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

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distinguish between time variations in the ring current source field and

spatial variations in the main and crustal fields sampled as the space-

craft flies over Earth. This is illustrated in Figure I4. A model of the

main field that includes secular variation, along with a model of

the crustal fields and possibly the daily variation, electrojets, and

field-aligned currents must be used to remove all these elements

before the induction analysis can be carried out. A convenient tool

for removing these contributions is the Comprehensive Field Model

of Sabaka et al. (2004).

Figure I5 shows GDS response functions from the MAGSAT and

Ørsted satellite missions, compared with a response function generated

using magnetic observatories. The agreement is generally good, and

radial conductivity models generated from observatory data also fit

the satellite responses fairly well. However, differences do exist. At

short periods, the satellite response is influenced by oceans (Constable

and Constable, 2004b). At long periods, there may be contamination

of the source-field geometry, and some differences are undoubtedly

due to the various analysis techniques. The subject of magnetic satel-

lite induction is relatively young and many issues remain to be

addressed. For example, there are complications to the ring current

geometry that have largely been ignored (e.g., Balasis et al., 2004).

The daily variation in the magnetic field has variously been considered

a source of noise (Constable and Constable, 2004b) and a signal for

3D induction studies (Velimsk and Everett, 2005). Ultimately, the goal

of satellite induction is to move beyond global response functions and

radial conductivity models toward true 3D conductivity structure.

Steven Constable

Bibliography

Balasis, G., Egbert, G.D., and Maus, S., 2004. Local time effects in

satellite estimates of electromagnetic induction transfer functions. Geo-

physical Research Letters, 31: L16610, doi:10.1029/2004GL020147.

Banks, R.J., 1969. Geomagnetic variations and the conductivity of the

upper mantle. Geophysical Journal of the Royal Astronomical

Society, 17: 457–487.

Constable, C.G., and Constable,S.C.,2004a.Satellite magnetic fieldmea-

surements: applications in studying the deep Earth. In Sparks, R.S.J.,

and Hawkesworth, C.T. (eds.) The State of the Planet: Frontiers and

Challenges in Geophysics, Geophysical Monograph 150. Washington,

DC: American Geophysical Union, pp. 147–159.

Constable, S., and Constable, C., 2004b. Observing geomagnetic

induction in magnetic satellite measurements and associated impli-

cations for mantle conductivity. Geochemistry Geophysics Geosys-

tems, 5: Q01006, doi:10.1029/2003GC000634.

Daglis, I.A., Thorne, R.M., Baumjohann, W., and Orsini, S., 1999. The

terrestrial ring current: origin, formation, and decay. Reviews of

Geophysics, 37: 407–438.

Didwall, E.M., 1984. The electrical conductivity of the upper mantle

as estimated from satellite magnetic field data. Journal of Geophy-

sical Research, 89: 537–542.

Olsen, N., 1999a. Induction studies with satellite data. Surveys in Geo-

physics, 20: 309–340.

Olsen, N., 1999b. Long-period (30 days–1 year) electromagnetic

sounding and the electrical conductivity of the lower mantle beneath

Europe. Geophysical Journal International, 138:179–187.

Olsen, N., Vennerstrm, S., and Friis-Christensen, E., 2003. Monitor-

ing magnetospheric contributions using ground-based and satellite

magnetic data. In Reigber, Ch., Luehr, H., and Schwintzer, P.

(eds.), First CHAMP Mission Results for Gravity, Magnetic and

Atmospheric Studies. Berlin: Springer-Verlag, pp. 245– 250.

Sabaka, T.J., Olsen, N., and Purucker, M.E., 2004. Extending

comprehensive models of the Earth’s magnetic field with Orsted

and CHAMP data. Geophysical Journal International, 159:

521–547.

Velimsk, J., and Everett, M.E., 2005. Electromagnetic induction by

Sq ionospheric currents in heterogeneous Earth: modeling using

ground-based and satellite measurements. In Reigber, Ch., Luehr, H.,

Schwintzer, P., and Wicke rt, J. (eds.) Earth Observation with

CHAMP Results from Three Years in Orbit. Berlin: Sprin ger -Verlag,

pp. 341–346.

Cross-references

CHAMP

Crustal Magnetic Field

EM, Marine Controlled Source

Geomagnetic Deep Sounding

Geomagnetic Spectrum, Temporal

Harmonics, Spherical

Magnetometers, Laboratory

Magnetosphere of the Earth

Magnetotellurics

Magsat

Ørsted

POGO (OGO-2, -4, and -6 spacecraft)

Ring Current

Secular Variation Model

Storms and Substorms, Magnetic

Transfer Functions

INHOMOGENEOUS BOUNDARY CONDITIONS

AND THE DYNAMO

Thermal core-mantle coupling and geodynamo

Modern observations indicate that the Earth’s magnetic field takes the

form of an approximate geocentric axial dipole, i.e., a dipole posi-

tioned at the Earth’s center and aligned with the axis of rotation. Paleo-

magnetic measurements indicate that, when it is averaged over a

sufficiently long time, this has been the case for the observable past.

This suggests that the observed Earth’s magnetic field is primarily

the result of a geodynamo consistent with turbulent flows and rapid

rotation (Moffatt, 1978). In consequence, the geocentric axial dipole

is widely employed to provide a reference state for the Earth’s mag-

netic field. Any persistent departure from the axial dipole is indicative

of the external influence such as inhomogeneous boundary conditions

on the geodynamo imposed by the overlying mantle (Hide, 1967;

Bloxham and Gubbins, 1987; Bloxham, 2000).

Convection is occurring in both the Earth’s outer core and mantle.

However, there exists a huge difference between the timescales of

mantle and core convection. Core convection has an overturn time of

several hundred years while that of mantle convection is a few

hundred million years. As far as the Earth’s mantle is concerned, the

core-mantle boundary is a fixed temperature interface. As far as the

Earth’s fluid core is concerned, the core-mantle boundary is rigid

and imposes a nearly unchanging heat-flux heterogeneity on the core

convection and dynamo.

The structure of the inhomogeneous boundary condition can be

inferred from the seismic tomography of the Earth’s lower mantle

(for example, Masters et al., 1996; van der Hilst et al., 1997). By

assuming that the hotter regions of mantle correspond to the lower

seismic velocity while the cold regions are related to the anomalously

high seismic velocity, the inhomogeneous boundary condition at the

core-mantle boundary for the core convection and dynamo can be

determined. The temperature variations above the core-mantle bound-

ary impose a nearly unchanging heat-flux heterogeneity on the core

dynamo.

416 INHOMOGENEOUS BOUNDARY CONDITIONS AND THE DYNAMO

Paleomagnetic and historical magnetic field measurements suggest

persistent distinct patterns of variation of the geomagnetic field taking

place in different regions of the Earth. For example, secular variation

under the Pacific region is much slower than that under the Atlantic

region (Bloxham and Gubbins, 1985; McElhinny et al., 1996). This

longitudinal asymmetry of the geomagnetic field, the so-called Pacific

dipole window, may be explained by thermal heterogeneity at the

lower mantle. Bloxham and Gubbins (1987) proposed that thermal

interaction whereby lateral variations in heat flux across the core-

mantle boundary drive core flows directly and influence the preexisting

deep convection. Furthermore, comparison of the geomagnetic field at

the core surface with lower mantle temperature or seismic velocity

suggests a close connection between them (Gubbins and Richards,

1986; Gubbins and Bloxham, 1987) and order-of-magnitude estimates

also suggest the variations are large enough to drive the core flow

required for secular variation of the Earth’s magnetic field (Bloxham

and Gubbins, 1987).

The inhomogeneous boundary condition in heat flux or temperature

at the core-mantle boundary, together with the strong effect of rotation,

drive fluid motions directly in the outer core which influence the

generation of geomagnetic field in the core. Moreover, an inhomoge-

neous boundary condition may also influence the core convection

being driven from below by locking it to the nonuniform boundary

condition (Zhang and Gubbins, 1993; Sarson et al., 1997).

