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

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NAGATA, TAKESI (1913–1991)

Born in Aichi Prefecture, Japan; graduated from the Physics Depart-

ment, University of Tokyo, 1936; research associate, Earthquake

Research Institute, University of Tokyo, 1937; associate professor,

1941 and professor in the Department of Geophysics, University of

Tokyo, 1952–1974; director of the National Polar Research Institute,

1973–1984; adjunct professor of University of Pittsburgh, 1962–1977;

Nagata was quite active in international cooperation and served as

bureau member of the International Union of Geodesy and Geophy-

sics (IUGG) for 1960–1963, president of the International Associa-

tion of Geomagnetism and Aeronomy (IAGA) for 1967–1971, and

vice-president of the Scientific Committee on Antarctic Research

(SCAR) for 1972–1976.

His doctoral thesis was devoted to a systematic experimental study

of the properties of the thermoremanent magnetization (TRM) in vol-

canic rocks (Nagata, 1943). This included, concurrent with the work

of Emile Thellier in France, the discovery of proportionality of the

TRM to the magnetizing field and additivity of partial TRM. In

1951, Nagata and his colleague, and students Syun-iti Akimoto and

Seiya Uyeda made a great sensation in geophysics community, by

the discovery of the self-reversal of the TRM in Haruna dacite. The

field reversal vs self-reversal continued to be a topic of hot controversy

through 1950s and 1960s until Allan Cox and others established

the polarity reversal timescale. Nagata and his colleagues studied not

only the TRM, but also various forms of remanent magnetization,

which are found in nature as well as are produced in the laboratory.

These included viscous remanent magnetization (VRM, with Yoshio

Shimuzu), chemical remanent magnetization (CRM, with Kazuo

Kobayashi), pressure-induced remanent magnetization (PRM, with

Hajimu Kinoshita), and shock remanent magnetization (SRM). The

textbook Rock Magnetism, which was first published in 1953 and then

revised in 1961, summarized all these works in rock magnetism, and

was very influential to the community till very recent times.

Nagata also took part in studying the magnetic properties of the

lunar rocks collected by the Apollo project and meteorites of various

types. Nagata’s scientific interest covered all the aspects of geomag-

netism and the newly developing space sciences. Besides rock magnet-

ism and paleomagnetism, he studied the main magnetic field, secular

variation, tectonomagnetic effects, ionosphere, magnetic storms, and

aurorae. Nagata became a very famous scientist in Japan and was influ-

ential in Japanese scientific policy on developing the polar exploration,

rocket and satellite experiments, and even on the earthquake prediction

program. His popularity arose mostly because he was the leader of the

Antarctic expeditions for three consecutive years (1956–1958). This

project was started as a part of the Japanese contribution to the Inter-

national Geophysical Year Program (1957). The expedition built the

Syowa Base on the Ongul Island in Antarctica and started various

scientific observations, which are continued to this day. One of the

prominent achievements of these expeditions was the discovery of

meteorites on the ice field in 1969. Nagata strongly promoted contin-

ued search in the following years, and more than 16000 meteorites

were recovered from the Antarctic ice surfaces since then. For the

scientific achievement and for public services, he was elected to Mem-

ber of Japan Academy (1983), and was awarded the Japan Academy

Prize (1951), the Order of Culture of Japan (1974), and the gold medal

of the Royal Astronomical Society, UK (1984).

Masaru Kono

Bibliography

Nagata, T., 1943. The natural remanent magnetism of volcanic rocks

and its relation to geomagnetic phenomena. Bulletin of Earthquake

Research Institute, 21:1–196.

Nagata, T., Akimoto, S., and Uyeda, S., 1951. Reverse thermo-

remanent magnetism. Proceedings of the Japan Academy, 27:

643–645.

Nagata, T., 1961. Rock Magnetism, revised edition. Tokyo: Maruzen,

350 pp.

NATURAL SOURCES FOR ELECTROMAGNETIC

INDUCTION STUDIES

Time changes of the magnetic field, regardless whether they are of

internal (core) or of external (in the atmosphere, ionosphere, and mag-

netosphere) origin, produce secondary currents in the Earth’s interior.

Observations of the superposition of the primary (inducing) and sec-

ondary (induced) electromagnetic field allows for a determination of

the electrical conductivity of the Earth’s interior.

