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wander”). Steinberger and O’Connell (2002) also find that the maxi-

mum speed of polar wander driven by mantle convection is about

100 km myr

1

(and incidentally that a fast rising plume head cannot

cause more than a few degrees of TPW during the few myr of its

ascent). A recent study by Greff-Lefftz (2004) investigates the influ-

ence of mantle plumes varying at different spatial wavelengths on

the time variations of TPW. In a first model, she shows that an upwel-

ling plume analytically represented as a sphere whose radius varies

as a function of the flux of material in the conduit and which traverses

the mantle at the Stokes velocity, produces very little wander of the

rotational axis. Greff-Lefftz then studies the effects of two superswells

which mimic the ones observed with seismic tomography, and con-

cludes that a doming regime within the mantle involves significant

polar wander. Some of the features of this TPW which are directly

linked to the periodicity of doming are reminiscent of observed phases

of slow and fast TPW, with similar peak velocities.

In all cases, isoviscous mantle models predict TPW rates much lar-

ger than observed, and a significant viscosity increase in the lower

mantle is required to stabilize the large scale pattern of convection

and bring TPW rates closer to observed values. This is also what is

needed for hotspot stability as well as matching the geoid. Steinberger

and O’Connell (2002) compare their model results for a number of

tomographic models and discuss the effects of compressibility, deep

mantle viscosity, thickness of a high viscosity layer in the deep mantle,

and chemical boundaries on rates of TPW. Their TPW estimates, one

of which going back to 100 Ma is shown in Figure T19a, are in qua-

litative agreement with observations (note that Figures 9 and 10 in

Steinberger and O’Connell (2002) are incorrect, corrections being

available at http://www.geodynamics.no/STEINBERGER/papers/gia

vol_fig9.pdf and http://www.geodynamics.no/STEINBERGER/papers/

giavol_fig10.pdf; B. Steinberger, personal communication, 2004).

Inertial interchange and true polar wander

If the principal directions of the nonhydrostatic imposed inertia tensor

remain unchanged, but the eigenvalues change and the maximum

nonhydrostatic imposed moment of inertia decreases whereas the inter-

mediate one increases, until the latter becomes larger than the former,

then a quasidiscontinuous 90



rotation becomes possible so that the

rotation axis will align with the new axis of maximum nonhydrostatic

moment of inertia (Fisher, 1974). More precisely, the preferred axis of

rotation moves instantaneously by up to 90



and the rotation axis will

move to its new stable position at a rate limited by adjustment of the

bulge. The rate also depends on the driving force, linked to the differ-

ence in maximum and intermediate eigenvalues. In such an inertial

interchange event, only the nonhydrostatic part is interchanged and

there is propagation of the equatorial bulge, which must always remain

equatorial. Such an occurrence is referred to as an inertial interchange

true polar wander (IITPW) event. Actually, the amplitude of an IITPW

event may not reach 90



. At the time when the former maximum and

intermediate nonhydrostatic imposed moments of inertia become equal,

the nonhydrostatic moment of inertia becomes equal along a whole

great circle (the tensor is prolate or flattened with cylindrical symme-

try) and the new axis of maximum imposed moment of inertia can

grow anywhere on this great circle. The fact that the Earth may in

the past have catastrophically exchanged two of its principal axes of

inertia in that way, i.e., that the whole lithosphere (and mantle) may

have rotated by up to 90



in only a few million years, bringing for

instance parts of the Earth which were close to the poles at the equator,

has become a new area of questioning in the geosciences. It is clear

from the available TPW curves going back to the early Mesozoic

that such an event has not occurred in the past 250 myr. For certain

parameter values (such as lower mantle viscosity) IITPW is encountered

in some numerical model runs. This was almost seen in Goldreich and

Toomre’s earliest calculations. Richards et al. (1999) find occasional

though infrequent inertial interchanges of polar axes with duration

of 20 myr, due to “avalanching” (discontinuous rearrangements in

geometry of subducting slabs) in the lower mantle (only one such event

occurs in a 600 myr numerical run).

A recent review of evidence for IITPW has been given by Evans

(2003). A series of paleomagnetic poles spanning an IITPW event

from any continent should fall on a great circle with the pole to that

great circles approximating the minimum nonhydrostatic imposed

moment of inertia (Evans, 1998). Paleomagnetic indications which

would support rather fast TPW in pre-Mesozoic time have been put

forward by Van der Voo (1994) and for very fast TPW by Kirschvink

et al. (1997). For pre-Jurassic time, ocean floor has been destroyed

(together with evidence of plate kinematics and many hotspot traces)

and TPW cannot be estimated in the way indicated above. Evans pro-

poses to obtain a crude estimate of TPW in the case (to be tested)