Inhomogeneous boundary conditions: models

With a uniform thermal boundary, convection takes place when and

only when a sufficient radial temperature gradient, measured by the

size of the Rayleigh number, exists to drive it. With a nonuniform ther-

mal boundary, there are two driving parameters: one measures the

radial buoyancy and the other the strength of the lateral heating. It fol-

lows that how an inhomogeneous boundary condition affects the core

convection and dynamo can be illustrated by a simple nonlinear ampli-

tude equation in the form

A ¼ðm þ iÞA  AjAj

þ E; (Eq. 1)

where the flow amplitude A is a complex variable, i ¼

ﬃﬃﬃﬃﬃﬃﬃ

1

; E is a

positive parameter measuring the strength of the imposed inhomoge-

neous boundary condition (thermal or nonthermal) at the base of man-

tle, and m is a positive parameter like the Rayleigh number in

connection with the deep core convection. The amplitude equation is

simple but provides a helpful mathematical framework in the under-

standing of complicated nonlinear dynamics affected by an imposed

inhomogeneous boundary condition.

Without lateral heterogeneity of the lower mantle, E ¼ 0, convection

is always in the form of an azimuthally traveling wave, such as con-

vection rolls aligned with the axis of rotation. With the influence of

the lateral heterogeneity E 6¼ 0, a steady equilibrium solution A

becomes possible and can be obtained by setting

¼ 0. Denoting

¼ X

þ iY

and Z ¼jA

¼ X

þ Y

, we obtain the cubic

equation

 2mZ

þ Zðm

þ 1ÞE

¼ 0 (Eq. 2)

for steady solutions of convection, which can be solved analytically

using a standard formula. The stability of a steady solution A

can

be investigated by linearizing the nonlinear equation by letting

A ¼ðX

þ xÞþiðY

þ yÞ; (Eq. 3)

where x and y are small perturbations of X

and Y

. Stability of the

nonlinear equilibrium A

is then related to the two linear equations

x ¼ðm  3X

 Y

Þx ð1 þ 2X

Þy; (Eq. 4)

y ¼ð1  2X

Þx þðm  3Y

 X

Þy: (Eq. 5)

The corresponding growth rate s of the perturbations, or stability of

the boundary-driven steady solution, is then described by

s ¼ðm  2jA

ÞðjA

 1Þ

1=2

: (Eq. 6)

Two important features are evident from the stability of the boundary-

driven steady solution: (i) a Hopf bifurcation (traveling wave convec-

tion) cannot occur if the amplitude is sufficiently large, jA

j > 1; (ii) a

necessary condition for the occurrence of a Hopf bifurcation is E <

ﬃﬃﬃ

In other words, the core convection and dynamo in the presence of an

inhomogeneous core-mantle boundary can be locked into the boundary

provided that the effect is sufficiently strong, E >

ﬃﬃﬃ

. It follows that

the Pacific dipole window may reflect the thermal structure of mantle

convection under the Pacific region.

Complex three-dimensional numerical simulations in rotating sphe-

rical geometry show a similar behavior revealed by the above simple

model, demonstrating that an inhomogeneous boundary condition

imposed by the lower mantle can alter the properties of core convec-

tion and dynamo in a fundamental way (Zhang and Gubbins, 1992,

1993; Sarson et al., 1997; Olson and Christesen, 2002). The mantle

convection imposes a different length scale upon the system of the

core convection and dynamo. When a geodynamo model uses the

inhomogeneous boundary condition derived from seismic tomography,

it can produce an anomalous magnetic field and westward fluid velo-

city which are largely consistent with the observed features of the

Earth’s magnetic field (Olson and Christensen, 2002).

Keke Zhang

Bibliography

Bloxham, J., 2000. Sensitivity of the geomagnetic axial dipole to

thermal core-mantle interactions. Nature, 405(6782): 63–65.

Bloxham, J., and Gubbins, D., 1985. The secular variation of the

Earth’s magnetic field. Nature, 317: 777–781.

Bloxham, J., and Gubbins, D., 1987. Thermal core-mantle interactions.

Nature, 325:511–513.

Gubbins, D., and Bloxham, J., 1987. Morphology of the geomagnetic

field and implications for the geodynamo. Nature, 325: 509–511.

Gubbins, D., and Richards, M., 1986. Coupling of the core dynamo

and mantle: thermal or topographic? Geophysical Research Letters,

13: 1521–1524.

Hide, R., 1967. Motions of the earth’s core and mantle, and variations

of the main geomagnetic field. Science, 157:55–56.

Masters, G., Johnson S., Laske, G., and Bolton, H., 1996. A shear-

velocity of the mantle. Philosophical Transactions of the Royal

Society of London, Series A, 354: 1385–1411.

McElhinny, M.W., McFadden, P.L., and Merrill, P.T., 1996. The myth

of the Pacific dipole window. Earth and Planetary Science Letters,

143:13–22.

Moffatt, H.K., 1978. Magnetic Field Generation in Electrically Con-

ducting Fluids. Cambridge, England: Cambridge University Press.

Olson, P., and Christensen U.R., 2002. The time-averaged magnetic

field in numerical dynamos with nonuniform boundary heat flow.

Geophysical Journal International, 151(3): 809–823.

Sarson, G.R., Jones, C.A., and Longbottom, A.W., 1997. The

influence of boundary region heterogeneities on the geodynamo.

Physics of the Earth and Planetary Interiors, 104:13–32.

van der Hilst, R.D., Widiyantoro S., and Engdahl E.R., 1997. Evidence

for deep mantle circulation from global tomography. Nature, 386:

578–584.

Zhang, K., and Gubbins, D., 1992. On convection in the Earth’s core

forced by lateral temperature variations in the lower mantle.

Geophysical Journal International,

108: 247–255.

INHOMOGENEOUS BOUNDARY CONDITIONS AND THE DYNAMO 417

Zhang, K., and Gubbins, D., 1993. Convection in a rotating spherical

fluid shell with an inhomogeneous temperature boundary condition at

infinite Prandtl number. Journal of Fluid Mechanics, 250:209–232.

Cross-references

Core, Magnetic Instabilities

Core Motions

Magnetoconvection

Magnetohydrodynamic Waves

Proudman-Taylor Theorem

INNER CORE ANISOTROPY

Evidence for anisotropy of inner core

Anisotropy is the general term used to describe a medium whose prop-

erties (i.e., elastic properties in the case of seismic anisotropy) depend

on orientation. Seismic waves in an anisotropic medium travel with

different speeds depending on both their particle motion and propaga-

tion directions. The Earth’s solid inner core was found to possess

significant anisotropy in seismic velocity in the 1980s and early

1990s. Before that time, the inner core was known to us as a feature-

less small solid ball (at a radius of 1220 km) of iron-nickel alloy with

some light elements.

The evidence for the anisotropy of the inner core came from two

different kinds of observations: directional variations of travel-times

of seismic body waves that go through the inner core and anomalous

splitting, splitting not explainable simply by Coriolis and ellipticity

effects, of the Earth’s normal modes that are sensitive to the structure

of the Earth’s core. Anomalies in inner core arrival times and in nor-

mal-mode splitting were observed in early 1980s (Masters and Gilbert,

1981; Poupinet et al., 1983) and the hypothesis that the inner core is

anisotropic was first proposed in 1986 (Morelli et al., 1986).

Subsequent studies using travel-time data (e.g., Shearer et al., 1988)

generally favored the existence of inner core anisotropy. However, the

interpretation that anomalous splitting of core-sensitive modes is pri-

marily caused by the anisotropy of the inner core was controversial

(e.g., Widmer et al., 1992). Strong support for the inner core anisotropy

was provided in the early 1990s when new sets of information started

to emerge. Measurements of high quality differential travel-times of

PKP waves (waves that pass through the Earth’s core) show large

travel-time anomalies (2–6 s) for rays traveling through the inner core

nearly parallel to the Earth’s spin axis (polar paths) (Creager, 1992;

Song and Helmberger, 1993; Vinnik et al., 1994). Reanalysis of arrival

time data also confirmed large travel-time anomalies (Shearer, 1994; Su

and Dziewonski, 1995). At the same time, Tromp (1993) demonstrated

that a simple transversely isotropic inner core explained the anoma-

lously split core-sensitive modes and the larger, newly observed PKP

differential travel-time anomalies reasonably well.