Mantle conductivity can be probed “from below” using signals ori-

ginating from the outer core. This method requires a precise determi-

nation of the field during rapid and isolated events, like geomagnetic

jerks (q.v.), and some a priori assumptions about the kinematics

of the fluid motion at the top of the core. Conductivity of mantle

and crust can also be studied “from above” by the analysis of field

changes of external origin, as the induced currents of these fluctuations

modify the observed electromagnetic field. Both methods require

good knowledge of the time-space structure of the inducing field.

The first approach has its strength in estimating the conductivity of the

deep mantle, whereas the second approach is suitable for probing

the conductivity of the crust and upper mantle down to the depths

of 1000 km or so. This article summarizes natural sources of external

origin only.

Two approaches are in use: the Geomagnetic Deep Sounding (q.v.)

(GDS) method utilizes time changes of the vertical and horizontal

magnetic field components; whereas Magnetotellurics (q.v.) (MT) uses

the horizontal components of magnetic and electric fields. GDS is used

for global soundings and with natural sources in the period range

between hours and years, whereas MT is mostly used for regional stu-

dies and with periods between milliseconds and a few hours due to the

decrease of the electric field strength with decreasing frequency.

Natural geomagnetic variations in the period range between a few

hours and a couple of days have been used for more than one century

to infer the electrical conductivity of the Earth’s mantle in the depth

range of a few hundred kilometers. The dominant sources for these

variations are the magnetospheric ring-current and the ionospheric cur-

rent system generated by wind systems in the upper atmosphere. The

latter produces periodic external field variations (periods of 24 h and

harmonics), whereas the magnetospheric ring-current contributes to

field variations in the whole period range between minutes and months.

These two sources are still the most important ones for inferring mantle

conductivity in the depth range of a few hundred kilometers.

Time-space structure of external sources

At the Earth’s surface, temporal variations of the magnetic field of

external origin, B

ext

¼rV

ext

, can be described by means of a scalar

potential V

ext

. For modeling its spatial dependency, the flat-Earth

approximation may be used to study phenomena that have a spatial

scale much smaller than the Earth ’s radius. Studying phenomena at

longer scales requires a spherical approach in which V

ext

is expanded

in a series of spherical harmonics (q.v.)

ext

t; r; y; fðÞ¼a

n¼1

m¼0

tðÞcos f þ s

tðÞsin f





cos yðÞ

¼ aRe

n¼1

m¼0

tðÞ



cos yðÞexp imf

()

(Eq. 1)

where ðr; y; fÞ are radius, colatitude, and longitude of a spherical

coordinate system, respectively, with a as the Earth’s radius, P

the associated Legendre function of degree n and order m, and

¼ q

 is

as the corresponding external expansion coefficients.

A similar expansion holds for the internal (induced) magnetic

field, B

int

¼rV

int

, with expansion coefficients i

and radial depen-

dence ða=rÞ

nþ1

instead of ðr=aÞ

. The horizontal scale-length of

a mode of degree n is l

¼ 2pa=ðn þ 1Þ40 000=ðn þ 1Þ km.

If conductivity depends only on depth (1D conductivity), each

expansion coefficient of the external field induces only one internal

coefficient of same degree n and order m, and the ratio of their Fourier

components (time dependence e

iot

), Q

ðoÞ¼i

ðoÞ



ðoÞ, depends

only on degree n.

Transfer functions (q.v.) like Q

or the C-response

n þ 1

1 ½ðn þ 1Þ=nQ

1 þ Q

depend on the frequency o as well as on the spatial scale l

(i.e., sphe-

rical harmonic degree n) of the source field, and on the electrical con-

ductivity distribution. Dependence of the C-response on spatial scale

and period is shown in Figure N1 for a typical model of mantle con-

ductivity. The horizontal parts of the curves present the range of l

, for

which source effects (the dependence of C

on l

) are negligible and

converge to the zero wave number response C

. For the given con-

ductivity model, this is true for variations of period T < 1 min. In the

limit of no induction for which jC

j¼l

=2p, the response (and hence

the induced field) is determined by the geometry of the source rather

than Earth’s conductivity. Because jC

jl

=2p, the maximum depth

for which conductivity can be determined is given by the spatial scale

of the source; with the chosen conductivity model it is for instance

not possible to probe the Earth’s conductivity using measurements of

the equatorial electrojet (EEJ) for periods >2h.

