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

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Kamide, Y., and Arballo, J.K. (eds.), Magnetic Storms. Geophysi-

cal Monograph 98, AGU, Washington DC, p. 77.

Tsurutani, B.T., Kamide, Y., Arballo, J.K., Gonzalez, W.D., and

Lepping, R.P., 1999. Interplanetary causes of great and superintense

magnetic storms, Physics and Chemistry of the Earth, 24: 101.

Tsurutani, B.T., Gonzalez, W.D., Lakhina, G.S., and Alex, S.,

2003. The extreme magnetic storm of September 1–2, 1859.

Journal of Geophysical Research, 108, A7, 1268, doi:10.1029/

2002JA009504.

von Humboldt, A., 1808. Annalen der Physik, 29: 425.

Cross-references

Gilbert, William (1544–1603)

Halley, Edmond (1656–1742)

406 HUMBOLDT, ALEXANDER VON AND MAGNETIC STORMS

IAGA, INTERNATIONAL ASSOCIATION OF

GEOMAGNETISM AND AERONOMY

History

The origin of the International Association of Geomagnetism and Aero-

nomy (IAGA) can be traced to the Commission for Terrestrial Magnetism

and Atmospheric Electricity, part of the International Meteorological

Organization, which was established in 1873. The Commission planned

the geomagnetic observation campaign for the First International Polar

Year, 1882–1883. Following the end of World War I, the International

Research Council (IRC) was established to promote science through inter-

national cooperation. At a meeting of the IRC in July 1919, the Interna-

tional Geodetic and Geophysical Union was formed, with Terrestrial

Magnetism and Electricity as Section D, and with its leadership provided

by the International Meteorological Organization. In 1930, the Interna-

tional Geodetic and GeophysicalUnionagreed to cooperate with the Inter-

national Meteorological Organization to organize a Second International

Polar Year, 50 years after the first. The Union changed its name to the

International Union of Geodesy and Geophysics (IUGG), its Sections

were renamed Associations, and the International Association of Terres-

trial Magnetism and Electricity (IATME) came into existence.

At the Brussels IUGG General Assembly in 1951, upper atmosphere

scientists lobbied to have their interests recognized within IATME.

Following the Brussels Assembly, Sydney Chapman (q.v.), who had

previously suggested replacing the term “Terrestrial Magnetism ” by

“Geomagnetism” coined the term “Aeronomy” and suggested adoption

of the name International Association of Geomagnetism and Aero-

nomy. The expansion of the scope of IATME was ratified at the

General Assembly in Rome in 1954, the new title IAGA was agreed,

and aeronomy was defined as “the science of the upper atmospheric

regions where dissociation and ionization are important.”

In 1950, Lloyd Berkner proposed a Third International Polar Year

to provide motivation to re-equip geophysical observatories, many of

which had been damaged or destroyed during World War II. The Inter-

national Council of Scientific Unions adopted and broadened the scope

of the idea, and designated July 1957 to December 1958 the Interna-

tional Geophysical Year (IGY). Observations were made in a number

of IUGG discipline areas, including geomagnetism. The IGY resulted

in a leap forward in geophysics through coordinated observational cam-

paigns and through the establishment of new observatories and the World

Data Center system. It was the beginning of the space age, and marked the

start of the modern era for IAGA science, which has expanded to include

solar-terrestrial interactions and studies of the Sun and the planets.

Present structure and organization

In 2005, IAGA is one of seven scientific associations of the IUGG.

It is an international nongovernmental organization deriving the major-

ity of its funding from the IUGG member nations. An Executive

Committee, elected by member countries, runs the Association, and

the scientific work is organized through a structure defined in the

Association’s Statutes and By-Laws:

Division I: Internal Magnetic Fields;

Division II: Aeronomic Phenomena;

Division III: Magnetospheric Phenomena;

Division IV: Solar Wind and Interplanetary Field;

Division V: Geomagnetic Observatories, Surveys, and Analyses.