An example of the evidence for the inner core anisotropy from

travel-time observations is shown in Figure I6. In analyzing travel-time

data, residuals of travel-times that seismic waves (phases) take from an

earthquake to arrive at recording stations are often formed by subtract-

ing the times predicted for a standard Earth model from measured

travel-times; similarly, residuals of differential travel-times are formed

Figure I6 (a) Ray paths of PKP(AB) and PKP(DF) phases at near antipodal distances. The PKP(AB) phase turns at mid-outer core and

the PKP(DF) phase passes through the inner core, sampling the bulk of the inner core at near antipodal distances as shown in this

example. (b) Residuals of differential PKP(AB)-PKP(DF) travel-times for near antipodal paths (modified from Sun and Song, 2002).

Assuming uniform cylindrical anisotropy in the inner core, the curve is the best fit to the data.

418 INNER CORE ANISOTROPY

by subtracting the time differences between two phases concerned pre-

dicted for a standard Earth model from measured differential travel-

times. Figure I6b shows the residuals of differential between AB and

DF branches of PKP waves (Figure I6a). Here the PKP(AB) is used

as a reference phase to form the differential travel times, which elim-

inates bias from uncertainties in earthquake origin times and reduces

the biases from earthquake mislocations and heterogeneous upper

mantle; heterogeneity in the outer core is assumed to be small because

of efficient mixing in the fluid core (Stevenson, 1987). The residuals

for the polar paths are systematically larger than those of the equatorial

paths, suggesting faster wave speed along the NS direction through the

inner core than along the equatorial plane. Assuming cylindrical aniso-

tropy with fast axis parallel to the spin axis, this data set indicates an

average anisotropy of about 2.5% in P-velocity in the inner core.

Three-dimensional structure of inner core anisotropy

and heterogeneity

The presence of significant anisotropy in the inner core is now well

accepted. The anisotropy appears to be dominantly cylindrical, with

the axis of symmetry aligned approximately with the NS spin axis of

the Earth. The detailed structure of the inner core anisotropy is still being

mapped out. Some studies suggest the inner core has a simple constant

anisotropy except for the innermost inner core (Ishii and Dziewonski,

2002). Other studies, however, suggest that the inner core anisotropy is

more complex, varying both laterally and in depth, although some of

the complexity may be due to contamination from the lowermost mantle

heterogeneity (Breger et al., 2000; Tromp, 2001).

The outermost part of the inner core appears nearly isotropic

(Shearer, 1994). The thickness of the weak anisotropy layer varies

from upper 100–250 km in the western inner core to upper 400 km

or more in the eastern inner core (Creager, 2000; Souriau et al.,

2003). The transition from isotropy in the upper inner core to strong

anisotropy in lower inner core under Central America appears to be

sharp enough to cause multipathing of seismic waves (Song and

Helmberger, 1998).

There is also growing evidence for strong lateral variation in inner

core structure. The inner core appears to vary on all scales, from the

scale of half a hemisphere to the scale of a few kilometers (Vidale

and Earle, 2000; Cormier and Li, 2002). At the uppermost 100 km

of the inner core, the P-velocity in the quasi-eastern hemisphere

(40



E–180



E) is isotropically faster than the quasi-western hemi-

sphere (180



W–40



E) by about 0.8% (Niu and Wen, 2001). At inter-

mediate depth, 100–400 km below the inner core boundary (ICB), the

inner core possesses a hemispherical pattern of a different form. The

quasi-western hemisphere is strongly anisotropic but the quasi-eastern

hemisphere is nearly isotropic (Tanaka and Hamaguchi, 1997). Deeper

into the inner core, significant anisotropy (3%) seems to exist in both

hemispheres (Creager, 2000; Souriau et al., 2003); however, in the

innermost 300–400 km of inner core, it is suggested that the form of

the anisotropy is distinctly different (Ishii and Dziewonski, 2002;

Beghein and Trampert, 2003).

Sources of inner core anisotropy

Apparent seismic velocity anisotropy can, in general, arise from pre-

ferred orientation of anisotropic crystals or from lamination of a solid.

The properties of the inner core are widely believed to be consistent

with those of anisotropic iron crystals in the hexagonal close-packed

(hcp) phase (e.g., Brown and McQueen, 1986). Thus, the anisotropy

is believed to be due to a preferred orientation of the hcp iron (e.g.,

Stixrude and Cohen, 1995). However, the mechanisms responsible

for creating such a preferred alignment are under debate.

One category of the proposed models involves texturing established

during the solidification of iron crystals at the surface of the inner

core. Possible mechanisms of solidification texturing include dendritic

growth of iron crystals as they solidify (Bergman, 1997) and the

development of anisotropic polycrystalline solid due to the presence

of thermal gradient and initial nucleation in the melt (Brito et al. , 2002).

However, solidification texturing alone cannot explain the observed

depth dependence of the anisotropy. The other category of the proposed

models involves the alignment of iron crystals from plastic deformation

in the inner core after solidification. Proposed mechanisms of plastic

deformation in the inner core include solid state thermal convection dri-

ven by internal heating (Jeanloz and Wenk, 1988); flow induced by

Maxwell stress (stress due to magnetic field) (Karato, 1999; Buffett

and Wenk, 2001); and flow induced by a differential stress field created

by preferential growth of the inner core in the equatorial belt, which

results from more efficient heat transport in the equator than near the

polar regions (Yoshida et al., 1996).

Implications of inner core anisotropy

The inner core anisotropy has important implications for improving our

understanding of the structure, composition, and dynamics of the

Earth’s deep interior. It has been suggested that the inner core is rotating

relative to the mantle (Song and Richards, 1996). Detailed mapping of

the lateral variations of the inner core anisotropic structure is crucial

for quantification of the rotation rate (Creager, 1997), which would con-

tribute to our understanding of the geodynamo (e.g., Glatzmaier and

Roberts, 1995; Kuang and Bloxham, 1997) and could influence our

interpretation of decadal variations in the length of day (Buffett and

Glatzmaier, 2000). The understanding of the source of the inner core ani-

sotropy is expected to improve our understanding of the inner core

evolution and its interactions with the outer core (e.g., Romanowicz

et al., 1996; Buffett, 2000). Viable models for the origin of anisotropy

must be compatible with the estimates of symmetry, depth-dependence

and lateral variations. The basic cylindrical symmetry of the inner core

anisotropy probably reflects the strong influence of rotation on the

dynamics of the fluid core. The absence of anisotropy from the upper-

most region of the inner core suggests that any texture acquired during

solidification is weak. However, a weak initial texture could be sub-

sequently amplified by grain growth and plastic deformation. In this

case, the rate of increase in anisotropy with depth is closely related

to the relative rates of inner core growth, grain growth, and strain accu-

mulation. The existence of sharp increase with depth and strong lateral

variations of inner core anisotropy poses serious restrictions of the

mechanisms responsible for the anisotropy. Improved models of the

anisotropic structure of the inner core from seismic imaging will be vital

in addressing these issues.

Xiaodong Song

Bibliography

Beghein, C., and Trampert, J., 2003. Robust normal mode constraints

on inner-core anisotropy from model space search. Science, 299:

552–555.

Bergman, M.I., 1997. Measurements of elastic anisotropy due to soli-

dification texturing and the implications for the Earth’s inner core.

Nature, 389:60–63.

Breger, L., Tkalcic, H., and Romanowicz, B., 2000. The effect of D”

on PKP(AB-DF) travel time residuals and possible implications

for inner core structure. Earth and Planetary Science Letters,

175: 133–143.

Brito, D., Elbert, D., and Olson, P., 2002. Experimental crystallization

of gallium: ultrasonic measurement of elastic anisotropy and

implications for the inner core. Physics of the Earth and Planetary

Interiors, 129: 325–346.

Brown, J.M., and McQueen, R.G., 1986. Phase-transitio ns, Gruneisen-

parameter, and elasticity for shocked iron between 77-GPa and

400-GPa. Geophysical Journal of the Royal Astronomical Society,

91: 7485–7494.