GDS requires a precise description of the time-space structure of

the potential V

ext

of the external field, but knowledge of the location

of the external sources (currents) is not required—provided they are

external to a sphere including the observation point (i.e., external to

Earth for ground observations). This means that the determination of

the equivalent source is sufficient for induction studies. The following

section focuses on the morphology rather than on the physical nature

of the various geomagnetic variations that are used for EM induction

studies.

Classification of geomagnetic variations

Table N1 presents a classification of magnetic variations in depen-

dence on period and Figure N2 shows a typical spectrum of the north

component of the geomagnetic field for a midlatitude site.

Magnetospheric ring-current

The ring current (q.v.) in the magnetosphere (q.v.) is probably the

source that has been used for most studies of mantle conductivity. To

first approximation, its spatial structure can be described by the single

spherical harmonic P

ðcos y

Þ , where y

is geomagnetic (dipole) cola-

titude. Hence only the expansion coefficient q

¼ e

of Eq. (1) is used.

Although the spatial structure of individual magnetic storms is often

more complicated and requires more coefficients, the validity of this

-assumption on average seems to be remarkably good, at least for

periods longer than a few days. For a P

source, and a 1D conductiv-

ity, only one internal coefficient, i

, is induced, and the sum of external

(inducing) and internal (induced) potential is

V ¼ V

ext

þ V

int

¼ e

þ i

r=aðÞ

cos y

(Eq. 2)

This allows for a determination of the C-response from magnetic data

of an individual site from observations of B

¼e

þ 2i



cos y

and

¼ e

þ i



sin y

at that site (r ¼ a) according to

oðÞ¼

a tan y

oðÞ

(Eq. 3)

This approach, known as Z/H-method, has been used by most

researchers to infer mantle conductivity at a few hundred kilometer

depths with periods between few days and several months.

Daily variations

Periodic external field (q.v.) variations at nonpolar latitudes (Sq varia-

tions) are caused by diurnal wind systems in the upper atmosphere,

which produce electric currents in the E-layer of the ionosphere

(q.v.) between 100 and 130 km altitude. Typical peak-to-peak ampli-

tudes at midlatitudes are 20–50 nT; amplitudes during solar maximum

are about twice as large as those during solar minimum. Sq variations

are restricted to the sunlit (i.e., dayside) hemisphere, and thus depend

mainly on local time T ¼ t þ f (t and f are UT and longitude

expressed in radians). The external potential (see Eq. (1)) of such local

NATURAL SOURCES FOR ELECTROMAGNETIC INDUCTION STUDIES 697

Figure N1 Absolute value of the C-response for a typical conductivity model (shown in the inset) as a function of horizontal

scale-length l

and period T of the source.

Table N1 Classification of geomagnetic variations (after Schmucker 1985, modified), with typical periods, amplitudes, and penetration

depths

Type of variation Symbol Typical period Typical amplitude Typical penetration depth

Solar cycle variations 11 years 10–20 nT >2000 km

Annual variation 12 months 5 nT 1500–2000 km

Semiannual variation 6 months 5 nT

Storm-time variation Dst Hours to weeks 50–500 nT 300–1000 km

Regular daily variation

At midlatitudes Sq 24 h and harmonics 20–50 nT 300–600 km

At low latitudes EEJ 50–100 nT

Substorms DP 10 min to 2 h 100 nT (1000 nT at p.l.) 100–300 km

Pulsations (¼Ultra low

frequency waves)

ULF 0.2–600 s 20–100 km

regular pc 150–600 s (pc5) 10 nT (100 nT at p.l.)

continuous 45–150 s (pc4) 2 nT

pulsations 5–45 s (pc2,3) 0.5 nT

0.2–5 s (pc1) 0.1 nT

Irregular transient pulsations pi 1–150 s 1 nT

Extreme low-frequency waves ELF sferics 1/5–1/1000 s <0.1 nT Tens of meters-kilometers

Schumann resonance oscillations 1/8 s <0.1 nT

Very low-frequency waves, whistlers VLF 10

–5

–10

–3

s Few meters-tens of meters

Note: If amplitude depends significantly on latitude, values are also given for polar latitudes (p.l., dipole latitude >65



698 NATURAL SOURCES FOR ELECTROMAGNETIC INDUCTION STUDIES

Figure N2 Top: Amplitude of magnetic variations (north component) at a midlatitude site for periods between 1 ms and 30 years,

estimated using data from the sites Niemegk/Germany (2 h–30 years), Kakioka/Japan (2 s–2 h), and Socorro/USA (1 ms–1 s).