Interdivisional Commission on History

Interdivisional Commission on Developing Countries

Several of the Divisions have Working Groups in specialist topic

areas and establish Task Groups to deal with specific issues.

IAGA’s purpose and linkages

IAGA’s “mission” is defined by the Association’s first Statute, which

states that IAGA should promote scientific studies of international

interest and facilitate international coordination and discussion of

research. An important defining characteristic of IAGA is, therefore,

to encourage inclusiveness in the scientific community, making excel-

lent science accessible to scientists worldwide. There is a particular

commitment to the less developed countries, and to the free exchange

of scientific data and information.

One way in which IAGA achieves its objectives is through the organi-

zation of meetings. IAGA Scientific Assemblies are held every 2 years,

and in conjunction with IUGG General Assemblies every 4 years. Smaller

scale meetings and specialized workshops make IAGA science accessible

to a wider audience and help younger scientists and scientists from devel-

oping countries to accelerate their learning. IAGA sponsors several such

meetings each year. They are held in all parts of the world, an important

factor in enabling attendance by scientists with limited resources.

Meetings enable scientific results to be presented and debated, new

ideas generated, and collaborations to be established. The major Assem-

blies are also used to conduct divisional and working group business

meetings, and matters of interest to IAGA are presented at open meetings

convened for discussions between the IAGA Executive, the official dele-

gates from member countries, and individual scientists. Resolutions

are adopted as a formal means for IAGA to express views on scientific

matters. Support is often given to scientific initiatives under considera-

tion by national or international agencies that will benefit IAGA science.

For example, a series of IAGA Resolutions supported the initiation of

and extensions to the International Equatorial Electrojet Year (IEEY)

project (1991–1994). The project not only produced good science, but

also resulted in investment in observational facilities at low-latitudes,

benefiting scientists in the less developed world. Although the IEEY

has finished, the impetus it gave to research in the equatorial regions con-

tinues. Similarly, IAGA has supported the Decade of Geopotential

Research, which appears likely to achieve its goal of securing uninter-

rupted geomagnetic field satellite survey measurements spanning a

decade (including the Ørsted and CHAMP missions).

IAGA science is also promoted through collaboration with other

bodies with similar interests. There are links with the other IUGG

Associations and with Inter-Association bodies including Studies of

the Earth ’s Deep Interior (SEDI) (q.v.) and the Working Group on

Electric and Magnetic Studies on Earthquakes and Volcanoes (EMSEV).

There are formal contacts for liaison with the International Lithosphere

Program (ILP), the Scientific Committee on Antarctic Research (SCAR),

the Committee on Space Research (COSPAR), and the Scientific

Committee on Solar Terrestrial Physics (SCOSTEP).

IAGA cooperates with the World Data Center system on the definition

of geomagnetic data exchange formats and management and preservation

of analog and digital databases. The Association has provided strong

support to INTERMAGNET (q.v.), the international program promoting

the modernization of magnetic observatory practice and the distribution

of data in near real time. IAGA advises bodies such as the International

Organization for Standardization (ISO).

IAGA science in the 21st century

IAGA science, because of the pervasiveness of the geomagnetic field

and its interactions with charged particles and electrically conducting

materials, is useful for studies of properties and processes in practi-

cally all parts of the solid Earth, the atmosphere, and the surrounding

space environment. As well as covering a vast range of length scales,

IAGA science covers timescales from seconds to billions of years.

Modern-day observatories record rapid variations during magnetic

storms caused by the interaction of the solar wind with the magneto-

sphere; the imprinting of the paleomagnetic field in rocks provides

records of geodynamic changes on geological timescales.

While IAGA provides an international focus for fundamental research

resulting in advances in understanding in specialist areas, national and

international funding for research often focuses on issues of societal

concern. IAGA science is providing answers to many important ques-

tions, and through its links to other bodies and projects the Association

is able to foster the building of the interdisciplinary teams required to

address complex problems of interest to society.