when TPW velocity would have been much faster than between-plate

motions (as in Figure T13b). This requires matching APW paths from

a majority of continental fragments, and extracting a large common

component of latitudinal drift (if it exists). Geological evidence of

subduction and collision and fossil hotspot traces can help in interpret-

ing the common APW record. Kirschvink et al. (1997) proposed in

this way that 90



of TPW had occurred in a brief interval of Early

Cambrian time (possibly 15 myr or less, i.e., TPW velocities in excess

of 600 km myr

1

!), coinciding with the famous biological Cambrian

explosion. Recall that numerical models place an upper limit of about

100 km myr

1

on TPW velocity; a full 90



IITPW event would take

3–20 myr for a modern Earth viscosity structure (Steinberger and

O’Connell, 2002). To this day, the issue remains contentious because

of the dearth of paleomagnetic records and possibility of problems

with unremoved overprints, dating uncertainties, etc. (see Evans,

2003). Various authors tend to make different data selections, and each

new datum published can still throw the balance in the opposite way.

For one school of thought, the terminal Proterozoic to late Paleozoic

APW for Gondwanaland (Figure T20) displays up to five large angular

swings, some of which reach 90



in amplitude. This oscillatory polar

wander is attributed to TPW about a common, long-lived minimum

inertial axis near eastern Australia, which would be the prolate axis

of Earth figure, inherited from the previous super-continent of Rodinia.

In this way, Evans (2003) links TPW episodes to supercontinental

cycles (Wilson-like but with durations on the order of 500 myr).

Figure T20 Terminal Proterozoic to late Paleozoic apparent

polar wander path for Gondwanaland. Oscillatory APW rotations

are interpreted as inertial interchange (IITPW) about a common,

long-lived, minimum inertial axis (I

min

) near eastern Australia

(after Evans, 2003).

966 TRUE POLAR WANDER

This is an exciting if controversial chapter of Precambrian paleomag-

netism that will require much more data than is currently available,

hence a concerted effort of the paleomagnetic community.

Most recent developments and conclusion

For the time being, the hypothesis that TPW is a go-stop-go phenom-

enon, with long standstills in the tens of millions of years, and periods

of faster, rather uniform polar wander at velocities often not exceeding

30 km myr

1

, cannot be discounted. Evidence for super fast events at

any time in the past remains to be demonstrated. Much recent model-

ing still failed to some extent to account for the slow values of typical

TPW velocity (0–30, and rarely up to 100 km myr

1

), and even more

so to account for the prolonged (50 myr) periods with almost no

TPW (standstills). Steinberger and O’Connell (2002) gave reasonable

velocities but predicted smooth evolutions, rather than the alternating

episodes, which some paleomagnetists feel they uncover from the data

(Figure T19a).

The similarity between TPW estimates for the Pacific plate and the

rest of the world (Besse and Courtillot, 2002), which are based on

completely different and independent data sets, may be taken as sup-

porting the idea that small yet significant TPW, on the order of 10



occurred since the Cretaceous, though it still requires careful verifica-

tion. Relatively fast rates before 50 Ma could be due to the variable

difference between the largest and intermediate nonhydrostatic princi-

pal moments of inertia and to combinations of peculiar configura-

tions of downgoing slabs and super-upwellings (Greff-Lefftz, 2004;

B. Steinberger, personal communication, 2004). As seen since the time

of Goldreich and Toomre, small differences may lead to faster rates. If

the two superswells remain more or less in the same locations, the pole

may move on the great circle perpendicular to the axis they form.

Figures T12 and T16 may indicate such a tendency for the segment

from 130 to 50 Ma, though as stated above the pre-80 Ma data have

increasing uncertainties as one goes back into the past. The importance

of the Pacific plate and severe limitations on presently available data

from that plate, the fact that the global paleomagnetic database still

is quite scant for certain continents and time windows, the fact that

many hotspot traces are not yet sufficiently constrained in terms of

age and paleolatitude, all point to the need for many more direct

(paleomagnetic) measurements as opposed to indirect/remote sensing

determinations of magnetization direction (i.e., “skewness” or “sea-

mount” data).

In a very recent paper, Steinberger et al. (2004) combine hotspot

motion in the large scale flow field of the mantle and intraplate defor-

mation to account for most of the post-65 Ma misfits between com-

puted and observed hotspot tracks. Motion of initially vertical plume

conduits is dominated by advection in the high viscosity lower mantle

and buoyant rising in the low viscosity upper mantle. Given the mantle

flow field and a preferred viscosity distribution, Steinberger et al.

(2004) find that computed hotspot motion fits observed tracks well

for the last 50 myr, i.e., since the time of the Hawaii-Emperor bend.

