

free magnetic poles, quite in contrast to the existence of free electric

charges. This condition is written r B ¼ 0, and therefore, the scalar

potential V satisfies Laplace ’s equation, r

V ¼ 0.

Solutions of Laplace ’s equations are called spherical harmonics (see

Harmonics, spherical), and the solutions V ðr ; y ; fÞ are called solid

spherical harmonics, to disting uish them from surface spherical harmo-

nics P

ð cos y Þ cos mf and P

ðcos yÞ sin mf , which do not satisfy

Laplace ’s equation.

The functions V

int

ð r ; y; fÞ and V

ext

ðr ; y ; f Þ , defined by

int

ðr ; y ; f Þ¼ a

n¼ 1

nþ 1

m¼0

cos m f þ h

sin m f



 P

ðcos yÞ; r > a ;

ext

ðr ; y ; f Þ¼ a

n¼ 1

m¼ 0

cos mf þ h

sin m f



 P

ðcos yÞ; r < a ; (Eq. 1)

are the potential functions for sources internal to the reference sphere

r ¼ a and for sources external to the reference sphere, respectively.

Subscripts i and e have been applied to coefficients g

and h

to indi-

cate internal or external fields. The initial factor a in (Eq. 1) has been

included so that the g and h coefficients will have the dimensions of

magnetic flux density. Gauss ’s first analysis of the main field to degree

and order N ¼ 4 used only the term V

int

ðr ; y ; f Þ , on the assumption

that the geomagnetic main field is a term of internal origin only.

Analysis of the field gives no indication as to the location of the inter-

nal and external sources. Therefore, the potential of the main field, or

its variations, is represented as a linear combination of the two types

given in (Eq. 1) , and applied to field measurements made in the region

between the ground and the ionosphere, or, in the case of satellite mag-

netic data, between the ionosphere and the magnetopause.

The current function representation

The field of internal origin can be represented by a system of surface

currents flowing over the surface of a sphere, concentric with and

within the minimum sphere over which observations are made. A

stream function Cðy; fÞ, with units of amperes, called the current

function, gives the surface current density Kðy; fÞ (in amperes per

meter) in the form

Kðy; fÞ¼

R sin y



¼e

rC ¼rðe

CÞ

(Eq. 2)

The vector rC is in the direction of Cðy; fÞ increasing, that is, directed

toward maxima, and from (Eq. 2) the electrical current flow is counter-

clockwise around maxima when seen from above. Note however, that

the maxima of Cðy; fÞ can be negative and the minima positive.

The current function is denoted Cðy; fÞ, with units of amperes, and

has a spherical harmonic representation

Cðy; fÞ¼

n¼1

m¼0

ðJ

cos mf þ J

sin mfÞP

ðcos yÞ; (Eq. 3)

Subscripts c and s have been added to the coefficients J

to indicate

application to cos mf and sin mf respectively. For a current function

in the ionosphere, of radius R, to represent the magnetic daily varia-

tions, whose coefficients have been determined relative to a sphere

of radius a, the current function coefficients in amperes are given by

¼ðaÞ

2n þ1

n þ1

ðg

; J

¼ðaÞ

2n þ1

n þ1

ðh

(Eq. 4)

For a current function within the Earth to represent main field coeffi-

cients that have been determined relative to a sphere of radius a, the

current function coefficients in amperes are given by

¼ðaÞ

2n þ1

nþ1

ðg

; J

¼ðaÞ

2n þ1

nþ1

ðh

(Eq. 5)

Global magnetic field separation

In studies of the geomagnetic daily variations, current systems in the

ionosphere are the basic source, and eddy currents are induced in the

Earth by the ionospheric currents, with only a very small contribution

from the magnetospheric current system. Therefore, for the study of

the geomagnetic daily variations, the potential function must include

terms of both internal and external origin, with the expectation that

the terms of external origin will be the greater of the two, being the

basic source of the phenomenon. The two types of potential can be

separated by numerical calculations as follows, the process being the

title of this article, “internal-external field separation.”

Magnetic flux density field components

The three components of the geomagnetic field are denoted X, Y, and Z.

The northward component is X, the eastward component Y, and the

vertically downward component Z. The components, X, Y, and Z in

that order, form a right-handed orthogonal system.