For instance, a natural goal for IAGA scientists is to be able to

understand and model the whole Sun-Earth system including the com-

plex interactions and feedbacks controlling the transfer of energy

momentum and matter between parts of the system. Research in this

area is proving relevant to the problem of how to disentangle natural

from anthropogenic causes of climate change. This area of science also

underpins the understanding of how “space weather” conditions affect

the risk to technological systems and human activities on the ground

and in space. For example, during magnetic storms, electrical power

distribution grids, radio communications, GPS accuracy, and satellite

operations can be adversely affected. Also in the geohazards area,

EMSEV is charged with establishing firm scientific understanding of

the generation mechanisms of any signals that may help to mitigate

the effects of earthquakes and volcanoes.

IAGA is responsible for the production of the International Geo-

magnetic Reference Field, used in a variety of scientific and “real

world” applications, including navigation, and hydrocarbons explora-

tion and production. The Association is responsible for the definition

of the most widely used magnetic activity indices, and works closely

with the International Service for Geomagnetic Indices, the body

responsible for their production and distribution.

IAGA has a long history, and its science remains vigorous and rele-

vant. Rapid advances in scientific understanding are resulting from

improved instruments, better observations and data analysis techni-

ques, the wealth of satellite data now routinely available, and the

power of modern computer technology. As the 50th anniversary of

the IGY approaches, IAGA is promoting the concept of an “Electronic

Geophysical Year” (eGY), for 2007–2008, taking advantage of the

modern capability to link distributed computing resources to multiple

remote sources of data and modeling codes to address scientific pro-

blems. This initiative is in line with the Association’s mission to

promote international scientific cooperation and collaboration, and has

the potential to advance the ability of scientists in developing countries

to participate in leading-edge research.

(The principal point of contact with the Association is the IAGA

Secretary General, and IAGA communicates with its members and

the public through its Web site and through issues of IAGA News.)

David Kerridge

Bibliography

Naoshi Fukushima, 1995. History of the International Association of

Geomagnetism and Aeronomy (IAGA). IUGG Chronicle, 226:

73–87.

The IAGA Web site: http://www.iugg.org/IAGA/

Cross-references

CHAMP

Chapman, Sydney (1888–1970)

Ørsted

SEDI

IDEAL SOLUTION THEORY

Consider two different substances; mix them together and in general

they will form a solution, like sugar and coffee, for example. We call

solvent the substance present in the largest quantity (coffee), and solute

the other (sugar). In general solutions may have more than one solute,

and/or more than one solvent, but for simplicity we will focus here

only on binary mixtures.

The behavior of solutions can be understood in terms of the chemical

potential m

, which represents the constant of proportionality between

the energy of the system and the amount of the specie i (Wannier, 1966):



S;V

(Eq. 1)

where E is the internal energy of the system, S is the entropy , V is the

volume, and N

is the number of particles of the specie i. Alternative equiva-

lent definitions of the chemical potential are (Wannier , 1966; Mandl, 1997):



T;V



T; p

¼T



E;V

(Eq. 2)

where F and G are the Helmholtz and Gibbs free energies of the sys-

tem, T is the temperature, and p is the pressure.

We recall the statistical mechanics definition of the Helmholtz free

energy for a classical system (Frenkel, 1996):

F ¼k

T ln

...

UðR

;...;R

;TÞ=k

; (Eq. 3)

408 IDEAL SOLUTION THEORY

where U ð R

;...; R

; T Þ is the potential energy which depends on the

positions ð R

;...; R

Þ of all the particles in the system and on T, k

the Boltzmann constant and L ¼ h =ð2 p Mk

T Þ

1=2

is the thermal wave-

length, with M being the nuclear mass and h the Plank ’s constant.

Consider now a solution with N

particles of solvent A and N

parti-

cles of solute X, with N ¼ N

þ N

. The Helmholtz free energy of this

system is:

F ¼k

T ln

3 N

! N

d R

...