Buffett, B.A., 2000. Dynamics of the Earth’s core. In Karato, S., Forte,

A.M., Liebermann, R.C., Masters, G., and Stixrude, L. (eds.),

INNER CORE ANISOTROPY 419

Earth’s Deep Interior: Mineral Physics and Tomography from the

Atomic to the Global Scale, American Geophysical Union Mono-

graph 117. Washington, DC: American Geophysical Union,

pp. 37–62.

Buffett, B.A., and Glatzmaier, G.A., 2000. Gravitational braking of

inner-core rotation in geodynamo simulations. Geophysical

Research Letters, 27: 3125–3128.

Buffett, B.A., and Wenk, H.R., 2001. Texturing of the inner core by

Maxwell stresses. Nature, 413:60–63.

Cormier, V.F, and Li, X., 2002. Frequency-dependent seismic attenua-

tion in the inner core. 2. A scattering and fabric interpretation.

Journal of Geophysical Research, 107(B12): doi:10.1029/2002

JB001796.

Creager, K.C., 1992. Anisotropy of the inner core from differential tra-

vel times of the phases PKP and PKIKP. Nature, 356: 309–314.

Creager, K.C., 1997. Inner core rotation rate from small-scale hetero-

geneity and time-varying travel times. Science, 278: 1284 –1288.

Creager, K.C., 2000. Inner core anisotropy and rotation. In Karato, S.,

Forte, A.M., Liebermann, R.C., Masters, G., and Stixrude, L. (eds.),

Earth’s Deep Interior: Mineral Physics and Tomography from the

Atomic to the Global Scale, American Geophysical Union Monograph

117. Washington, DC: American Geophysical Union, pp. 89–114.

Glatzmaier, G.A., and Roberts, P.H., 1995. A three-dimensional con-

vective dynamo solution with rotating and finitely conducting inner

core and mantle. Physics of the Earth and Planetary Interiors, 91:

63–75.

Ishii, M., and Dziewonski, A.M., 2002. The innermost inner core of

the earth: evidence for a change in anisotropic behavior at the

radius of about 300 km. PNAS, 99(22): 14026–14030.

Jeanloz, R., and Wenk, H.R., 1988. Convection and anisotropy of the

inner core. Geophysical Research Letters, 15:72–75.

Karato, S., 1999. Seismic anisotropy of the Earth’s inner core resulting

from flow induced by Maxwell stresses. Nature, 402: 871–873.

Kuang, W.J., and. Bloxham, J., 1997. An earth-like numerical dynamo

model. Nature, 389: 371–374.

Masters, G., and Gilbert, F., 1981. Structure of the inner core inferred

from observations of its spheroidal shear modes. Geophysical

Research Letters, 8: 569–571.

Morelli, A., Dziewonski, A.M., and Woodhouse, J.H., 1986. Aniso-

tropy of the inner core inferred from PKIKP travel-times. Geophy-

sical Research Letters, 13: 1545–1548.

Niu, F.L., and Wen, L.X., 2001. Hemispherical variations in seismic

velocity at the top of the Earth’s inner core. Nature, 410:1081–1084.

Poupinet, G., Pillet, R., and. Souriau, A., 1983. Possible heterogeneity

of the Earth’s core deduced from PKIKP travel-times. Nature, 305:

204–206.

Romanowicz, B., Li, X.D., and Durek, J., 1996. Anisotropy in the

inner core: could it be due to low-order convection? Science,

274(5289): 963–966.

Shearer, P.M., 1994. Constraints on inner core anisotropy from PKP(DF)

travel-times. Journal of Geophysical Research, 99:19,647–19,659.

Shearer, P.M., Toy, K.M., and Orcutt, J.A., 1988. Axi-symmetric Earth

models and inner-core anisotropy. Nature, 333: 228–232.

Song, X.D., and Helmberger, D.V., 1988. Seismic evidence for an

inner core transition zone. Science, 282: 924–927.

Song, X.D., and Helmberger, D.V., 1993. Anisotropy of Earth’s inner

core. Geophysical Research Letters, 20: 2591–2594.

Song, X.D., and Richards, P.G., 1996. Observational evidence for

differential rotation of the Earth’s inner core. Nature, 382: 221–224.

Souriau, A., Garcia, R., and Poupinet, G., 2003. The seismological

picture of the inner core: structure and rotation. Comptes Rendus

Geoscience, 335(1): 51–63.

Su, W.J., and Dziewonski, A.M., 1995. Inner core anisotropy in three

dimensions. Journal of Geophysical Research, 100: 9831–9852.

Sun, X.L., and Song, X.D., 2002. PKP travel times at near antipodal

distances: implications for inner core anisotropy and lowermost

mantle structure. Earth and Planetary Science Letters, 199:

429–445.

Stevenson, D.J., 1987. Limits on lateral density and velocity variations

in the Earth’s outer core. Geophysical Journal of the Royal Astro-

nomical Society, 88:311–319.

Stixrude, L., and Cohen, R.E., 1995. High-pressure elasticity of iron

and anisotropy of Earth’s inner core. Science, 267: 1972 –1975.

Tanaka, S., and Hamaguchi, H., 1997. Degree one heterogeneity and

hemispherical variation of anisotropy in the inner core from PKP

(BC)-PKP(DF) times. Journal of Geophysical Research, 102:

2925–2938.

Tromp, J., 1993. Support for anisotropy of the Earth’s inner core from

free oscillations. Nature, 366: 678–681.

Tromp, J., 2001. Inner-core anisotropy and rotation. Annual Review of

Earth and Planetary Sciences, 29:47–69.

Vidale, J.E., and Earle, P.S., 2000. Fine-scale heterogeneity in the

Earth’s inner core. Nature, 404(6775): 273–275.

Vinnik, L., Romanowicz, B., and Breger, L., 1994. Anisotropy in the

center of the inner-core. Geophysical Research Letters, 21(16):

1671–1674.

Widmer, R.W., Masters, G., and Gilbert, F., 1992. Observably split mul-

tiplets—data analysis and interpretation in terms of large-scale aspheri-

cal structure. Geophysical Journal International, 111:559–576.

Yoshida, S., Sumita, I., and. Kumazawa, M., 1996. Growth-model of the

inner core coupled with the outer core dynamics and the resulting elas-

tic anisotropy. Journal of Geophysical Research

, 101:28085–28103.

Cross-references

Core Convection

Core Properties, Theoretical Determination

Geodynamo, Energy Sources

Geodynamo, Numerical Simulations

Grüneisen’s Parameter for Iron and Earth’s Core

Inner Core Composition

Inner Core Oscillation

Inner Core Rotation

Inner Core Rotational Dynamics

Inner Core Seismic Velocities

Lehmann, Inge (1888–1993)

INNER CORE COMPOSITION

Why is the inner core important?

The solid inner core is complex and not yet fully understood. This

is hardly surprising given that the temperature of the Earth’ s core (q.v.)

is in the range 5000–6000 K and inner core pressures are 330–

360 GPa. Knowledge of the exact composition and structure of the

Earth’s inner core would enable a better understanding of the internal

structure and dynamics of the Earth as a whole; in particular, better

constraints on core composition ( q.v.) would not only have fundamen-

tal implications for models of the formation, differentiation, and evolu-

tion of the Earth, but would also enable successful interpretation of

seismic observations which have revealed inner core anisotropy

(q.v.), layering and heterogeneity (e.g., Creager, 1992; Song, 1997;

Beghein and Trampert, 2003; Cao and Romanowicz, 2004; Koper

et al., 2004). The elastic anisotropy of the inner core is well estab-

lished: seismic velocities of the inner core (q.v.) show P-wave veloci-

ties 3% faster along the polar axis than in the equatorial plane

(e.g., Creager, 1992). However, more recent seismic observations sug-

gest further complexity. The evidence is for a seismically isotropic

upper layer, with lateral variations in thickness of 100–400 km,

420 INNER CORE COMPOSITION

overlaying an irregular, nonspherical transition region to an anisotropic

lower layer (Song and Helmberger, 1998; Ouzounis and Creager,

2001; Song and Xu, 2002). The existence of an isotropic upper layer

implies that the magnitude of the seismic anisotropy in the lower inner

core must be significantly greater than previously thought, possibly as

much as 5%–10%. The observed layering also implies that the upper

and lower inner core are compositionally or structurally different.