The mathematical expressions for the field components over the

reference sphere, r ¼ a, are

X ¼



r¼a

; Y ¼

a sin y



r¼a

; Z ¼



r¼a

; (Eq. 6)

INTERNAL EXTERNAL FIELD SEPARATION 449

and therefore in a region free of magnetic sources and electric currents,

the ambient magnetic field can be derived from fields of internal and

external origin, and the components will have the mathematical form

X ð a; y; f Þ¼

n¼ 1

m ¼0



ð g

þ g

Þ cos mf þðh

þ h

Þ sin m f



ð cos y Þ

d y

;

Y ð a; y; f Þ¼

n¼ 1

m ¼0



ð g

þ g

Þ sin m f ðh

þ h

Þ cos m f



sin y

ð cos y Þ;

Z ð a; y; f Þ¼

n¼ 1

m ¼0





ð n þ 1Þ g

þ ng



cos mf

þðn þ 1Þ h

þ nh



sin mf



ð cos yÞ: (Eq : 7)

Because the radial dependence of the internal and external fields is

known, (Eq. 7) can be easily adapted for calculations using magnetic

field measurements which are not made over the surface of a sphere,

and where the coordinates of the point at which each measurement is

made is given in terms of geocentric coordinates, r ; y; f. From the

equations for the horizontal components of the field, namely X and

Y, it will be seen that the coefficients involve only ðg

þ g

Þ and

ð h

þ h

Þ, so that from the X component only, it is possible to deter-

mine the Y components. However, from these two elements only, it is

not possible to separate the coefficients into internal and external parts,

meaning it is not possible to determine g

and g

separately. How-

ever, the coefficients ð n þ 1Þ g

þ ng



and ðn þ 1Þ h

þ nh



as determined from the radial or vertical component Z, will allow the

separation of the coefficients and therefore allow separation of the

field into parts of internal and external origin, respectively.

The nonpot enti al field

It will be seen from (Eq. 7) , that the coefficients from the northward

component of the field X , obtained in the form ð g

þ g

Þ and

ð h

þ h

Þ, can be used to estimate the values of the eastward compo-

nent Y. Should the estimated values of Y not be in agreement with the

observed values of Y, then to resolv e the situation, a nonpotential field

is introduced, as shown below by coefficients g

and h

. The radial

dependence required for the internal and external fields is quite defi-

nite, but the radial dependence of the nonpotential field depends upon

the hypothesis chosen for the origin of the fields; for example, Earth-

air currents, or field-aligned currents.

The nonpotential field B

ðr ; y ; f Þ is

ð r ; y ; f Þ¼

sin y

] V



¼r rV

ð r ; y; fÞ;

¼r rV

ðr ; y ; f Þ½; (Eq: 8)

and has no radial component. The scalar function V

ð r ; y; fÞ (with

units of magnetic flux density) is given by

ðr; y; fÞ¼

n¼1

m¼0

ðrÞ

ðaÞ

cos mf þ h

sin mf



ðcos yÞ:

(Eq. 9)

The function q

ðrÞ cannot be determined from analysis of theory or

data alone, but requires a hypothesis to be made on the form of the

electrical current system.

The field components of the magnetic field over the reference

sphere, r ¼ a, are

X ða; y; fÞ¼

n¼1

m¼0

ðg

þg

Þcosmf þðh

þh

Þsin mf



þðg

sinmf h

cos mfÞ

sin y

; (Eq: 10)

Y ða; y; fÞ¼

n¼1

m¼0

ðg

þ g

Þsin mf ðh

þ h

Þcos mf





sin y

ðg

cos mf þ h

sin mfÞ

;

(Eq. 11)

Zða ; y; fÞ¼

n¼1

m¼0



ðn þ 1Þg

þng



cos mf

þðn þ1Þh

þnh



sin mf



ðcos yÞ: (Eq: 12)

The electrical current system comes only from the nonpotential

field as

ðr; y; fÞ¼

rB

ðr; y; fÞ

n¼0

m¼0

ðaÞ

ðrÞnðn þ 1Þe

ðrÞ





 e

]

sin y

]



cos mf þ h

sin mf



ðcos yÞ



(Eq. 13)

The hypothesis of Earth-air currents requires q

ðrÞ¼1

r when the

current system of (Eq. 13) reduces to a radial term only. An expression

for a field of internal origin, along whose field lines the electrical cur-

rent system travels, can also be found (Winch et al., 2005).

The representation of (Eqs. 10– 12) can be interpreted as a represen-

tation of the magnetic field over a sphere in terms of the three indepen-

dent and orthogonal vector spherical harmonics, usually given in

complex form as Y

n;nþ1

ðy; fÞ; Y

n;n

ðy; fÞ; Y

n;n1

ðy; fÞ.