 U ðR

;...;R

;T Þ=k

(Eq. 4)

According to (Eq. 2) , we have:

] F

] N



T ; V

¼ F ð N

; N

þ 1ÞF ð N

; N

Þ; (Eq. 5)

which can be evaluated using (Eq. 4)

¼ k

T ln

ð N

þ 1Þ

d R

...

d R

N þ 1

 U ðR

;...;R

N þ1

; T Þ=k

...

 U ðR

;...;R

;T Þ=k

(Eq. 6)

The ratio of the two integrals is an extensive quantity, but m

is an inten-

sive quantity; therefore it is useful to rewrite the expression as follows:

¼k

T ln

ðN

þ 1 Þ

N L

d R

...

d R

N þ1

U ð R

;...; R

; R

N þ 1

;T Þ= k

d R

...

U ðR

;...;R

;T Þ= k

()

(Eq. 7)

so that the value in curly brackets is now independent on system size.

By setting c

¼ N

= N (which in the limit of large N and N

is the same

asð N

þ 1 Þ= N ÞÞ and

¼k

T ln

N L

...

N þ1

 U ðR

;...;R

N þ 1

;T Þ=k

...

U ð R

;...; R

; T Þ=k

()

(Eq. 8)

we can rewrite the chemical potential in our final expression:

ðp ; T ; c

Þ¼ k

T ln c

ðp ; T ; c

Þ: (Eq. 9)

The first term of (Eq. 9) depends only on the number of particles of

solute present in the solution, while the second term is also responsible

for all possible chemical interactions. For small concentration of solute

we can make a Taylor expansion of

¼ m

þ l c

þ o ð c

Þ; (Eq. 10)

where l ¼ð]

= ]c

p ;T

. If the solution is so dilute that the particl es

of the solute do not interact with each other, we can stop the expansion

to the first term:

ðp; T ; c

Þ¼k

T ln c

þ m

ðp; T Þ: (Eq. 11)

We define ideal solution a system in which (Eq. 11) is strictly

satisfied.

To find an expression for the chemical potential of the solvent we

employ the Gibbs-Duhem equation, which for a system at constant

pressure and constant temperature reads (Wannier, 1966):

¼ 0: (Eq. 12)

In particular, in our two-components system the Gibbs-Duhem equation

implies:

þ c

¼ 0; (Eq. 13)

which gives (Alfè et al ., 2002a):

ðp; T;c

Þ¼m

ðp; TÞþðk

T þl

ðp; TÞÞlnð1 c

þl

ðp; TÞc

þOðc

Þ; (Eq: 14)

where m

is the chemical potential of the pure solvent. To linear order

in c

, this gives:

ðp; T; c

Þ¼m

ðp; T Þk

þ Oðc

Þ: (Eq. 15)

Notice that this expression for m

is not restricted to ideal solutions.

Though m

is the chemical potential of the pure solvent, observe that

is not the chemical potential of the pure solute, unless the validity

of (Eq. 11) extends all the way up to c

¼ 1.

Volume of mixing

It is often interesting to study the change of volume of a solution as a

function of the concentration of the solute. To this end, it is useful to

express the volume of the system as the partial derivative of the Gibbs

free energy with respect to pressure, taken at constant temperature and

number of particles:

V ¼ð]G=]pÞ

T;N

: (Eq. 16)

If we now add to the system one particle of solvent at constant pressure,

the total volume changes by v

, and becomes V þ v

.Wecallv

the par-

tial molar volume of the solvent. The total Gibbs free energy is G þ m

,so

that according to (Eq. 16) v

¼ð]m

=]pÞ

T;N

¼ð]m

=]pÞ

T;c

,where

the last equality stems from the fact that m

only depends on N

and N

through the molar fraction c

(we assume here that c

does not change

when we add one particle of solvent to the system, this is obviously true

if the number of atoms of solvent N

is already very large). The partial

volume in general depends on c

, p,andT, but under the assumption of

ideality v

¼ð]m

=]pÞ

T;c

, and it depends only on p and T.Inanideal

solution v

is the same as in the pure solvent.