Small-scale heterogeneities in the Earth’s inner core have also been

observed, possibly associated with phase changes, a “mushy layer,”

melt inclusions and/or compositional differences (Cao and Romanowicz,

2004; Koper et al., 2004). The question now arises as to the me-

chanisms by which such complexity can occur, all of which could

be highly compositionally dependent. Therefore, we cannot test any

hypotheses for the observed features without knowing the inner core

composition.

The inner core is not just made of iron

The exact composition of the Earth’s inner core is not very well

known. On the basis of cosmochemical and geochemical arguments,

it has been suggested that the core is an iron alloy with possibly as

much as 5 wt% Ni and very small amounts (only fractions of a

wt% to trace) of other siderophile elements such as Cr, Mn, P, and

Co (McDonough and Sun, 1995). On the basis of materials-density/

sound-wave velocity systematics, Birch (1964) further concluded that

the core is composed of iron that is alloyed with a small fraction of

lighter elements. The light alloying elements most commonly sug-

gested include S, O, Si, H, and C, although minor amounts of other

elements, such K, could also be present (e.g., Poirier, 1994; Gessmann

and Wood, 2002). From seismology it is known that the density jump

across the inner core boundary is between 4.5% and 6.7% (Shearer

and Masters, 1990; Masters and Gubbins, 2003) indicating that there

is more lighter element alloying in the outer core. The evidence thus

suggests that the outer core contains 5%–10% light elements, while

the inner core has 2%–3% light elements. Our present understanding

is that the Earth’s solid inner core is crystallizing from the outer core

as the Earth slowly cools and the partitioning of the light elements

between the solid and liquid is therefore crucial to understanding the

evolution and dynamics of the core.

Which phase of iron exists in the inner core?

Before tackling the more detailed problem of inner core composition

(q.v.) in terms of alloying elements, it is essential to know what crys-

talline structure(s) are present and also their seismic properties, as

these will greatly affect both interpretations made from seismic data

and also the possible alloying mechanism. Many experimentalists have

put an enormous effort over the last 10–15 years into obtaining a

phase diagram of pure iron under core conditions, but above relatively

modest pressures and temperatures there is still much uncertainty.

Experimental techniques have evolved rapidly in recent years, and

today, using diamond anvil cells or shock wave experiments (q.v.),

the study of minerals at pressures up to 200 GPa and temperatures

of a few thousand Kelvin are possible. These studies, however, are still

far from routine and results from different groups are often in conflict.

At low pressures and temperatures the phase diagram of iron is well

understood: the body-centered-cubic (bcc) phase is stable at ambient

conditions, transforming to the hexagonal close-packed phase (hcp) at

high pressure (>10–15 GPa) and to the face-centered-cubic phase at high

temperature (>1200 K). Both experiments and also theoretical calcula-

tions of the static, zero-Kelvin solid (Stixrude et al., 1997; Vočadlo

et al., 2000), have suggested that the hcp phase has a wide stability field

at high pressures and temperatures right to the conditions of the Earth’s

inner core. However, this assumption that iron must have the hcp struc-

ture at core conditions has recently been challenged (Brown, 2001;

Beghein and Trampert, 2003), especially if the presence of lighter

elements is included (Lin et al., 2003). It now seems very possible that

a bcc phase might be formed (Vočadlo et al., 2003). Previously, the bcc

phase of iron was considered an unlikely candidate for an inner core-

forming phase because athermal calculations show it to be elastically

unstable at high pressures, with an enthalpy considerably higher than

that of hcp iron (Stixrude and Cohen, 1995; Söderlind et al., 1996;

Vočadlo et al., 2000). However, more recent ab initio molecular

dynamics calculations at core pressures and temperatures have sug-

gested that the bcc phase of iron becomes entropically stabilized at core

temperatures. Although for pure iron the thermodynamically most

stable phase is still the hcp phase, the free energy difference is so very

slight that a small amount of light element impurity could stabilize the

bcc phase at the expense of the hcp phase (Vo čadlo et al., 2003).

Alloying elements

It is generally assumed that the small amount of nickel alloyed to iron

in the inner core is unlikely to have any significant affect on core prop-

erties (q.v.) as nickel and iron have sufficiently similar densities

to be seismically indistinguishable, and addition of small amounts of

nickel are unlikely to appreciably change the physical properties

of iron. However, the presence of light elements in the core does have

an affect on core properties. The light element impurities most often

suggested are sulfur, oxygen, and silicon. Although these alloying sys-

tems have been experimentally studied up to pressures of around

100 GPa (e.g., Li and Agee, 2001; Lin et al., 2003; Rubie et al., 2004)

there seems little prospect of obtaining experimental data for iron

alloys at the highly elevated pressures and temperatures of the Earth’s

inner core.

An alternative approach to understanding inner core composition

(q.v.) is to simulate the behavior of these iron alloys with ab initio calcu-

lations which are readily able to access the pressures and temperatures

of the inner core. Alfè et al. (2000, 2002) calculated the chemical poten-

tials of iron alloyed with sulfur, oxygen, and silicon. They developed

a strategy for constraining both the impurity fractions and the tempera-

ture at the inner core boundary (ICB) based on the supposition that the

solid inner core and liquid outer core are in thermodynamic equilibrium

at the ICB. For thermodynamic equilibrium the chemical potentials

of each species must be equal both sides of the ICB, which fixes the

ratio of the concentrations of the elements in the liquid and in the solid,

which in turn fixes the densities. If the core consisted of pure iron, equal-

ity of the chemical potential (the Gibbs free energy in this case) would

tell us only that the temperature at the ICB is equal to the melting tem-

perature of iron (q.v.) at the ICB pressure of 330 GPa. With impurities

present, the ab initio results reveal a major qualitative difference

between oxygen and the other two impurities: oxygen partitions strongly

into the liquid, but sulfur and silicon, both partition equally in the solid

and liquid. Having established the partitioning coefficients, Alfè et al.

(2002) then investigated whether the known densities of the outer and

inner core, estimated from seismology, could be matched by one of

their calculated binary systems. For sulfur and silicon, their ICB density

discontinuities were considerably smaller than the known seismological

value at that time of 4.5%  0.5% (Shearer and Masters, 1990); for oxy-

gen, the discontinuity was markedly greater than that from seismology.

Therefore none of these binary systems were plausible, i.e., the core can-

not be made solely of Fe/S, Fe/Si, or Fe/O. However, the seismic data

can clearly be matched by a ternary/quaternary system of iron and oxy-

gen together with sulfur and/or silicon. A system consistent with seismic

data could contain 8 mol% oxygen and 10 mol% sulfur and/or silicon

in the outer core, and 0.2 mol% oxygen and 8.5 mol% sulfur and/or

silicon in the inner core (Alfè et al., 2002). However, it should be remem-

bered that it is likely that several other light elements could exist in

the inner core and would therefore have to be considered before a

true description of inner core composition could be claimed.

Lidunka Vočadlo

INNER CORE COMPOSITION 421

Bibliography

Alfè, D., Gillan, M.J., and Price, G.P., 2000. Constraints on the com-

position of the Earth’s core from ab initio calculations. Nature,

405: 172–175.

Alfè, D., Gillan, M.J., and Price, G.P., 2002. Ab initio chemical poten-

tials of solid and liquid solutions and the chemistry of the Earth’s

core. Journal of Chemical Physics, 116: 7127–7136.

Beghein, C., and Trampert, J., 2003. Robust normal mode constraints

on inner-core anisotropy from model space search. Science, 299:

552–555.

Birch, F., 1964. Density and composition of the mantle and core.

Journal of Geophysical Research, 69: 4377–4388.

Brown, J.M., 2001. The equation of state of iron to 450 GPa: another

high pressure solid phase? Geophysical Research Letters, 28:

4339–4342.

Cao, A., and Romanowicz, B., 2004. Hemispherical transition of

seismic attenuation at the top of the Earth’s inner core. Earth and

Planetary Science Letters, 228: 243–253.