Magnetic daily variations

The magnetic daily variations of solar and lunar type originate in the

ionosphere by a dynamo process, so that in contrast to the main mag-

netic field in which the internal coefficients are almost the only signif-

icant terms, the magnetic daily variations are dominantly of external

origin. The extra complication of dependence on time adds an extra

dimension to the complexity of the analysis. A very basic assumption

of local time t* dependence on time, where t* ¼ t þ f, and t is univer-

sal time, can reduce the complexity, but ignores significan t nonlocal

time terms that arise because of the inclination of the Earth’s geomag-

netic and geographic axes. A less restrictive assumption is that of

westward movement only, since the solar and lunar magnetic varia-

tions are driven by the Sun, one can expect that eastward moving var-

iations will be mostly insignificant.

The analysis begins with Fourier analysis of the elements X, Y, Z,at

each observatory. Thus

X ða; y; f; tÞ¼

M¼1

ða; y; fÞcos Mt þ B

ða; y; fÞsin Mt½;

Y ða; y; f; tÞ¼

M¼1

ða; y; fÞcos Mt þ B

ða; y; fÞsin Mt½;

Zða; y; f; tÞ¼

M¼1

ða; y; fÞcos Mt þ B

ða; y; fÞsin Mt½:

(Eq. 14)

It is the standard practice to do separate spherical harmonic analyses of

the A and B coefficients, to obtain internal and external coefficients

nAi

; h

nAi

and g

nAe

; h

nAe

; g

nBi

; h

nBi

and g

nBe

; h

nBe

450 INTERNAL EXTERNAL FIELD SEPARATION

of the potential functions V

ðr ; y ; f Þ and V

ð r ; y ; f Þ, where

ðr ; y ; f Þ¼a

n ¼1

m ¼0



nþ1

nAi

cos mf þ h

nAi

sin mf







nAe

cos mf þ h

nAe

sin mf



ðcos y Þ;

(Eq. 15)

ðr ; y ; f Þ¼ a

m¼ 1

n¼ 0



n þ1

nBi

cos mf þ h

nBi

sin m f







nBe

cos mf þ h

nBe

sin m f



ðcos yÞ;

(Eq. 16)

where only a limited range of m is used, for example, m ¼ M  1; M ;

and M þ 1.

However, if one were to include the following expression for

ðr ; y ; f Þ, which contains only the g and h coefficients appearing

in V

ð r ; y; fÞ , along with the least-squares analysis of V

ð r ; y; fÞ ,

ðr ; y ; f Þ¼a



nþ1

nAi

cos m f  g

nAi

sin mf







nAe

cos m f  g

nAe

sin m f



ðcos yÞ;

(Eq. 17)

then the combination

ðr ; y ; fÞ cos Mt þ V

ðr ; y; f Þ sin Mt

¼ a

n¼1

m¼0



nþ1

nAi

cos ðm f þ Mt Þþh

nAi

sin ðm f þ Mt Þ



ðcos y Þ

þ a

n¼1

m¼0



nAe

cos ðm f þ Mt Þþh

nAe

sin ðm f þ Mt Þ



ðcos yÞ:

(Eq. 18)

consists only of terms with argument mf þ Mt , which are westward

moving. In the special case that m ¼ M , the terms with argument

mf þ Mt reduce to local time t *, and mt * ¼ m ðt þ f Þ.

The use of (Eqs. 15 and 17) together doubles the number of equa-

tions of condition for the westward moving terms. Because the mag-

netic variation “ follows the Sun ” and moves westward, the eastward

moving terms are therefore much smaller, and in the first instance,

can be regarded as random noise. Analysis of residuals after removing

the westward moving part can be done by using an expression for

 V

ð r ; y; fÞ in place of (Eq. 17) for V

ð r ; y; fÞ.