But the change in track direction at the bend is explained only when

an alternative plate circuit through East Antarctica, Australia, and the

Lord Howe rise is used rather than the traditional circuit through West

Antarctica. This leads to East versus West Antarctic motion with a

rotation pole close to the boundary and deformations which the

authors believe are compatible with geologic evidence. Remaining

pre-65 Ma misfits are attributed to unquantified motion internal to

New Zealand. Only a combination of the two effects (hotspot motion

and intraplate deformation) successfully predicts the geometry of the

four selected seamount chains in the Pacific and Indo-Atlantic hemi-

spheres. If correct, their analysis at the same time invalidates the

notion of a hotspot-mantle reference frame or of separate hemispheres

(for Steinberger and colleagues plumes indicate local flow and not

motion of hemispheric cells) and replaces it with limited, predictable

inter-hotpot motion. But TPW can still be calculated, i.e., a “mean

mantle” reference frame can still be evaluated. The Hawaiian hotspot

would have moved faster between 80 and 50 Ma, and at the same time

TPW would have been faster prior to 50 Ma. TPW would account

alone for paleolatitudinal changes of the Reunion hotspot, whereas

the two effects would be required for the Hawaiian hotspot.

Combining Steinberger et al. (2004) preferred model for the finite

rotation of the African plate in the “mean mantle ” reference frame with

the synthetic apparent polar wander path for South Africa (Besse

and Courtillot, 2002, Table 5, with correction given in Besse and

Courtillot, 2003), one can derive a TPW curve in the “mean mantle”

reference frame (or if one prefers, the “apparent polar wander path

of the mean mantle”) that takes hotspot motions into account. This is

shown in Figure T19b (B. Steinberger, personal communication,

2004). The curve captures most of the features of the original BC02

observed TPW (standstill between 10 and 50 Ma, faster TPW in the

correct direction prior to that back to 80 Ma) though with somewhat

larger amplitudes.

We have seen that a number of scientists suggest possible links

between (1) TPW episodes, or major changes between TPW episodes,

or IITPW events if indeed they have occurred in the past, (2) reorgani-

zations in the geometry of subduction zones or plume and superplume

generation (or any other major geodynamical events occurring in the

mantle), and (3) major biotic changes. These tantalizing hypotheses

will likely keep analyses of polar wander very much alive in the com-

ing decade, despite the somewhat bothering feeling that TPW still

remains an elusive geophysical phenomenon.

Acknowledgments

I am thankful to Emilio Herrero-Bervera and David Gubbins for inviting

this contribution. I am particularly thankful to J. Besse, A. Cazenave, R.

Gordon, M. Greff-Lefftz, K. Lambeck, J. Laskar, J.L. Le Mouël,

M. McElhinny, R. O’Connell, J.P. Poirier, Y. Ricard, J. Tarduno and

R. Van der Voo for very useful comments on an earlier version of

this paper. Special thanks to B. Steinberger for particularly detailed

and helpful comments and help with several parts of Figure T19. IPGP

Contribution NS 2094.

Vincent Courtillot

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TRUE POLAR WANDER 969

ULVZ, ULTRA-LOW VELOCITY ZONE

Nearly half way to Earth ’s center, the boundary between the solid silicate

rock mantle and the liquid iron-alloy outer core was long thought to be a

sharp discontinuity between the two vastly different regimes. Recently,

detailed seismological analyses have depicted the core-mantle boundary

(CMB) as being far from simple, and in fact shows evidence for an addi-

tional thin veneer of anomalous properties in certain geographical

regions. Imaged as thin as a couple of km, and up to 50-km thick, these

unique zones are characterized by strong reductions in the speeds of seis-

mic waves relative to the overlying mantle. These areas have thus been

dubbed “ultra-low velocity zones” (ULVZs).

Seismic probes

Seismology remains the most direct remote sensing tool for deciphering

the subtleties of Earth’s inaccessible deep interior. This is most com-

monly accomplished through the use of elastic energy that propagates

away from earthquakes, traveling through the entire interior of the pla-

net; some energy propagates continuously through the Earth, some

reflects from local or global boundaries between contrastingly different

materials, and some of it, in special cases, diffracts along boundaries

between strongly contrasting media. Each of these types has provided

evidence for extremely sluggish patches at the CMB.

Four of the most commonly utilized seismic probes (or “phases”)

to date are SPdKS referenced to SKS, and precursors (seismic energy

that just slightly precedes a later more dominant phase) to the waves

PcP, ScP,orPKP (Figure U1). Over the past decade a variety of

research groups have documented anomalies in these arrivals and

attributed them to CMB structure (see, e.g., Garnero et al., 1998).