Creager, K.C., 1992. Anisotropy of the inner core from differen-

tial travel-times of the phases PKP and PKIKP. Nature, 356:

309–314.

Gessmann, C.K., and Wood, B.J., 2002. Potassium in the Earth’s core?

Earth and Planetary Science Letters, 200:63–78.

Koper, K.D., Franks, J.M., and Dombrovskaya, M., 2004. Evidence

for small-scale heterogeneity in Earth’s inner core from a global

study of PkiKP coda waves. Earth and Planetary Science Letters,

228: 227–241.

Li, J., and Agee, C.B., 2001. Element partitioning constraints on the

light element composition of the Earth’s core. Geophysical

Research Letters, 28:81–84.

Lin, J-F., et al

., 2003. Sound velocities of iron-nickel and iron-silicon

alloys at high pressures. Geophysical Research Letters, 30:

doi:10.1029/2003GL018405.

Masters, G., and Gubbins, D., 2003. On the resolution of density

within the Earth. Physics of the Earth and Planetary Interiors,

140: 159–167.

McDonough, W.F., and Sun, S-S., 1995. The composition of the Earth.

Chemical Geology, 120: 223–253.

Ouzounis, A., and Creager, K.C., 2001. Isotropy overlying and iso-

tropy at the top of the inner core. Geophysical Research Letters,

28: 4331–4334.

Poirier, J-P., 1994. Light elements in the Earth’s outer core: a critical

review. Physics of the Earth and Planetary Interiors, 85: 319–337.

Rubie, D.C., Gessmann, C.K., and Frost, D.J., 2004. Partitioning of

oxygen during core formation of the Earth and Mars. Nature,

429:58–61.

Shearer, P., and Masters, G., 1990. The density and shear velocity con-

trast at the inner core boundary. Geophysical Journal International,

102: 491–498.

Söderlind, P., Moriarty, J.A., and Wills, J.M., 1996. First-principles

theory of iron up to Earth’s core pressures: structural, vibrational

and elastic properties. Physical Review B, 53: 14,063–14,072.

Song, X., 1997. Anisotropy of the Earth’s inner core. Reviews in Geo-

physics, 35(3): 297–313.

Song X., and Helmberger, D.V., 1998. Seismic evidence for an inner

core transition zone. Science, 282: 924–927.

Song, X., and Xu, X., 2002. Inner core transition zone and anomalous

PKP(DF) waveforms from polar paths. Geophysical Research

Letters, 29:1–4.

Stixrude, L., and Cohen, R.E., 1995. Constraints on the crystalline

structure of the inner core—mechanical instability of bcc iron at

high pressure. Geophysical Research Letters,

22: 125–128.

Stixrude, L., Wasserman, E., and Cohen, R.E., 1997. Composition and

temperature of the Earth’s inner core. Journal of Geophysical

Research, 102: 24729–24739.

Vočadlo. L., et al., 2000. Ab initio free energy calculations on the

polymorphs of iron at core conditions. Physics of the Earth and

Planetary Interiors, 117: 123–127.

Vočadlo. L., et al., 2003. Possible thermal and chemical stabilisation

of body-centred-cubic iron in the Earth’s core. Nature, 424:

536–539.

Cross-references

Core Composition

Core Properties, Physical

Core Properties, Theoretical Determination

Core Temperature

Inner Core Anisotropy

Inner Core Seismic Velocities

Melting Temperature of Iron in the Core, Experimental

Melting Temperature of Iron in the Core, Theory

Shock Wave Experiments

INNER CORE OSCILLATION

Earth’s inner core, identified in relatively recent time (Lehmann, 1936)

(q.v.), can be considered to be an elastic solid on timescales of seismic

waves. With a radius of 1220 km and hence containing less than 1% of

Earth’s volume, the inner core’s importance to our understanding of

Earth structure far exceeds both its relative size and our knowledge

of its properties.

Decadal changes in Earth’s magnetic field, linked to torsional oscilla-

tions (q.v.) of the fluid outer core, can produce corresponding oscillations

of the inner core through electromagnetic coupling. Since the inner core

is well coupled gravitationally to the mantle, both changes in LOD (q.v.)

and polar motion of the mantle on a decade timescale could be used to

constrain torsional oscillations (Dumbery and Bloxham, 2003) (see also

Inner core rotation).

Gravitational force is responsible for holding the slightly denser

inner core at Earth’s center in the surrounding fluid core. Thus the

inner core will return to this central equilibrium position if displaced

axially and subsequently oscillate at periods of a few hours. This fact

was initially recognized by Slichter (1961) who also realized that

Earth’s rotation would lead to two additional circular modes, one pro-

grade and one retrograde if the inner core were displaced in a direction

perpendicular to the rotation axis.

Theoretical values of three modes of oscillation, often referred to as

the Slichter triplet, depend on the physical properties of the core

described by the Earth model chosen, as well as the method used to

calculate their periods. In the case of the Earth model 1066A (Gilbert

and Dziewonski, 1975), for example, the buoyancy oscillation period

without Earth rotation or degenerate period, is reported as 4.599 h by

Rogister (2003), 4.309 h by Rieutord (2002), and 4.45471 h by Smylie

et al. (2001). The central period of the triplet has been calculated using

normal mode theory (Rogister, 2003), yielding estimates near 5.309 h

for the Earth model PREM (Dziewonski and Anderson, 1981) and

4.529 h for 1066A which closely agree with those from perturbation

methods (e.g., Dahlen and Sailor, 1979; Crossley et al., 1992) that

ignored ellipticity and centrifugal effects. A central period of 4.255 h

for 1066A has been found by Rieutord (2002) who reminded us

that the buoyancy of the inner core is determined by the difference

between the mean density of the inner core and its surrounding fluid

rather than the density jump at the inner core-outer core boundary. An

even shorter central period of 3.7926 h is predicted (Smylie et al.,

2001) for the Cal8 Earth model (Bullen and Bolt, 1985) with a higher

density inner core that experiences a larger restoring force when

displaced.

422 INNER CORE OSCILLATION

The Slichter triplet has been the subject of search in gravimetric

records since a movement of the inner core will produce a small

change in Earth’s gravitational field. Following the Chilean earthquake

of May 22, 1960, a peak in the gravimetric record near 86 min was

tentatively identified as an inner core oscillation, implying a much

denser inner core than would be consistent with existing Earth models.

Significant attempts had been made to detect the Slichter triplet

by locating gravimeters near the South Pole where the diurnal and

semidiurnal tidal effects are small (Rydelek and Knopoff, 1984) but

there was no identification of the triplet.

In recent years, stable, low noise, superconducting gravimeters have

allowed for the measurement of changes in gravity down to

2  10

11

2

in Earth’s gravity field of about 9.8 ms

2

. Thus,

long records can be analyzed in the frequency domain for three spec-

tral peaks separated by precisely the amount predicted by the Earth

model chosen. Even with the above sensitivity, however, the signal-

to-noise ratios are so small that no one has yet observed the Slichter

triplet in a single gravimetric record. By combining several supercon-

ducting gravimetric records with a wide geographical distribution,

through a method known as product spectral analysis (Smylie et al.,

1993), a claim has been made (Smylie et al., 2001) to have observed

the Slichter triplet at periods 3.5822, 3.7656, and 4.0150 h with a statis-

tical error of 0.04%. These observed values are reported to correspond

to periods of 3.5168, 3.7926, and 4.1118 h predicted from the Cal8

model assuming the fluid core is inviscid. This identification and the

method of analysis reported by Smylie et al. (2001) are yet to be widely

accepted. Other groups have either failed to find the Slichter triplet

(Hinderer et al., 1995) or, more recently, have reported several possible

candidate signals for the Slichter triplet depending on the Earth model

chosen (Rosat et al., 2004). Still others have cautioned (Florsch et al.,

1995) that there is a high likelihood in finding significant fits to a

triplet of spectral peaks even if one chooses the frequencies at random.