Separat ion using Cartesian compo nents

For a Cartesian coordinate system at the center of the Earth, the x-axis

directed toward the intersection of the equator and the Greenwich mer-

idian, the y-axis at the intersection of the equator and the 90



E meri-

dian, and the z- axis directed toward the North Pole. If P ; G ; X ;

denote field components parallel to the x-, y- and z- axes, then

P ¼Z sin y cos f  X cos y cos f  Y sin f ;

G ¼Z sin y sin f  X cos y sin f þ Y cos f ;

X ¼Z cos y þ X sin y : (Eq : 19)

The method requires the surface spherical harmonic analysis of the

Cartesian field elements, P ; G; X. Coefficients a

; b

; c

; d

; e

; f

;

are determined using

P ¼

N þ 1

n¼0

m¼0

cos mf þ b

sin m f



ðcos yÞ;

G ¼

N þ1

n¼ 0

m¼ 0

cos mf þ d

sin mf



ð cos y Þ;

X ¼

N þ1

n¼ 0

m¼ 0

cos mf þ f

sin mf



ðcos y Þ: (Eq: 20)

By forming specified orthogonal combinations of the computed

coefficients, the internal, external, and nonpotential coefficients are

determined independently, so that, for example, if one decided to have

only internal terms in the model, there is no need to repeat the calcula-

tion (see Winch, 1968 for the necessary details).

Su rface integral method

Kahle and Vestine (1963) put forward a method of surface integrals for

separating a potential function V ð y ; fÞ , calculated as a set of numerical

values over the globe, into its terms of internal and external origin. The

method first requires the determination of the numerical values of

V ð y ; f Þ by integration of the given X values with respect to colatitude

y and integration of Y values with respect to east longitude f. The

reconciliatio n of values of potential from the two different elements

is discussed by Price and Wilkins (1963), and the method applied to

the analysis of Sq variations for the International Polar Year.

Using the known potential function V, the internal and external com-

ponents of V are determined from a form of Green ’ s third identity,

ext

 V

int

2 p

ðV þ 2aZ Þ

d S

: (Eq. 21)

The separation into internal and external parts is done using the

numerical arrays determined by (Eq. 21) and the known array

V ðy ; f Þ¼ V

ext

ð y; fÞþV

int

ð y ; f Þ: (Eq. 22)

Weaver (1964) describes a method for separating a local geomag-

netic field into its external and internal parts using two-dimensional

Fourier analyses of the X, Y, and Z components. The formulae for

separating the X field are

ð X þ M

Z Þ; X

ðX  M

Z Þ;

where

Z ¼

1

Zu; vðÞ

x  u

x  uðÞ

þ y  vðÞ

du d v:

A simple metho d

In order to determine the direction and strength of the external field in mag-

n etic dail y v ar iatio n s tud ies , with ou t the need for an y an aly sis at all, the h or-

izontal components can be rotated clockwise through 90



. For the Sq field,

it can be shown that the method is accurate to within 10% of the maximum

overhead current circulation, with largest errors occurring in middle and

equatorial latitudes, e.g., Winch (1966). The method is useful for checking

results of other more complicated forms of analysis and interpolation.

Denis Winch

Bibliography

Gauss, C.F., 1838. Allgemeine Theorie des Erdmagnetismus, Resultate

aus den Beobachtungen des magnetischen Vereins im Jahre 1838.

INTERNAL EXTERNAL FIELD SEPARATION 451

(Rep rint ed in Werk e, Bd. 5 , 1 21 , s ee also th e trans lati on b y Mrs. Sab ine

and Si r Jo hn Hersch el, Bart, Tay lo r, R ichard , 1 84 1. S cien tifi c M em oi rs

Sel ected from th e Tran sa ctio ns of Fore ig n A cad emies of Sci ence an d

Learned Societies and from Foreign Journals, 2:184–251 .)

Kahle, A.B., and Vestine, E.H., 1963. Analysis of surface magnetic fields

by integrals. Journal of Geophysical Research, 68:5505–5515.

Price, A.T., and Wilkins, G.A., 1963. New methods for the analysis of

geomagnetic fields and their application to the Sq field of 1932 –

1933. Philosophical Transact ions of the Royal Society of London,

Series A, 256:31– 98.

Weaver, J.T., 1964. On the separation of local geomagnetic fields into

external and internal parts. Zeitschrift für Geophysik, 30:29– 36.

Winch, D.E., 1966. The Sq overhead current system approximation.

Planetary and Space Science , 14 : 163– 172.

Winch, D.E., 1968. Analysis of the geomagnetic field by means of

Cartesian components. Physics of the Earth and Planetary Inter-

iors, 1 : 347– 360.

Winch, D.E., Ivers, D.J., Turner, J.P.R., and Stening, R.J., 2005. Geo-

magnetism and Schmidt quasi-normalization. Geophysical Journal

International , 160: 487– 504.

Cross- refere nces

Harmonics, Spherical

Harmonics, Spherical Cap

IONOSPHERE

The ionosphere is the weakly ionized region of the upper atmosphere

above 60 km altitude where free electrons and ions form a plasma that

influences radio wave propagation and conducts electrical currents.