ScP is a seismic phase that departs from the earthquake as an S wave,

and upon reflection at the CMB, converts to a P wave (Figure U1a). If

a low velocity boundary layer is present at the CMB, several additional

arrivals are possible (Figure U1a, second panel). The relative timing

and amplitude of these arrivals is apparent in a computer generated

“synthetic” seismogram 60



in arc away from a 500-km deep hypothe-

tical earthquake (third panel). If the top of the layer is diffuse, then

these arrivals diminish in amplitude, which remains an active direction

for current research.

Figure U1b shows PcP, which also contains pre- and postcursors,

analogously to ScP, as well as some of the additional arrival geome-

tries, and a synthetic seismogram showing the additional arrivals.

One challenge in data analyses is to identify the later arrivals, since

they are commonly obscured by the coda of the main PcP phase,

i.e., additional arrivals due to (for example) reverberations in Earth’s

crust due to the PcP wave.

Waves that travel into the Earth’s core can contain important infor-

mation about anomalous properties at the CMB, which they traverse

at least twice. The phase PKP has been used to detect CMB structures

that scatter energy resulting in precursory arrivals to PKP. Figure U1c

shows PKP paths, along with an associated reference arrival PKiKP

that reflects from the inner core boundary. Anomalous topography to

the ULVZ or inclusions of low velocity material can give rise to pre-

cursory arrivals, as shown in the theoretical predictions in the bottom

panel.

Another important probe of the CMB is an S wave that encounters the

CMB at a critical angle to produce a P wave that diffracts along the CMB

(Pd), then continues into the core as a P wave, then back through the

mantle as an S wave (Figure U1d). This phase, SPdKS, has short segments

of P wave diffraction at the core entry and exit locations. Additional inter-

nal reflections within the layer are also emerging as important (e.g.,

SPuPKS). Certainly other possible seismic probes of ULVZ structure

are possible, as long as seismic energy either refracts, diffracts, or reflects

at the CMB.

An important next step in ULVZ research will be to find geographical

regions that permit analysis of more than one particular seismic phase,

since different waves are sensitive to different ULVZ structural compo-

nents. For example, the precursor analyses (Figure U1a-c) utilize short

period energy, which is particularly sensitive to sharp contrasts in prop-

erties, and not able to well-resolve gradational changes in properties.

SPdKS, on the other hand, is less sensitive to such contrasts, but very

sensitive to the velocity structure within the layer, particularly at dis-

tances where the Pd segment in SPdKS is short.

Ultra-low velocity boundary layer possibilities

The seismic phases introduced in Figure U1 have played a critical role

in revealing several possibilities for transitional structure between the

core and mantle. Three main possibilities are highlighted here: a layer

on the mantle side of the CMB (which is most commonly referred to

as ULVZ), a layer on the core-side of the CMB (essentially a core-

rigidity zone, CRZ), and some thickness over which the mantle

changes into the core (hereafter denoted as a core-mantle transition

zone, CMTZ) (Figure U2). It is important to recognize these as end-

member models, and that any combination of these is equally possible.

Mantle ultra-low velocity zone

ULVZ thickness has been imaged between 5 and 50km, with strong

lateral variations. The most commonly explored model parameters

are those compatible with partial melt of the lowermost mantle, which

results in a three times larger reduction in shear velocity (e.g., 30%)

than that for compressional waves. Density increases are also possible

(Figure U2a).

Core-rigidity zone

If large density increases and shear velocity decreases are considered

in ULVZ modeling, one must allow for the possibility of the layer

residing on the core-side of the CMB (Figure U2b). The liquid outer

core of the Earth is predominantly iron, along with a minor constitu-

ency of some lighter element(s). As the Earth cools, the solid inner core

of the Earth grows, releasing the lighter elements into the outer core,

which may result in “underplating” of the CMB in a sedimentation

process (see Buffett et al., 2000). Thus, isolated regions of nonzero rigid-

ity may exist beneath positive topography, or, “hills” on the CMB, where

such sediments can accumulate and concentrate (up to a couple km thick;

Rost and Revenaugh, 2001). If electrically conductive, the CRZ may

affect Earth’s magnetic field, nutations, and possibly even magnetic field

reversal paths.

Core-mantle transition zone

Finally, we consider the possibility of a transitional zone between the

mantle and core over some finite thickness (Figure U2c). Chemical

reactions between the silicate rock mantle and liquid iron-alloy outer

core (see Knittle and Jeanloz, 1989) can result in a thin mixing

zone—an effective blurring of the CMB. The CMTZ can appropriately

cause precursors to the short period waves (Figure U1a-c) as well as

delay the SPdKS relative to SKS (Figure U1d; Garnero and Jeanloz,

2000).

Figure U2 P-wave (a) and S-wave (b) velocity and density (r) versus depth for ultra-low velocity boundary layering (shaded regions) on

(a) the mantle-side of the core-mantle boundary (CMB) (a ULVZ) (b) the core-side of the CMB (a CRZ), and (c) a finite thickness

transition between the mantle and core (CMTZ).