Similarly, the partial molar volume of the solute is: v

¼ð]m

=]pÞ

T;c

which becomes independent on c

under the assumption of ideality.

Notice that this is not in general equal to the partial volume of

the pure solute.

As an illustration of the applicability of the ideal solution approxi-

mation, I mention the recent first-principles calculations of the density

of the Earth’s liquid outer core as a function of the concentration of

light impurities like sulfur, silicon, and oxygen in liquid iron. As

reported in (Gubbins et al., 2004), explicit first-principles calculations

of the density of the core were not able to resolve any departure from

the prediction of ideal solution theory. However, we shall see below

that for other properties ideal solution theory is not necessarily a good

working hypothesis.

Solid-liquid equilibrium

We want to study now the conditions that determine the equilibrium

between solid and liquid, and in particular how the solute partitions

between the two phases. Thermodynamic equilibrium is reached

when the Gibbs free energy of the system is at its minimum (Wannier,

1966; Mandl, 1997), and therefore, 0 ¼ dG ¼ d ðG

þ G

Þ, where

IDEAL SOLUTION THEORY 409

superscripts s and l indicate quantities in the solid and in the liquid,

respectively. In a multicomponent system, the Gibbs free energy can

be expressed in terms of the chemical potentials of the species present

in the system (Wannier, 1966; Mandl, 1997):

G ¼

: (Eq. 17)

Using (Eq. 17) and the Gibbs-Duhem equation (12) , we obtain:

dG ¼

: (Eq. 18)

If the system is isolated, particles can only flow between the solid and

the liquid, and we have dN

¼dN

, which implies:

dG ¼

ðm

 m

Þ: (Eq. 19)

If m

< m

there will be a flow of particles from the solid to the liquid

region ðdN

> 0Þ, so that the Gibbs free energy of the system is low-

ered. The opposite will happen if m

> m

. The flow stops at equili-

brium, which is therefore reached when m

¼ m

. In particular, in our

two-components system, the equilibrium between solid and liquid

implies that the chemical potentials of both solvent and solute are

equal in the solid and liquid phases:

ðp; T

; c

Þ¼m

ðp; T

; c

Þ;

ðp; T

; c

Þ¼m

ðp; T

; c

Þ; (Eq. 20)

where T

is the melting temperature of the solution at pressure p.Using

(Eq. 9), we can rewrite the first of the two equations above as:

ðp; T

ÞþkT

lnc

ðp; T

ÞþkT

lnc

; (Eq. 21)

from which we obtain an expression for the ratio of concentrations of

solute between the solid and the liquid:

¼ expf½

ðp; T

Þ

ðp; T

Þ=kT

g: (Eq. 22)

In general

, because the greater mobility of the liquid can

usually better accommodate particles of solute, and therefore their

energy (chemical potential) is lower. This means that the concentration

of the solute is usually smaller in the solid.

Equation (22) was used by Alfè et al. (2000, 2002a,b) to put con-

straints on the composition of the Earth’s core. The constraints came

from a comparison of the calculated density contrast at inner core

boundary, and that obtained from seismology, which is between

4.5%  0.5% (Shearer and Masters, 1990) and 6.7%  1.5% (Masters

and Gubbins, 2003). This density contrast is significantly higher than

that due to the crystallization of pure iron, and therefore must be due

to the partitioning of light elements between solid and liquid. This par-

titioning for some candidate impurities can be obtained by calculating

and

.Alfèet al. (2000, 2002a,b) considered sulfur, silicon, and

oxygen as possible impurities, and using first-principles simulations, in

which the interactions between particles were treated using quantum

mechanics, obtained the partitions for each impurity. The calculations

showed that for both sulfur and silicon

and

are very similar,

which means that c

and c

are also very similar, according to

(Eq. 22). As a result, the density contrast of a Fe/S or a Fe/Si system

is not much different from that of pure Fe, and still too low when com-

pared with the seismological data. By contrast, for oxygen

and

are very different, and the partitioning between solid and liquid is very

large. This results in a much too large density contrast, which also

does not agree with the seismological data. The conclusion from these

calculations was that none of these binary mixtures can be viable for

the core. The density contrast can of course be explained by ternary or

quaternary mixtures. Assuming no cross-correlated effects between

the chemical potentials of different impurities, Alfè et al.(2002a,b)