The plasma is created by solar extreme-ultraviolet and X-ray radiation

impinging on the atmosphere and at high latitudes in the northern and

southern auroral ovals (q.v. ), by energetic particles precipitating from

the magnetosphere (q.v.). Plasma is destroyed through chemical reac-

tions that lead to electron-ion recombination. The ionizing solar radia-

tion varies by about a factor of two over the 11-year solar sunspot

cycle, which results in significant solar-cycle variations in the plasma

density. Figure I27 shows typical altitude profiles of the mid-latitude

electron density at day and night for years of minimum and maximum

solar activity. For historical reasons relating to radio sounding of the

ionosphere, the region of maximum density above 150 km is called

the F-region (or layer), the region around the secondary maximum

density at about 110 km is called the E region, and the region below

about 90 km is called the D region.

The ionosphere refracts, reflects, retards, scatters, and absorbs radio

waves in a manner that depends on the radio wave frequency. Around-

the-Earth communications are possible by utilizing ionospheric and

ground reflections of waves at frequencies below about 3– 30 MHz

(100 to 10 m wavelength), depending on the peak electron density.

However, frequent collisions between electrons and air molecules in

the D region remove energy from the radio waves, leading to partial

or even complete absorption, depending on the electron density.

At higher frequencies, radio waves penetrate entirely through the iono-

sphere, allowing radio astronomy and communications with space-

craft. Nevertheless, such signals can still be degraded by refraction

and scattering off of small-scale density irregularities. In the case of

geolocation signals like those of the Global Positioning System

(GPS), variable and uncertain ranging errors can be introduced by

ionospheric signal retardation. The retardation is proportional to the

total electron content (TEC), or height-integrated electron density.

A typical global pattern of TEC is shown in Figure I28. The TEC tends

to be larger in winter than in summer, because of slower chemical loss

in winter.

The ionospheric electrons and ions are strongly influenced by the

geomagnetic field, and tend to move in spirals along geomagnetic-field

lines. In the F- region, where collisions with air molecules are infre-

quent, the plasma diffuses rapidly along the magnetic field, but not

across it. Winds in the upper atmosphere can also push the ions along

the field lines. Plasma motion across magnetic field lines, on the other

hand, is produced by electric fields. In the presence of an electric field

E and a magnetic field B , electrons and ions drift perpendicular to both

fields at the velocity E  B/ B

. In the upper F- region, where ion life-

times are long, the ions and electrons can be transported vertically

and horizontally over significant distances between the times they

are produced and lost, giving rise to a pattern of plasma density

that depends on the geomagnetic-field configuration. As seen in

Figure I28, a relative minimum in TEC tends to form along the mag-

netic equator in the afternoon and evening. It is created by an upward

E  B/B

plasma drift during the day, with subsequent rapid plasma dif-

fusion along the magnetic field, driven downward and away from the

magnetic equator by gravity and plasma pressure gradients. Maxima in

Figure I27 Altitude profiles of electron density at 18



N, 67



W, September equinox, representative of noon and midnight, solar

minimum (solid lines) and solar maximum (dashed lines), with the F, E, and D regions indicated.

452 IONOSPHERE

the F-region ion density build up about 1500 km on either side of the

magnetic equator.

The geomagnetic influence on ion and electron mobility makes the

electrical conductivity of the ionosphere highly anisotropic. The rela-

tively free motion of electrons along the magnetic-field direction gives

rise to large conductivity in that direction. In fact, the large parallel

conductivity extends far into space, out to many Earth radii, and per-

mits electric current s to flow relatively easily along geomagnetic-field

lines from one hemisphere of the Earth to the opposite hemisphere.

In the direction perpendicular to the geomagnetic field, current

can flow in response to an electric field only when the electrons and

positive ions move at different velocities. Their common drift at the

velocity E  B /B

in the upper F-region does not produce current.

However, at lower altitudes, ion-neutral collisions deflect the ion

motion away from the velocity E  B /B

, while the electrons continue

to drift at that velocity so that current flows perpendicular to the mag-

netic field. Part of this current, called Pedersen current, is in the direc-

tion of E, and is associated with a Pedersen conductivity. Another part

of the current, called Hall current, flows in the B  E direction, oppo-

site to the electron velocity, and is associated with a Hall conductivity.