The rotational splitting of the Slichter triplet should include a contri-

bution from viscosity of the liquid outer core as noted by Smylie

(1999). Using boundary layer theory, he calculated the viscosity of

the outer core fluid in a layer next to the inner core boundary, based

on the small discrepancy between the observed and predicted triplet per-

iods. He found a very high kinematic viscosity, close to 10

1

, that

was interpreted as confirming the semifluid nature of the layer at the

base of the fluid core as the source of energy for the geodynamo. Such

a large viscosity, however, brings into question the validity of results

obtained by using only the leading term of the asymptotic series, as

pointed out by Rieutord (2002). Future models that include dissipation

due to turbulence (see Core turbulence) and partial solidification in the

boundary layer around the inner core would decrease estimates of visc-

osity of the fluid core.

Periods of the Slichter triplet are extremely sensitive to the mean

density of the inner core (q.v.), about 3 h for each gm cm

3

for the

axial mode (Smylie et al., 2001), and thus would provide an indepen-

dent estimate of that important quantity. Confirmation of the measured

periods of the Slichter triplet will provide the basis for an estimation of

the density jump at the inner core-outer core boundary, that is central

to estimation of the inner core’s age and its role in a geodynamo

driven by compositional convection. Further improvement in signal-

to-noise ratio of gravity measurements and a larger excitation of the

inner core, whose source remains unknown, are needed to validate

the detection of the Slichter triplet.

Keith Aldridge

Bibliography

Bullen, K.E., and Bolt, B.A., 1985. An Introduction to the Theory of

Seismology. Cambridge: Cambridge University Press.

Crossley, D., Rochester, M., and Peng, Z., 1992. Slichter modes and

Love numbers. Geophysical Research Letters, 19: 1679–1682.

Dahlen, F.A., and Sailor, R.V., 1979. Rotational and elliptical splitting

of the free oscillations of the Earth. Geophysical Journal of the

Royal Astronomical Society, 58: 609–623.

Dumbery, M., and Bloxham, J., 2003. Torque balance, Taylor’s con-

straint and torsional oscillations in a numerical model of the geody-

namo. Physics of the Earth and Planetary Interiors , 140:29– 51.

Dziewonski, A.M., and Anderson, D.L., 1981. Preliminary Reference

Earth Model (PREM). Physics of the Earth and Planetary Interiors,

25:297–356.

Florsch, N., Legros, H., and Hinderer, J., 1995. The search for weak

harmonic signals in a spectrum with applications to gravity data.

Physics of the Earth and Planetary Interiors, 90: 197–210.

Gilbert, F., and Dziewonski, A.M., 1975. An application of normal

mode theory to the retrieval of structural parameters and source

mechanisms from seismic spectra. Philosophical Transactions of

the Royal Society of London, Series A, 278: 187– 269.

Hinderer, J., Crossley, D., and Jensen, O., 1995. A search for the Slich-

ter triplet in superconducting gravimeter data. Physics of the Earth

and Planetary Interiors, 90: 221–241.

Lehmann, I., 1936. P

. Publication Bureau Central Seismologique

International, Series A, 14:87–115.

Rieutord, M., 2002. Slichter modes of the Earth revisited. Physics of

the Earth and Planetary Interiors, 131: 269–278.

Rogister, Y., 2003. Splitting of seismic-free oscillations and of the Slich-

ter triplet using the normal mode theory of a rotating, ellipsoidal

earth. Physics of the Earth and Planetary Interiors, 140:169–182.

Rosat, S., Hinderer, J., Crossley, D., and Boy, J.P., 2004. Performance

of superconducting gravimeters from long-period seismology to

tides. Journal of Geodynamics, 38: 461–476.

Rydelek, P., and Knopoff, L., 1984. Spectral analysis of gapped data:

search for the mode

at the South Pole. Journal of Geophysical

Research, 89: 1899–1911.

Slichter, L.B., 1961. The fundamental free mode of the Earth’s inner core.

Proceeding of the National Academy of Sciences USA, 47:186–190.

Smylie, D.E., 1999. Viscosity near earth’s solid inner core. Science,

284: 461–463.

Smylie D.E., Hinderer, J., Richter, B., and Ducarme, B., 1993. The

product spectra of gravity and barometric pressure in Europe.

Physics of the Earth and Planetary Interiors, 80: 135–157.

Smylie, D.E., Francis, O., and Merriam, J.B., 2001. Beyond tides—

determination of core properties from superconducting gravimeter

observations. Journal of the Geodetic Society of Japan, 47:364–372.

Cross-references

Core Density

Core Turbulence

Inner Core Rotation

Lehmann, Inge (1888–1993)

Length of Day Variations, Decadal

Oscillations, Torsional

INNER CORE ROTATION

Observational evidence of inner core rotation is based on changes in

the travel-time of seismic waves. The rotation rate appears to be a

few tenths of a degree per year eastward with respect to the mantle.

Early specul ations

The inner core with radius of about 1215 km resides concentrically

within the much larger fluid outer core, which has a low viscosity

(e.g., Poirier, 1998). Patterns of convection within the fluid core

INNER CORE ROTATION 423

associated with the geodynamo are presumed to undergo temporal var-

iations because the Earth’s magnetic field is changing on timescales

ranging over several orders of magnitude. It is therefore reasonable

to speculate (Gubbins, 1981; Anderson, 1983) that the inner core

might have a rotation rate somewhat different from that of the rest of

the solid Earth, which is dominated by the daily rotation. If such rela-

tive rotation could be detected, it would provide information on the

energy of convection patterns that maintain the geomagnetic field.

The study of inner core motion relative to the mantle and crust is

difficult, because of the remoteness of the inner core (more than

5150 km from the Earth’s surface where the nearest observations can

be made) and its small size (about 0.7% of the Earth’s volume). Also

there are intrinsic difficulties in telling whether a spherical object is

rotating, unless a marker on or within the object can be identified

and tracked if it moves.

First claims, based on seismological observations

and implications

The first published claim of observational evidence for inner core

rotation, relative to the mantle and crust, was given by Song and

Richards (1996). They noted that seismic waves originating in the

South Sandwich Islands (in the southernmost South Atlantic) and

recorded in Alaska, which had traveled through the inner core,

appeared to have traveled systematically faster for earthquakes in the

later years during the period from 1967 to 1995, compared to observa-

tions of seismic waves from earlier earthquakes in this time period.

The rate of travel-time decrease amounted to about 0.01 s y

1

—

a value that was close to the precision of measurement.

More detailed studies by Creager (1997), Song (2000), and Li and

Richards (2003), have provided additional support for travel-time

change of about this same value, for seismic P-waves crossing the

inner core. Figure I7 shows a clear example of PKIKP waves (which

pass through the inner core) showing a faster arrival for the later earth-

quake, when the seismograms are aligned on PKP waves (which avoid

the inner core).

Song and Richards (1996) interpreted the travel-time change as an

effect of anisotropy, which causes P-waves to travel with speeds that

depend on direction relative to a crystalline axis that rotates with the

inner core. Creager (1997) persuasively argued for a more important

marker of inner core rotation, namely a lateral gradient of the P wave-

speed (increasing from east to west) in the part of the inner core tra-

versed by PKIKP waves. He and Song (2000), Richards (2000), and

Li and Richards (2003) concluded the observed travel-time changes

indicate an eastward rotation of the inner core amounting to a few

tenths of a degree per year.

The concept of an inner core rotating fast enough to be detected on a

human timescale has attracted numerous investigators since 1996.

Dehant et al. (2003) describe inner core research in mineral physics,

seismology, geomagnetism, and geodesy. The rate of inner core rota-

tion is an indication of the vigor of convection in the outer core, asso-

ciated with the geodynamo. A nonzero rotation rate can be used to

place limits on the outer core’s viscosity (Buffett, 1997).

Counterclaims, and additional methods and evidence

Several papers since 1996 have argued that the seismological evidence

for inner core rotation is equivocal. Thus, Souriau and Poupinet (in

Dehant et al., 2003) claim the reported travel-time changes of PKIKP

waves on the path between the South Sandwich Islands and Alaska are

an artifact of mislocated earthquakes. Early reports of purported

changes in the absolute arrival times (not differential times) of PKIKP

waves were later dismissed as based on inadequate evidence.