Figure U1 Ray paths, seismic arrivals due to a ULVZ, and synthetic seismograms for (a) ScP, (b) PcP, (c) PKP, and (d) SPdKS. Synthetic

seismogram predictions of (a) and (c) are from Garnero and Vidale (1999) and Wen and Helmberger (1998), respectively.

ULVZ, ULTRA-LOW VELOCITY ZONE 971

ULVZ geograp hic dist ribution

To gain insight into the possible origin of ultra-low velocity layering at

the CMB, it is instructive to compare results to other phenomena, such

as gross properties of the deep mantle as revealed by shear wave tomo-

graphy. Figure U3 compares the strongest variations in shear wave

velocity with ULVZ distributions. There is suggestion of a connection

between ULVZ and low seismic wave speeds (Figure U3a,b ). This

ULVZ distribution also correlates strongly with hot spot volcanism at

Earth ’s surface (Williams et al., 1998). However, an examination of

a larger data set of higher quality broadband data reveals shorter scale

variations, with some CMB patches showing evidence for both support

and lack of an anomalous layer. Figure U3c summarizes ULVZ likeli-

hood using broadband digital SPdKS data. The correlation with large-

scale lower mantle shear velocity is more difficult to assess. Greater

geographical coverage in future studies will allow more confidence

in such comparisons. A main limitation in achieving greater spatial

coverage is uneven earthquake and seismometer distribution on the

globe, limiting where the deep interior can be probed.

Discuss ion and summ ary

While confident correlations between ULVZ layering and bulk mantle

properties may be premature at present, the existence of the layer is

clear, from a variety of studies and methods. While not constrained, it

is instructive to briefly consider possible scenarios relating CMB struc-

ture to the thermal, chemical, and dynamical environment. Figure U4

displays a multitude of possibilities beneath upwelling and downwelling

mantle regimes. The point here is to recogn ize the variety of structures

and their scale lengths that are possible, yet unresolved at present, and

hence future work should seek to sharpen our focusing ability for such

possibilities.

Beneath upwelling regions, possibilities include (but certainly are

not limited to) (a) a combination of ULVZ, CMTZ, and CRZ structures

in the hottest lowermost mantle regions; (b) convection

sented in Figure U1 for the same patch of the CMB will also greatly

within a par-

tially molten ULVZ which can sweep chemical heterogeneity into

localized piles within the ULVZ; (c) large- and fine scale CMB (as

well as ULVZ) topography, resulting in (d) multiple scale CRZs of

variable strength; (e) some ULVZ melt entrainment into overlying con-

vection currents, which may result in (f ) mantle plume genesis, and

(g) aligned melt pockets from strong boundary layer shear flow, yield-

ing seismic anisotropy; and (h) chemical mixing between the ULVZ

and outer core (or CRZ) material, giving rise to local (or widespread)

CMB blurring, including chemical coupling (or interactions).

Beneath downwelling regions, similar phenomena exist, but perhaps

suppressed in the vertical dimension (a) spatially organized ULVZ to

the front of downwelling motions, where plume instabilities (thus local

warmer zones) have been shown to exist (Tan et al., 2002); (b) a thin

(undetectable?) ULVZ throughout region; (c) small- and large-scale

CMB topography, which may provide localized basins or wells for

material with density intermediate to that of the mantle and core;

(d) possible chemical contamination from melt from either CMB che-

mical reaction product entrainment or ponding of former oceanic crust;

and (e) anisotropy due to high strains resulting from overlying subduc-

tion stresses (McNamara et al ., 2002). While provocative, Figure U4

depicts the likely scenario of CMB topography that is intimately

coupled to ULVZ, CMTZ, and CRZ chemistry and dynamics. Further-

more, these structures probably play an important role with electro-

magnetic, gravitational, thermal, and topographic coupling between

the mantle and core.

Future analyses should incorporate more realistic 3D wave propaga-

tion tools for predictions to compare to data (see, e.g., Helmberger

et al., 1998). Analyses that utilize more that one of the wave types pre-

reduce uncertainties.

Lastly, it is clear that ULVZ structure is an intimate part of the core-

mantle transition, and likely reflects core processes that may be related

to the geodynamo. For example, if the ULVZ is enriched in iron from

the core, it may affect geomagnetic reversal path geometries, which to

Figure U3 (a) Shear velocity distribution in the lowermost 250km

of the mantle from the model of Grand (2002). Light shaded areas

have velocities equal to or lower than 1% relative to the global

average, dark areas are at or great than þ1%. (b) Fresnel zones of

SPdKS sampling at the CMB from long period analog data. Light

shading is for suggested ULVZ presence; dark shading for ULVZ

absence, and no shading represents no data sampling. (c) Same as

(b), except using modern broadband digital data, and shading

represents the likelihood of ULVZ presence. For each 1



1



section of the CMB with data coverage, the following ratio is

constructed and plotted: (# of records requiring an ultra-low

velocity layer)/(total # of records for that cell). Thus, a value of 1

indicates all data that traversed that cell are anomalous; a value

of 0 represents the case where no data sampling a particular

region are anomalous (after Thorne and Garnero, 2004).