Bottom: Skin depth d ¼

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

rT=pm

for a uniform half-space in dependence on resistivity r and period T.

NATURAL SOURCES FOR ELECTROMAGNETIC INDUCTION STUDIES 699

time phenomena consists of elementary modes of the form

r=aðÞ

exp imT, with periods of 24/m h. Coefficients representing

most of the power are those with n ¼ m þ 1, i.e., e

; e

; :::: Typically,

four Fourier terms, m ¼ 1–4 (periods 24,...,8 h), are used, which

results in a somewhat restricted period range of a factor of four; there-

fore Sq variations provide conductivity estimates only in a rather

limited depth range between roughly 300 and 600 km. The earliest

attempts (Schuster, 1889; Chapman (q.v.), 1919) to determine mantle

conductivity have used Sq as the inducing source.

There is about a fivefold enhancement of the daily variation near the

dip-equator, called EEJ. Its latitudinal width is about 6



–8



, which

requires spherical harmonics up to degree n ¼ 20–30 or higher.

Seasonal and solar cycle variation

The amplitudes of Sq variations depend on the season and on the

11-year cycle of solar activity, but because of vanishing ionospheric

conductivity (due to vanishing solar radiation) ionospheric currents are

almost zero at night. This requires ionospheric currents that vary with

season and solar cycle (i.e., there exists a true long-period variation in

addition to a modulation of the daily variation). In addition, there is also

a pronounced seasonal (mainly semiannual) and solar cycle variation of

the magnetospheric ring current. Induction studies using semiannual,

annual, and 11-year signals provide information on the conductivity

of the lower mantle. However, reliable estimates of transfer functions

at such long periods are hampered by contamination by short-term

secular variation of the core field. The main spherical coefficients

are e

(semiannual, solar cycle variation) and e

(annual variation).

Magnetospheric substorms, DP variations

Magnetic storms and substorms (q.v.) are irregular variations caused

by the interaction of the Earth’s magnetic field with the solar wind.

Ionospheric currents in the auroral regions, called polar electrojets

(PEJ), are linked to the magnetosphere by field-aligned currents. Both

currents are highly dependent on solar wind conditions. Their mag-

netic field variation, called disturbed polar (DP) variation, has a typical

timescale of a few minutes to hours and a horizontal scale-length of a

few hundred kilometers.

Geomagnetic pulsations, ULF and ELF waves, sferics,

and whistlers

Geomagnetic pulsations (q.v.), i.e., ultralow-frequency (ULF) waves,

cover roughly the period range from fractions of a second to a few

minutes. On the basis of their waveform, pulsations are classified into

pulsations continuous (pc) and pulsations irregular (pi). Their ampli-

tudes range from 100 to 0.1 nT, with longer periods exhibiting larger

amplitudes. Typical amplitudes are 1 nT at midlatitudes and 10 nT at

polar latitudes for a period of 30 s. There are several mechanisms that

produce pulsations; resonant oscillation of the Earth’s main field in

response to changes in the solar wind is one of them. The typical spa-

tial size of pulsations at midlatitudes is a thousand kilometers and

longer.

Extremely low-frequency (ELF) waves covering periods from milli-

seconds to seconds originate from thunderstorm lightnings and are

called atmospherics of sferics. This part of the spectrum shows, in par-

ticular, Schumann resonance oscillations (with peaks at 8 Hz and mul-

tiples) caused by standing waves in the waveguide formed by the

Earth’s surface and the ionosphere. Whistlers are sferics that travel

along Earth’s magnetic field lines from one hemisphere to the other.

As higher frequencies travel faster than the lower ones the lightning

wave is dispersed into a whistler tone.

Nils Olsen

Bibliography

Chapman, S., 1919. The solar and lunar diurnal variations of terrestrial

magnetism. Philosophical Transactions of the Royal Society of

London, Series A, 218:1–118.

Schmucker, U., 1985. Sources of the geomagnetic field. Landolt-

Börnstein, Berlin-Heidelberg: Springer-Verlag. New-Series, 5/2b,

section 4.1.

Schuster, A., 1889. The diurnal variations of terrestrial magnetism.

Philosophical Transactions of the Royal Society of London, Series A,

180:467–518.