proposed an inner core containing about 8.5% of sulfur and/or silicon

and almost no oxygen, and an outer core containing about 10% of sulfur

and/or Si, and an additional 8% of oxygen.

It is worth noting that these calculations (Alfè et al., 2000, 2002a,b)

also showed that the dependence of

and

on c

and c

was

significant, and therefore departure from ideal solution behavior. If

nonideal effects were ignored, the calculations would result in an outer

core containing about 12% of sulfur and/or silicon, and about 6% of

oxygen.

Shift of freezing point

The partitioning of the solute between the solid and the liquid is gen-

erally responsible for a change in the melting temperature of the mix-

ture with respect to that of the pure solvent. To evaluate this, we

expand the chemical potential of the solvent around the melting tem-

perature of the pure system, T

ðp; T

; c

Þ¼m

ðp; T

; c

Þs

dT þ (Eq. 23)

where dT ¼ðT

 T

Þ,ands

¼]m

]TðÞ

T¼T

is the entropy of the

pure solven t at T

. We now impose continuity across the solid-liquid

boundary:

ðp; T

Þs

dT  kT

¼ m

ðp; T

Þs

dT  kT

;

(Eq. 24)

where we have considered only the linear dependence of m

on c

(See Eq. 15). Noting that m

ðp; T

Þ¼m

ðp; T

Þ we have

dT ¼

 s

ðc

 c

Þ: (Eq. 25)

Since usually c

< c

, there is generally a depression of the freezing

point of the solution.

Using (Eq. 25), Alfè et al. (2002a,b) estim ated a depression of about

600–700 K of the melting temperature of the core mixture with respect

to the melting temperature of pure Fe, and they suggested an inner

core boundary temperature of about 5600 K.

Dario Alfè

Bibliography

Alfè, D., Gillan, M.J., and Price, G.D., 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.D., 2002a. Ab initio chemical

potentials of solid and liquid solutions and the chemistry of the

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

Alfè, D., Gillan, M.J., and Price, G.D., 2002b. Composition and

temperature of the Earth’s core constrained by combining ab initio

calculations and seismic data. Earth and Planetary Science Letters,

195:91–98.

Frenkel, D., and Smit, B., 1996. Understanding Molecular Simulation.

San Diego, CA: Academic Press.

Gubbins, D. et al., 2004. Gross thermodynamics of two-component

core convection. Geophysical Journal International, 157:

1407–1414.

Mandl, F., 1997. Statistical Physics, 2nd edn. New York: John Wiley &

Sons.

410 IDEAL SOLUTION THEORY

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

within the Earth. Physics of the Earth and Planetary Interiors, 140:

159–167.

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

contrast at the inner core boundary. Geophysical Journal Interna-

tional, 102: 491–498.

Wannier, G.H., 1966. Statistical Physics. New York: Dover Publications.

IGRF, INTERNATIONAL GEOMAGNETIC

REFERENCE FIELD

History of the IGRF

The IGRF is an internationally agreed global spherical harmonic

model of the Earth’s magnetic field whose sources are in the Earth’s

core (see Harmonics, spherical and Main field modeling). It is revised

every 5 years under the auspices of the International Association of

Geomagnetism and Aeronomy (see IAGA, International Association

of Geomagnetism and Aeronomy).