Figure I29 shows typical daytime altitude profiles of the parallel, Hall,

and Pedersen conductivities. In the E-region the conductivities vary

by about 40% over the solar cycle, but in the F- region the percentage

variation is much greater. Unlike the TEC, which represents primarily

F-region plasma, the height-integrated Pedersen and Hall conductiv-

ities vary mainly with the E-region plasma densities, which have short

lifetimes and therefore depend directly on the solar and auroral ioniza-

tion. They maximize during daylight, and at night in the auroral zone.

The electric field that drives current in the conductive medium is the

field present in the reference frame moving with the air, E þ v  B ,

where v is the wind velocity. Upper atmospheric winds drive electric

current by moving the conductive medium through the geomagnetic

field, thereby driving an ionospheric dynamo. Convergent or divergent

wind-driven currents create space charge and an electrostatic field E

that drives offsetting divergent or convergent current . The ionospheric

dynamo is the main source of quiet-day ionospheric electric fields

and currents, and of their associated geomagnetic daily variations, at

middle and low latitudes (see Periodic external fields). At high magnetic

latitudes, electric fields and currents connect along geomagnetic-field

lines with sources in the outer magnetosphere. They intensify greatly

during magnetic storms (see Storms and substorms ), and can produce

strong heating and dynamical changes in the upper atmosphere and

ionosphere.

For further information about the ionosphere and ionospheric pro-

cesses, see Kelley (1989) and Schunk and Nagy (2000).

Arthur D. Richmond

Figure I29 Solid lines: altitude profiles of the noon-time parallel

), Pedersen (s

), and Hall (s

) conductivities at 18



N, 67



September equinox, solar minimum. Dashed line: Pedersen

conductivity at solar maximum.

Figure I28 Global map of TEC at 12 UT, December solstice, solar maximum. Local time increases with longitude as shown on the

bottom scale. Contours are spaced at intervals of 10  10

electrons per square metre. The thick solid line is the magnetic equator.

IONOSPHERE 453

Bibliography

Kelley, M.C., 1989. The Earth’s Ionosphere. San Diego: Academic

Press.

Schunk, R.W., and Nagy, A.F., 2000. Ionospheres: Physics, Plasma

Physics and Chemistry, Cambridge University Press.

Cross-references

Auroral Oval

Magnetosphere

Periodic External Fields

Storms and Substorms, Magnetic

IRON SULFIDES

General

Iron sulfides are generally quoted as minor magnetic minerals and the

interest of paleomagnetists for this family of minerals progressively

developed only during the last 10–15 years. This was due partly to

the fact that their occurrence was originally believed to be restricted

to peculiar geological environments (i.e., sulfidic ores, anoxic sulfate-

reducing sedimentary environments) and partly to their metastability

with respect to pyrite (FeS

), which is paramagnetic. Magnetic iron sul-

fides were therefore not expected to carry a stable remanent magnetiza-

tion and to survive over long periods of geological time in sedimentary

environments. However, their occurrence as main carriers of a remanent

magnetization stable through geological times has been increasingly

reported in recent years from a large variety of rock types, primarily

as a result of more frequent application of magnetic methods to charac-

terize the magnetic mineralogy in paleomagnetic samples. The recogni-

tion of the widespread occurrence of magnetic iron sulfides as stable

carriers of natural remanent magnetizations (NRMs) in rocks propelled

specific researches on their fundamental magnetic properties.

Pyrrhotite: magnetic properties

Among magnetic iron sulfides, the pyrrhotite solid solution series

(Fe

1x

S; with x varying between 0 and 0.13) exhibits a wide range

of magnetic behaviors. Stochiometric pyrrhotite FeS (troilite) shows

a hexagonal crystal structure based upon the NiAs structure, with alter-

nating c-planes of Fe and S (Figure I30). In each Fe-layer the Fe

2þ

ions

are ferromagnetically coupled, while neighboring Fe-layers are coupled

antiferromagnetically to each other via intervening S

2

ions. The nonstoi-

chiometric pyrrhotites are cation deficient. The increase of Fe defi-

ciency affects both the crystallographic and magnetic structures:

ordering of Fe vacancies leads to an alternation of partially and

fully filled Fe layers, the hexagonal structure distorts to monoclinic

and the magnetic ordering turns from antiferromagnetic to ferrimag-

netic. Pyrrhotite shows strong magnetocrystalline anisotropy, with

the easy directions of magnetization confined in the crystallographic

basal plane (the magnetic crystalline anisotropy constant K

is posi-

tive and estimated at ca. 10

3

, see Dunlop and Özdemir,

1997). The crystallographic c-axis perpendicular to the basal plane

is the axis of very hard magnetization.