Cross-references

Chapman, Sydney (1888–1970)

Geomagnetic Deep Sounding

Geomagnetic Jerks

Geomagnetic Pulsations

Harmonics, Spherical

Ionosphere

Magnetosphere of the Earth

Magnetotellurics

Periodic External Fields

Ring Current

Storms and Substorms, Magnetic

Transfer Functions

EL, LOUIS (1904–2000)

Louis Néel was born in Lyon, France. He followed the classic French

academic path to excellence: starting from the “classes préparatoires

Maths Sup” of Lycée du Parc in Lyon, he joined the Ecole Normale

Supérieure de Paris and later obtained the “Agrégation de Physique.”

His early vocation for magnetism led him to defend a thesis under

the supervision of Pierre Weiss in 1932 in Strasbourg, where he set

up the theoretical basis that grounded his later discovery of antiferro-

magnetism (Néel, 1936; the term antiferromagnetism was later coined

by Bitter). Mainly, his input was to introduce the concepts of quantum

mechanics in magnetism (following Heisenberg exchange interaction

concept), turning the uniform molecular field of Pierre Weiss into a

local field. He became professor in Strasbourg in 1937 and gained

Figure N3 Louis Ne

el (1904–2000).

700 NE

EL, LOUIS (1904–2000)

international recognition soon after. During World War II, he moved to

Grenoble where he spent the rest of his career. His central contribution

to modern magnetism was quite lately acknowledged by a Nobel Prize,

shared in 1970 with Hannes Halfven. Both of them, top physicists,

have grounded a discipline of geophysics: rock magnetism for the for-

mer, magnetospheric and space plasma physics for the latter. One can

appreciate his place in modern magnetism knowing that his scientific

contributions are at the origin or central to the understanding of anti-

ferromagnetism, ferrimagnetism, fine-grained magnetism, thermore-

manence, viscosity theory in single- and multidomains, theories of

the Rayleigh law and hysteresis cycle, domain walls, exchange and

surface anisotropies, coupling interaction and self-reversal, for the

most notable. To get a more detailed account of his scientific contri-

butions one can refer to his Nobel lecture (Néel, 1970) as well as to

Prévot and Dunlop (2001).

Closer to our concerns, Louis Néel gained interest in paleomagnet-

ism very early mostly through its rapid passage as the director of

Clermont-Ferrand Geophysical Observatory in 1931 (30 years after

B. Brunhes). At that time the nature of natural remanent magnetization

(NRM) was a full mystery and this may have triggered a good part of

Louis Néel theoretical breakthroughs. His most prized contribution in

rock magnetism concerns the single domain theory of relaxation time,

thermoremanence, and viscous remanence (Néel, 1949). This theory

turned paleomagnetism from magic to science. In the original paper

the theory was validated using the experimental results of Thellier on

baked clays, going against the often-observed reluctance of physicists

to use natural samples as a valid model. Nicely, this rather exotic con-

tribution for a physicist nowadays is the most cited paper of Louis

Néel, mostly in the nongeophysics literature. This is a beautiful exam-

ple of the input of Earth sciences into physics, balancing the more

common backward input. On the other hand, Louis Néel and his cow-

orkers were able to synthesize and measure the highly anisotropic

magnetization of the predicted ordered form of Fe-Ni alloy (Néel

et al., 1964). As this ordering appears only below 320



C, that is, at

a temperature where atomic diffusion is negligible, they used a trick

to enhance this diffusion: neutron bombardment. Much later, another

trick was found—ultralow cooling rates—only available in meteorite

parent bodies; the Fe-Ni ordered phase, tetrataenite, was “redis-

covered” (e.g., Wasilewski, 1988).