972 ULVZ, ULTRA-LOW VELOCITY ZONE

the first order appear anticorrelated with ULVZ distributions (Garnero

et al., 1998). Certainly, uneven geographic distribution of patches of

partially molten and/or chemically unique ULVZ material can result

in variability in core heat flow that may affect core fluid motions, pos-

sibly relating to Earth’s magnetic field generation and variability.

Ed J. Garnero and M. Thorne

Bibliography

Buffett, B.A., Garnero, E.J., and Jeanloz, R., 2000. Sediments at the

top of the Earth’s core. Science, 290: 1338–1342.

Garnero, E.J., and Jeanloz, R., 2000. Earth’s enigmatic interface.

Science, 289:70–71.

Garnero, E.J., and Vidale, J., 1999. ScP; a probe of ultralow-velocity

zones at the base of the mantle. Geophysical Research Letters,

26: 377–380.

Garnero, E.J., Revenaugh, J.S., Williams, Q., Lay, T., and Kellogg, L.H.,

1998. Ultralow velocity zone at the core-mantle boundary. In

Gurnis, M., Wysession, M., Knittle, E., and Buffet, B. (eds.) The

Core-Mantle Boundary. Washington, DC: American Geophysical

Union, pp. 319–334.

Grand, S.P., 2002. Mantle shear-wave tomography and the fate of

subducted slabs. Philosophical Transactions of the Royal Society

of London A, 360: 2475–2491.

Helmberger, D.V., Wen, L., and Ding, X., 1998. Seismic evidence that

the source of the Iceland hotspot lies at the core-mantle boundary.

Nature, 396: 251–255.

Knittle, E., and Jeanloz, R., 1989. Simulating the core-mantle bound-

ary: an experimental study of high-pressure reactions between sili-

cates and liquid iron. Geophysical Research Letters, 16: 609–612.

McNamara, A.K., van Keken, P.E., and Karato, S.I., 2002. Develop-

ment of anisotropic structure in the Earth’s lower mantle by

solid-state convection. Nature, 416: 310–314.

Rost, S., and Revenaugh, J., 2001. Seismic detection of rigid zones at

the top of the core. Science, 294: 1911–1914.

Tan, E., Gurnis, M., and Han, L., 2002. Slabs in the lower mantle and

their modulation of plume formation. Geochemistry, Geophysics,

Geosystems, 3(11): 1067 (doi: 10.1029/2001GC000238).

Thorne, M.S., and Garnero, E.J., 2004. Inferences on ultralow-velocity

zone structure from a global analysis of SPdKS waves. Journal of

Geophysical Research, 109: B08301 (doi: 10.1029/2004JB003010).

Wen, L., and Helmberger, D.V., 1998. Ultra-low velocity zones near

the core-mantle boundary from broadband PKP precursors.

Science, 279: 1701–1703.

Williams, Q., Revenaugh, J.S., and Garnero, E.J., 1998. A correlation

between ultra-low basal velocities in the mantle and hot spots.

Science, 281: 546–549.

Cross-references

Core Composition

Core Properties, Physical

Core, Boundary Layers

Core-Mantle Boundary

Core-Mantle Boundary Topography, Implications for Dynamics

Core-Mantle Boundary Topography, Seismology

Core-Mantle Boundary, Heat Flow Across

Core-Mantle Coupling, Electromagnetic

Core-Mantle Coupling, Thermal

Core-Mantle Coupling, Topographic

as a Boundary Layer

, Anisotropy

, Composition

, Seismic Properties

Earth Structure, Major Divisions

Geodynamo, Numerical Simulations

Seismic Phases

UNITS

Scientific units were standardized to the current Système Internationale

d’unités (SI) in about 1970. For the most part conversion involves

applying simple factors of 10 to convert centimeters and grams to

meters and kilograms, but in magnetism conversion is more compli-

cated and confusing because the old cgs system had, for historical

reasons, two sets of units for electricity and magnetism: electrostatic

and electromagnetic units. The latter, abbreviated to emu, concern us

here. Understanding of emu is necessary to understand the old, and

some not so old, literature. The paleomagnetic community has been

particularly slow to convert to SI, and even today some papers give

results in emu.