The concept of an IGRF grew out of discussions concerning the pre-

sentation of the results of the World Magnetic Survey (WMS). The

WMS was a deferred element in the program of the International

Geophysical Year, which, during 1957–1969, encouraged magnetic

surveys on land, at sea, in the air, and from satellites and organized

the collection and analysis of the results. At a meeting in 1960, the

Committee on World Magnetic Survey and Magnetic Charts of IAGA

recommended that, as part of the WMS program, a spherical harmonic

analysis be made using the results of the WMS, and this proposal was

accepted. Another 8 years of argument and discussion followed this

decision and a summary of this, together with a detailed description of

the WMS program, is given by Zmuda (1971). The first IGRF was rati-

fied by IAGA in 1969.

The original idea of an IGRF had come from global modelers,

including those who produced such models in association with the

production of navigational charts. However, the IGRF as it was first

formulated was not considered to be accurate or detailed enough for

navigational purposes.

The majority of potential users of the IGRF at this time consisted of

geophysicists interested in the geological interpretation of regional

magnetic surveys. An initial stage in such work is the removal of a

background field from the observations that approximates the field

whose sources are in the Earth’s core. With different background fields

being used for different surveys, difficulties arose when adjacent sur-

veys had to be combined. An internationally agreed global model,

accurately representing the field from the core, eased this problem

considerably.

Another group of researchers who were becoming increasingly

interested in descriptions of the geomagnetic field at this time were

those studying the ionosphere and magnetosphere and behavior of cos-

mic rays in the vicinity of the Earth. This remains an important user

community today.

Development of the IGRF

The IGRF has been revised and updated many times since 1969 and a

summary of the revision history is given in Table I1 (see also Barton,

1997, and references therein).

Each generation of the IGRF comprises several constituent models

at 5-year intervals, some of which are designated definitive. Once a

constituent model is designated definitive it is called a Definitive Geo-

magnetic Reference Field (DGRF) and it is not revised in subsequent

generations of the IGRF.

New constituent models are carefully produced and widely docu-

mented. The IAGA Working Group charged with the production of

the IGRF invites submissions of candidate models several months in

advance of decision dates. Detailed evaluations are then made of

all submitted models, and the final decision is usually made at an

IAGA Assembly if it occurs in the appropriate year, otherwise by the

IAGA Working Group. The evaluations are also widely documented.

The coefficients of the new constituent models are derived by taking

means (sometimes weighted) of the coefficients of selected candidate

models. This method of combining several candidate models has been

used in almost all generations as, not only are different selections of

available data made by the teams submitting models, there are many

different methods for dealing with the fields which are not modeled

by the IGRF, for example the ionospheric and magnetospheric fields

and crustal fields. The constituent main field models of the most recent

generation of the IGRF (IAGA, 2005) extend to spherical harmonic

degree 10 up to and including epoch 1995.0, thereafter they extend

to degree 13 to take advantage of the excellent coverage and quality

of satellite data provided by Ørsted and CHAMP (see Ørsted and

CHAMP). The predictive secular variation model extends to degree 8.

Future of the IGRF

Firstly, no model of the geomagnetic field can be better than the data

on which it is based. An assured supply of high-quality data distribu-

ted evenly over the Earth’s surface is therefore a fundamental prerequi-

site for a continuing and acceptably accurate IGRF. Data from

magnetic observatories (see Observatories, overview) continue to be

the most important source of information about time-varying fields.