A great lesson from Louis Néel’s career (Néel, 1991) is that while

being so sharp in his personal scientific work he was so broad in his

interests and inspiration. His hobby was woodwork. It would be a

large error to remember him mainly as a theoretician: he demonstrated

great skills as an experimentator and as a man of action and organiza-

tion. When the Nazi troops approached Strasbourg in 1939 he orga-

nized practically by himself the evacuation of the most sensitive

equipments of the Strasbourg University in a train convoy. Soon after

he was responsible for battleship demagnetization to avoid the trigger-

ing of magnetic mines moored at the entrance of French ports. It took

him less than 6 months to set up original ship-size demagnetization

systems in several major ports and efficiently “immunize” more than

500 ships. He was fully involved in practical and engineering magnet-

ism, for example through military research or through the push of

improving the magnetic materials used in recording or electromechani-

cal devices. When he arrived in Grenoble, there were a handful of phy-

sicists in the university. When he retired from his leading position

there 30 years after, thousands of people were involved in various fun-

damental and applied physics research institutes. As the leading

builder of this top European center for solid-state physics, he early

recognized that subdisciplines of theoretical and experimental physics

have to work in close connection to solve the complex problems facing

modern physics. As a result, it is nowhere else than in Grenoble, where

it is possible to walk with the same sample from a neutron reactor to a

synchrotron x-ray source via world record high-magnetic field facil-

ities, finding all possible types of magnetic, spectroscopic, and other

measuring devices in between. The Louis Néel scientific impetus is still

visible today in the strong contribution of Grenoble laboratories—first

of all, the Louis Néel laboratory: http://lab-neel.grenoble.cnrs.fr — to

the advanceme nt of magnetism (du Trémolet de Lacheisserie et al.,

2002). These textbooks include a foreword by Louis Néel, acknowled-

ging the fact that he was going on to actively participate in the science

community until the term of his tremendously filled life.

Pierre Rochette

Bibliography

Du Trémolet de Lacheisserie, E., Gignoux, D., and Schlenker, M.,

2002. Magnetism, (two volumes) I-Fundamentals, II-Applications.

Dordrecht: Kluwer, 507 and 517 pp.

Néel, L., 1936. Théorie du paramagnétisme constant application au

manganese. Comptes Rendus De I’Académie des Sciences Paris,

203: 304–306.

Néel, L., 1949. Théorie du traînage magnétique des ferromagnétiques

en grains fins avec applications aux terres cuites. Annales De Géo-

physique, 5:99–136.

Néel, L., 1970. Magnetism and the local molecular field, Nobel Prize

lecture. Available at: http://www.nobel.se/physics/laureates/1970/

Néel-lecture.html.

Néel, L., 1991. Un siècle de Physique. Paris: Odile Jacob, 365 pp.

Néel, L., Paulevé, J., Dautreppe, D., and Laugier, J., 1964. Magnetic

properties of an iron-nickel single crystal ordered by neutron bom-

bardment. Applied Physics, 35: 873–876.

Prévot, M., and Dunlop, D., 2001. Louis Néel: 40 years of magnetism.

Physics of the Earth and Planetary Interiors, 126:3–6.

Wasilewski, P., 1988. Magnetic characterization of the new mineral

tetrataenite and its contrast with isochemical taenite. Physics of

the Earth and Planetary Interiors, 52: 150–158.

NONDIPOLE FIELD

The nondipole (ND) field is that part of the internal geomagnetic field

remaining after the major geocentric dipole contribution has been

removed. It is distinct from the nonaxial-dipole (NAD) field for which

only the component of the geocentric dipole that is parallel to Earth’s

rotation axis is subtracted. Figure N4a/Plate 4a shows the strength of

the total scalar field at Earth’s surface, with the spatial variations

dominated by the dipole field, while in Figure N4b/Plate 4b the dipole

contribution has been subtracted to reveal the substantially more com-

plex nondipole field. Two source regions contribute to the ND field:

the dynamo in Earth’s core that is also responsible for the dipole part

of the geomagnetic field produces the largest part; the other source

is Earth’s lithosphere (see Crustal magnetic field). Nondipole field

contributions are significant, but contribute only a small fraction of the

average magnetic energy at the surface, as can be seen in Figure N5a,

which shows





r¼a

, the squared average value of the field

strength over the Earth’s surface, average radius r ¼ a, as a function of

spherical harmonic degree, l.Thisgeomagnetic spatial power spec-

trum (q.v.) falls off rapidly with increasing l (decreasing wavelength),

up to about degree 12, then flattens out and remains roughly constant

out to the shortest resolvable wavelengths. The ND field between degrees

2 and 11 is dominated by sources in Earth’s core, while above degree 15

the core contribution is overwhelmed by that from lithospheric magnetic

anomalies (see Magnetic anomalies, modeling; Magnetic anomalies,

long wavelength;andMagnetic anomalies, marine). Between degrees

11 and 15, it is difficult to isolate the primary source, although time var-

iations (Figure N5b) in the core part at these spatial scales will be better

characterized with new high-quality satellite data. Temporal variations

in the lithospheric field occur on geological timescales, but direct mea-

surements over the past few centuries will only sense changes in inducing

fields. These are very small at timescales of the order of a year or longer.

NONDIPOLE FIELD 701