SI achieved the worthy goal of unifying the system of units for both

electricity and magnetism; it also removed some factors of 4p from the

basic equations (Table U1). The critical difference between the two

systems arises from the distinction between magnetic induction or flux

density B and magnetic field intensity H. The dimensions of H differ

in the two systems of units, as does the magnetic moment per unit

Figure U4 Possible CMB scenarios beneath regions of (a)

upwelling, and (b) downwelling (see text for details). Significant

(or total) uncertainty exists for many wavelengths of interest,

which include: scale-length over which ULVZ phenomena affects

the lowermost mantle (l

), scale lengths of roughness of the top

of the ULVZ (l

), ULVZ thickness distribution (l

), dimension of

isolated core-rigidity zones (l

), scale of roughness of the CMB,

including the thickness of transition from pure core-to-mantle

), lateral and vertical scale of long wavelength CMB

topography, and hence possible anomalous zones contained

within the topographic depressions/elevations (l

), and isolated

thermochemical domes, scatterers, or anomalous shapes within

the ULVZ (l

Table U1 Relevant equations in SI and emu systems of units

SI Emu

B ¼ 

H þ MB¼ H þ 4p M

P ¼ 

MP¼ M

M ¼ w

HM¼ w

emu

H=4p

Further discussion is given in the appendix of Jackson’s (1999), 3rd edition. Butler

(1992) and Blakely (1996) also have appendices on systems of units.

UNITS 973

volume of a material M. Furthermore, the definition of M differs

by a numerical factor of 4p between the two systems, which has the

undesirable effect that the dimensionless susceptibility w differs.

The magnetic polarization P (usually denoted as J in paleomagnetism

but this is used in MHD (q.v.) exclusively for electric current density),

has the same dimensions as B in both systems. Confusion propagates

because of sloppy terminology: it is standard practice in geomagnetism

and paleomagnetism to refer to B as the magnetic field rather than

magnetic induction, and magnetization is used to mean either M or P

(Table U2).

David Gubbins

Bibliography

Blakely, R.J., 1996. Potential Theory in Gravity and Magnetic Appli-

cations. Cambridge: Cambridge University Press.

Butler, R.F., 1992. Paleomagnetism: Magnetic Domains to Geologic

Terranes. Boston: Blackwell Scientific.

Jackson, J.D., 1999. Classical Electrodynamics, 3rd edition. New

York: Wiley.

Cross-references

Magnetohydrodynamics

UPWARD AND DOWNWARD CONTINUATION

Potential fields known at a set of points can be expressed at neighbor-

ing higher or lower spatial locations in a source free region using the

continuation integral that results from one of Green’s theorems (see,

e.g., Blakely, 1995). The principal uses of this concept are to adjust

altitude of observations to a datum as an aid to the interpretation of

a survey (see Crustal magnetic field), reduce short-wavelength data

noise by continuing the field upward, and increasing the horizontal

resolution of anomalies and their sources by continuing the field

downward. It is possible to continue the field upward or downward in

a number of different ways depending on the application at hand; for

example, designing continuation operators in spatial or wavenumber

space (Henderson and Zietz, 1949; Dean, 1958), using harmonic func-

tions (Courtillot et al., 1978; Shure et al., 1982; Fedi et al., 1999), and

deriving physical property variations of sources causing the fields

(Dampney, 1969; Emilia, 1973; Langel and Hinze, 1998). Applications

also vary widely: from environmental and exploration applica-

tions involving short-wavelength anomaly fields over small height

differences (a few meters to kilometers) to global distribution of

anomalies measured by satellites in which anomalies are downward

continued from satellite altitudes (300–700km) to Earth’s surface

and also downward continuing the core part of the Earth’s field all

the way to the top of the core to decipher features of core circulation

over time.

The effect of upward/downward continuation process on the fields

can be understood by examining the continuation operator in the

wavenumber domain. The operator has the form e

jkjz

, where jkj is

the wavenumber (jkj¼2l where l is the full wavelength) and z

is the continuation level (Dean, 1958). The negative sign in the expo-

nent indicates upward continu ation (away from the sources of the

field) and the positive sign implies the downward continuation (toward

the sources of the field). The response of the continuation operator

with respect to wavelength is illustrated in Figure U5, which shows

that shorter wavelengths are attenuated and smoothed in the process

of upward continuation, whereas in downward continuation the shorter

wavelengths are amplified and sharpened. Both operations are suscep-

tible to errors in the data and their results can be rendered invalid or at

least severely compromised due to the quality of data. For example, if

measurement errors are primarily short-wavelength, then the nature of

downward continuation operator which amplifies primarily the short-

wavelength components of the data can severely distort the downward

continued result. On the other hand, if the long-wavelength portion

of the field is contaminated, for example, by inaccurate compilation

of different surveys having different base levels, then the retention of

the corrupt long wavelengths in the process of upward continuation

can render the result unusable (Ravat et al., 2002).