Figure I7 One minute segments of short-period seismograms recorded at College, Alaska, for two earthquakes in the South

Sandwich Islands (March 28, 1987 and August 14, 1995). For 30 s following the PKP arrival, and for an additional 3 min (not shown

here), these seismograms (passed in the band from 0.6 to 3 Hz) show excellent waveform agreement for signals that have traversed

the Earth but not via the inner core. For the PKIKP waveform, from time 250 to 255 s, an insert shows an expanded view of the

narrowband filtered version of the two arrivals (in the passband from 0.8 to 1.5 Hz) that have traversed the inner core. With the two

seismograms aligned on the PKP phase, it is seen that the PKIKP phase of the later event (shown in gray) traveled slightly faster. An

explanation is that the inner core rotated during the 8-year period between the earthquakes, in a manner that provided a faster path

for the later PKIKP signal through the inner core.

424 INNER CORE ROTATION

Laske and Masters have used normal mode data to study inner core

inhomogeneities. Some modes appear to indicate eastward rotation,

others westward, and their paper in Dehant et al. (2003) concludes the

rate is only marginally indicative of a small eastward rotation, about

0.15



1

(but alternatively estimated as 0.34  0.13



1

if the nor-

mal modes likely to be most contaminated by upper mantle struc-

ture are excluded). Vidale and Earle (2000) used backscatter from

within the inner core, following PKIKP waves, to find an eastward

rotation of the inner core amounting to a few tenths of a degree

per year.

It appears that the strongest claims of evidence for inner core rota-

tion derive from differential traveltimes, for earthquakes separated by

several years and which occur at essentially the same location, gener-

ating very similar waveforms. The evidence for inner core rotation is

still under debate, and consensus on inner core rotation will likely

depend on whether examples such as that given in Figure I7 can be

accumulated, since waveform doublets avoid artifacts of event mislo-

cation. A report on 18 high-quality doublets with time separation of

up to 35 years in the South Sandwich Islands region, observed at up

to 58 stations in and near Alaska, provides such an accumulation

(see Zhang et al., 2005).

Paul G. Richards and Anyi Li

Bibliography

Anderson, D.L., 1983. A new look at the inner core of the Earth. Nat-

ure, 302 : 660.

Buffett, B.A., 1997. Geodynamic estimates of the viscosity of the

Earth’s inner core. Nature, 388: 571–573.

Creager, K.C., 1997. Inner core rotation rate from small-scale hetero-

geneity and time-varying travel times. Science, 278: 1284 –1288.

Dehant, V., Creager, K.C., Karato, S., and Zatman, S. (eds.), 2003.

Earth’s Core: Dynamics, Structure, Rotation, Geodynamics series

31. Washington, DC: American Geophysical Union, p. 279.

Gubbins, D., 1981. Rotation of the inner core. Journal of Geophysical

Research, 86: 11695–11699.

Li, A., and Richards, P.G., 2003. Using doublets to study inner core

rotation and seismicity catalog precision. G-Cubed, 4: 1072,

doi:10.1029/2002GC000379.

Poirier, J.P., 1998. Transport properties of liquid metals and viscosity

of the Earth’s core. Geophysical Journal of the Royal Astronomical

Society, 92:99–105.

Richards, P.G., 2000. Earth’s inner core— discoveries and conjectures.

Astronomy and Geophysics, 41:20–24.

Song, X., 2000. Joint inversion for inner core rotation, inner core ani-

sotropy, and mantle heterogeneity. Journal of Geophysical

Research, 105: 7931–7943.

Song, X., and Richards, P.G., 1996. Seismological evidence for differ-

ential rotation of the Earth’ s inner core. Nature, 382: 221–224.

Vidale, J.E., and Earle, P.S., 2000. Slow differential rotation of

the Earth’s inner core indicated by temporal changes in scattering.

Nature, 405: 445–448.

Zhang, J., Song, X., Li, Y., Richards, P.G., Sun, X., and Waldhauser, F.,

2005. Inner core differential motion confirmed by earthquake wave-

form doublets. Science,

310(5752): 1279.

Cross-references

Core Motions

Geodynamo

Geodynamo, Energy Sources

Geomagnetic Spectrum, Temporal

Inner Core Anisotropy

Inner Core Composition

Inner Core Seismic Velocities

Lehmann, Inge (1888–1993)

Length of Day Variations, Long Term

INNER CORE ROTATIONAL DYNAMICS

For several decades after its discovery in 1936, the Earth’s solid inner

core (IC) played only a passive role in geodynamics. Now the ICs

material properties, internal structure, and rotational dynamics are

lively concerns of geomagnetism, seismology, and geodesy. Suppose

the mantle spins about its figure axis e

at rate O relative to the stars,

i.e., 2p/O ¼ 1 sidereal day (sd). In principle the IC can exhibit:

a. differential rotation, i.e., spin relative to the mantle at angular rate

Do about the IC figure axis i

(where i

is possibly inclined at angle

E to e

) and

b. small periodic changes in orientation of i

relative to e

(wobble)

and relative to the stars (nutation).

The spinning IC can be regarded as a gyroscope bathed in the sur-

rounding liquid outer core (OC), and will orient itself relative to the

mantle in response to the torques exerted on it. Changes in OC flow

will cause fluid pressure torques at the inner core boundary (ICB).

The dominantly iron IC (see Inner core composition) is expected to

have an electrical conductivity comparable to that of the OC, allowing

it to be penetrated by changing magnetic fields generated by dynamo

action in the OC, and experience electromagnetic torques as a result

of Lenz’s law. The OC viscosity is probably so small near the ICB that

viscous torques are negligible (see Core viscosity). The vital impor-

tance of gravitational torques, exerted on the body of the IC not only

by the OC but also by the mantle, has been realized only in the past

two decades.

Braginsky (1964) first noted that one boundary condition on the

geomagnetic dynamo is a (possibly nonzero) value of Do fixed by

the requirement of zero net electromagnetic torque on the IC. Gubbins

(1981) pointed out that any equatorial component of Do would be

shielded by the electrically conducting lower mantle, and (by modeling

the OC as a solid spherical shell rotating with the mantle) showed that

a steady axial component could result from the balance of two electro-

magnetic torques: one exerted by the dynamo-generated field in the

OC, and the other induced by the nonzero Do itself. Such a torque

balance was incorporated in their 2-D numerical hydromagnetic

dynamo model by Hollerbach and Jones (1993), who found that

the IC (by virtue of its finite electrical conductivity and solidity)

played a crucial role in stabilizing dynamo operation. This was con-

firmed by the numerical 3-D model of a self-sustaining geodynamo

created by Glatzmaier and Roberts (1995). This model predicted that,

under the balance of both electromagnetic and viscous torques (assum-

ing an artificially large value for OC viscosity for computational rea-

sons), the IC rotates dominantly eastward relative to the mantle at a

few degrees per year, changing on a timescale of 500 years. However

Kuang and Bloxham (1997) found that a much smaller, more realistic,

value of OC viscosity leads to an alternative dynamo in which Do

fluctuates, on a timescale of several thousand years, between eastward

and westward values. (See Geodynamo, numerical simulations for

details.) Buffett and Glatzmaier (2000) showed that dynamo models

incorporating gravitational torques between the mantle and IC yield

much smaller values of Do, on average about 0.17 or 0.02



1

east-

ward according as viscous torques do or do not act on the ICB.

Seismological evidence that the IC departed from isotropy and radial

stratification began to emerge nearly two decades ago (see Inner core ani-

sotropy and Inner core composition for details). Using such nonuniformi-

ties to directly determine IC rotation became an exciting new branch

of seismology when Song and Richards (1996) realized that any tilt of

the anisotropy axis away from the rotation axis would cause a systematic

change with time in the travel-times of P-waves through the IC from

the same source location to the same seismograph. They used 30 years

of data to estimate a tilt of about 10



and Do ﬃ 1



1

eastward. Su

et al. (1996), analyzing a different but equally long data set, found Do

ﬃ 3



1

. However most subsequent studies, involving the passage

INNER CORE ROTATIONAL DYNAMICS 425