The more Fe-rich, hexagonal, pyrrhotites (F

, and possible

) are antiferromagnetic at room temperature and are

characterized by a l transition at temperatures between ca. 180



and 220



C, depending on composition, above which they exhibit

ferrimagnetism. The l transition represents a change in the vacancy-

ordering pattern of the crystal structure and is distinctive and diagnos-

tic of hexagonal (Fe-rich) pyrrhotites. The Curie temperature for the

different compositions of hexagonal pyrrhotites varies between

210



C and 270



The most Fe-deficient pyrrhotite (F

) is monoclinic and ferrimag-

netic at room temperature, with a Curie temperature of ca. 325



C. It

has no l transition, but it shows a diagnostic low-temperature transi-

tion in remanence and coercivity at 30–35 K (Rochette et al., 1990).

Natural pyrrhotite usually occurs as a mixture of superstructures of

monoclinic and hexagonal types, which results in an intermediate

overall composition. Magnetic properties of pyrrhotite and their depen-

dence from grain size and temperature have been investigated in detail

in a number of specific studies (e.g., Clark, 1984; Dekkers, 1988,

1989, 1990; Menyeh and O’Reilly, 1991, 1995, 1996; Worm et al.,

1993; O’Reilly et al., 2000). Monoclinic ferrimagnetic pyrrhotite

) has a saturation magnetization (J

)of18Am

1

at room

temperature. The magnetic susceptibility of pyrrhotites is field indepen-

dent in grains smaller than 30 mm, however for larger grains the mag-

netic susceptibility (w) and its field dependence increase with

increasing grain size (1  10

–5

–7  10

–5

1

). Conversely, the

coercivity parameters all increase with decreasing grain size. The room

temperature coercive force (H

) ranges from 10 to 70 kA m

1

(i.e.,

12–88 mT for coercive force expressed as magnetic induction B

)

Figure I30 Sketch of the crystalline structure of stoichiometric troilite (FeS). The structure is basically hexagonal, with alternating

layers of Fe

2þ

and S

2

ions. The c-axis of hexagonal symmetry is the axis of very hard magnetization and is perpendicular to the

basal planes. Elemental magnetic moments are parallel within a particular cation basal plane. The alternating Fe

2þ

layers define the

two magnetic sublattices with oppositely directed magnetic moments. In nonstoichiometric monoclinic pyrrhotite Fe

, the cation

vacancies are preferentially located on one of the two magnetic sublattices, giving rise to ferrimagnetism.

454 IRON SULFIDES

and for synthetic powders with grain size in the range 1–24 mm, it

could be fitted by a power-law dependence of the form H

/ L

, where

L is the particle size and n ¼0.38 (O’Reilly et al., 2000). During

hysteresis measurements and isothermal remanent magnetization

(IRM) acquisition experiments pyrrhotite powders approach complete

saturation only in fields greater than 1 T, with the magnetic hardness

increasing with decreasing grain sizes (O’Reilly et al., 2000).

In synthetic monoclinic pyrrhotites the critical size for the transition

from the single-domain (SD) to the multidomain (MD) state, with typi-

cal lamellar domains normal to the c-axis, is estimated at a mean value

of ca. 1 mm. The micromagnetic structures of hexagonal synthetic pyr-

rhotites are far more complex than that of monoclinic pyrrhotites, with

typical wavy walls and a significantly smaller size of the individual

magnetic domains (O’Reilly et al., 2000).

The remanent magnetization carried by pyrrhotites can be of prime

importance for paleomagnetic studies, but various factors may compli-

cate the paleomagnetic interpretation of the data obtained from the

classical demagnetization treatments. During alternating field (AF)

demagnetization pyrrhotite-bearing samples were reported to acquire

significant gyromagnetic and rotational remanent magnetization (RRM)

in fields higher than 20 mT (Thomson, 1990) and upon heating at

temperatures greater than 500



C during thermal demagnetization pyrrho-

tite transforms irreversibly to magnetite and, via subsequent further oxida-

tion and heating, to hematite (Dekkers, 1990), producing new magnetic

phases that may acquire new remanent magnetizations in the laboratory.

Furthermore, self-reversal phenomena of pyrrhotite have been earlier

reported under various laboratory experiments (Everitt, 1962; Bhimasan-

karam, 1964; Bhimasankaram and Lewis, 1966). Recent studies linked

such phenomena to crystal twinning (Zapletal, 1992) and/or to a close

coexistence of pyrrhotite and magnetite crystals, the latter being nucleated

from direct oxidation of the pyrrhotite grains during heating (Bina and

Daly, 1994).