The most straightforward upward/downward continuation of a field is

performed from one level surface to another level surface (Henderson

Table U2 Dimensions and units of physical quantities used in geomagnetism

Physical quantity Dimension SI Emu Conversion factor

Length L m cm 10

Mass M kg G 10

3

Time T s s 1

Charge Q coulomb (C) coulomb 1

Electric current QT

1

ampere (A) abamp 10

Potential difference L

2

Q volt (V) emu 10

8

Electric field LMT

2

QVm

1

emu 10

6

Resistance L

1

2

ohm emu 10

9

Resistivity L

1

2

ohmm emu 10

11

Conductivity L

2

1

siemensm

1

emu 10

Magnetic flux L

1

weber (W) maxwell 10

8

Magnetic induction B MT

1

tesla (T) gauss 10

4

Magnetic field intensity L

1

QAm

1

oersted ðMT

1

Þ 10

=4p

Inductance L

2

henry (H) emu 10

9

Permeability LMQ

2

1

Dimensionless 4p  10

7

Magnetic moment density L

1

QAm

1

emu ðMT

1

Þ 10

=4p

Magnetic polarization MT

1

T gauss 10

4

Susceptibility Dimensionless w

emu

LMTQ denote length, mass, time, and charge. The conversion factor in the right column should be used to multiply a value in emu to yield the SI value. Note the difference in

definition for H, M, and w between the two systems. The siemen is sometimes called the mho.

974 UPWARD AND DOWNWARD CONTINUATION

and Zietz, 1949; Henderson, 1970). This is often useful for interpreta-

tion and joining two adjacent surveys carried out at different altitudes.

As aid in interpretation, upward continuation allows one to assess the

effect of deeper sources because in this process the effect of shallower,

short-wavelength features is attenuated. Preferential upward and down-

ward continuation operators have been designed that can help attenuate

only the shallow, short-wavelength part of the spectrum, leaving the

deeper, long-wavelength part unaltered or, alternatively, preferentially

amplify only the deeper part of the spectrum without the deleterious

effects of amplifying short-wavelength noise (Pawlowski, 1995). Thus,

under certain situations, it is possible to isolate a magnetic anomaly sig-

nal from different depth layers of the crust. Downward continuation into

the region of sources leads the continuation integral to diverge even in

the case of noise-free data; in the case of high data density noise-free

data the depths at which the continuation integral blows up (data begin

to vary wildly) can be used to infer the depth to the top of the shallow

magnetic sources in the region.

When airborne magnetic surveys (see Aeromagnetic surveying) are

conducted in rugged terrain made up of magnetic formations, it is

not advisable to view the data at constant altitude because effects of

topographic variations can lead to anomaly artifacts. In such situations,

one might prefer to “continue” level survey data at some constant

distance away from topography (on a constant terrain clearance or

“draped” surface). Challenges of maintaining the constant terrain

clearance of aircrafts in a rugged topography may require one to adjust

the data further until the survey is accurately draping. Conversely,

flying conditions can lead to unintentional altitude variations in

surveys originally intended to be flown at constant barometric altitude

(level survey), and such surveys need datum corrections as well. Two

types of procedures have been commonly used in accomplishing

datum transformations from level-to-drape and drape-to-level surfaces:

Taylor’s series approximation and equivalent source concept. Taylor’s

series allows extrapolation of a function to nearby points and, given

vertical derivatives of the field and certain approximations regard-

ing behavior of the field, the series yields adequate values of level-

to-drape transformation. Similarly, an iterative Taylor’s series can be

used for drape-to-level transformation (Cordell and Grauch, 1985).

The equivalent source method (Dampney, 1969) employs Green’s

equivalent layer concept and uses a set of sources with arbitrary mag-

netization (often induced dipoles because of their simplicity; Emilia,

1973) to approximate the field. This process is equivalent to finding

the potential that satisfies the observed field. The inverted magnetiza-

tion of the sources is then used to predict the field in the neighborhood

of observations. Use of local harmonic functions (Fedi et al., 1999)

can also be useful for these purposes.

Dhananjay Ravat

Bibliography

Blakely, R.J., 1995. Potential Theory in Gravity and Magnetic Appli-

cations. Cambridge:Cambridge University Press.

Cordell, L., and Grauch, V.J.S., 1985. Mapping basement magnetiza-

tion zones from aeromagnetic data in the San Juan basin,

New Mexico. In Hinze, W.J. (ed.) The Utility of Regional Gravity

and Magnetic Anomaly Maps. Tulsa: Society of Exploration Geo-

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Courtillot, V., Ducruix, J., and Le Moüel, J.L., 1978. Inverse methods

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Figure U5 Amplitude response of upward and downward continuation operators with respect to wavelength for certain heights (z )of

continuation.

UPWARD AND DOWNWARD CONTINUATION 975