Greigite: magnetic properties

The iron sulfide greigite (Fe

) is the ferrimagnetic inverse thiospinel

of iron and its crystalline structure is comparable to that of magnetite

(Fe

) in which sulfur replace oxygen atoms. In the cubic close-

packed crystal structure of greigite, the tetrahedral A-sites are filled

by Fe

3þ

ions and the octahedral B-sites are filled half by Fe

3þ

ions

and half by Fe

2þ

ions (Figure I31).

Greigite is characterized by a high magnetocrystalline anisotropy

(with a positive magnetic crystalline anisotropy constant K

estimated

at ca. 10

3

, see Diaz Ricci and Kirschvink, 1992; Dunlop and

Özdemir, 1997) and its magnetic easy axis is aligned along the

<100> crystallographic direction. Basic magnetic properties at room

temperature in synthetic greigite powders were systematically investi-

gated by Dekkers and Schoonen (1996), indicating a minimum lower

bound for the saturation magnetization (J

)of29Am

1

, a mag-

netic susceptibility (w)betweenca.5 10

–5

and 20  10

–5

1

and intermediate coercivities (i.e., IRM acquisition curves saturate

after application of fields 0.7–1T).

Greigite is unstable during heating to temperature higher than ca.

200



C. As a consequence of such instability the magnetic susceptibil-

ity and the magnetization in greigite-bearing sediments both undergo

significant changes during heating (see Krs et al., 1990, 1992;

Reynolds et al., 1994; Roberts, 1995; Horng et al., 1998; Sagnotti

and Winkler, 1999; Dekkers et al., 2000): a major drop is generally

observed between ca. 250



C and 350



C, reflecting decomposition of

greigite in nonmagnetic sulfur, pyrite, and marcasite, followed by a

dramatic increase above 350–380



C and a subsequent decrease above

400–450



C, indicating progressive production of new magnetic

phases (pyrrhotite, then magnetite/maghemite, and finally hematite).

Thermal decomposition of greigite precludes direct determination of

its Curie temperature.

Greigite does not show any low temperature (5–300 K) phase tran-

sition (Roberts, 1995; Torii et al., 1996; Dekkers et al., 2000), though

a broad J

maximum peak value was observed at 10 K during cooling

from 300 to 4 K (Dekkers et al., 2000).

Typical for greigite are: low to intermediate coercivities, with spec-

tra that partly overlap those of magnetite and pyrrhotite (i.e., for

natural greigite-bearing sediments and synthetics greigite the published

values for the coercivity of remanence (B

) ranges from 20 to 100 mT,

while for the coercivity (B

) varies from 13 to 67 mT), maximum

unblocking temperatures in the range 270–380



C, the lack of low-

temperature phase transitions and the presence of distinct stable SD

properties (i.e., Roberts, 1995). With regards to these latter properties,

in particular, greigite-bearing sediments show: (a) SD-like hysteresis

ratios, with M

often exceeding 0.5 (where M

is the saturation

remanent magnetization and M

is the saturation magnetization) and

often lower than 1.5, (b) high values of the SIRM/k ratio (where

SIRM is the saturation IRM and k the low-field magnetic susceptibil-

ity), (c) a sensitivity to field impressed anisotropy and (d) a marked

tendency for acquisition of gyromagnetic remanent magnetization

(GRM) and RRM. GRM and RRM acquisition in greigite-bearing

samples has been investigated in the detail in several specific studies

(Snowball, 1997a,b; Hu et al., 1998; Sagnotti and Winkler, 1999;

Stephenson and Snowball, 2001; Hu et al., 2002) that have shown that

greigite has the highest effective gyrofield (B

) reported so far for all

magnetic minerals (of the order of several hundred microteslas for a

peak AF of 80 mT) and that gyromagnetic effects are powerful indica-

tors for the presence of greigite in sediments.

Figure I31 Sketch of the ½ of a unit cell of greigite (Fe

). The

crystalline structure of greigite is basically the same inverse spinel

structure typical for magnetite (Fe

) in which S

2

ions

substitute O

2

ions. Cations are both in tetrahedral (A-site) and

octahedral (B-site) coordination with S

2

ions. In greigite the easy

axis of magnetization is the <100> crystallographic axis.

IRON SULFIDES 455