However their spatial distribution is poor and although data from

other sources such as repeat stations (see Repeat stations), Project

MAGNET (see Project MAGNET), and marine magnetic surveys

(see Magnetic surveys, marine) have all helped to fill in the gaps,

Table I1 Summary of IGRF history

Full name Short name Valid for Definitive for

IGRF 10th generation (revised 2004) IGRF-10 1900.02010.0 1945.02000.0

IGRF 9th generation (revised 2003) IGRF-9 1900.02005.0 1945.02000.0

IGRF 8th generation (revised 1999) IGRF-8 1900.02005.0 1945.01990.0

IGRF 7th generation (revised 1995) IGRF-7 1900.02000.0 1945.01990.0

IGRF 6th generation (revised 1991) IGRF-6 1945.01995.0 1945.01985.0

IGRF 5th generation (revised 1987) IGRF-5 1945.01990.0 1945.01980.0

IGRF 4th generation (revised 1985) IGRF-4 1945.01990.0 1965.01980.0

IGRF 3rd generation (revised 1981) IGRF-3 1965.01985.0 1965.01975.0

IGRF 2nd generation (revised 1975) IGRF-2 1955.01980.0 

IGRF 1st generation (revised 1969) IGRF-1 1955.01975.0 

IGRF, INTERNATIONAL GEOMAGNETIC REFERENCE FIELD 411

the best spatial coverage is provided by near-polar satellites. Measure-

ments made by the POGO satellites (1965–1971) (see POGO (OGO-2,

-4, and -6 spacecraft)), Magsat (1979–1980), POGS (1990–1993),

Ørsted (1999–), and CHAMP (2000–) have all been utilized in the pro-

duction of the IGRF.

Secondly, the future of the IGRF depends on the continuing ability

of the groups who have contributed candidate models to the IGRF

revision process to produce global geomagnetic field models. This

ability is dependent on the willingness of the relevant funding authori-

ties to continue to support this type of work.

Thirdly, the continued interest of IAGA is a necessary requirement

for the future of the IGRF. This is assured as long as there is, as at pre-

sent, a large and diverse group of IGRF-users worldwide. One reason

why the IGRF has gained the reputation it has is because it is endorsed

and recommended by IAGA, the recognized international organization

for geomagnetism.

A topic still under discussion is how best to extend the IGRF back-

ward in time. The current generation includes non-definitive models

at 5-year intervals covering the interval 1900.0 –1940.0, and, more

importantly, some of the earlier DGRFs are of questionable quality.

Constructing an internationally acceptable model that describes the

time variation better than the IGRF using splines is one way forward

(see Time-dependent models of the geomagnetic field ).

Susan Macmillan

Bibliography

Barton, C.E., 1997. International Geomagnetic Reference Field: the

seventh generation. Journal Geomagnetism and Geoelectricity,

49: 123–148.

International Association of Geomagnetism and Aeronomy (IAGA),

Division V, Working Group VMOD: Geomagnetic Field Modeling,

2005. The 10th-Generation International Geomagnetic Reference

Field. Geophysical Journal International, 161, 561–565.

Zmuda, A.J., 1971. The International Geomagnetic Reference Field:

Introduction, Bulletin International Association of Geomagnetism

and Aeronomy, 28: 148–152.

Cross-references

CHAMP

Harmonics, Spherical

IAGA, International Association of Geomagnetism and Aeronomy

Magnetic Surveys, Marine

Magsat

Main Field Modeling

Observatories, Overview

Ørsted

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

Project MAGNET

Repeat Stations

Time-dependent Models of the Geomagnetic Field

INDUCTION ARROWS

Introduction

The history of continuous magnetic field observations in Germany

dates back to the 19th century (see Observatories in Germany).

Modern observatory work began in 1930, with the foundation of the

geomagnetic observatory in Niemegk, south of Potsdam. When a sec-

ond observatory started operation in the late 1940s in Wingst, northern

Germany, scientists soon noticed reversed signal amplitudes in the

vertical field components between the two locations.

This observation was unexpected because magnetic field disturbances

were known to be generated by large-scale processes in the Earth’satmo-

sphere, far away from the surface of the Earth (see Natural sources for EM

induction studies). Hence, for external sources, the magnetic field varia-

tions should have been very similar, given the relatively short distance

between the two observatories. However, it was soon speculated that this

peculiar behavior may be caused by electromagnetic induction of currents

into an electrically conducting region deep in the earth’sinterior.When

portable magnetometers became available, this phenomenon was investi-

gated more systematically. With measurements following a N-S oriented

profile at selected field sites, Schmucker (1959) could not only confirm

the observatory results but could also confine the width of this North

German anomaly to approximately 100 km.

Northern Germany was not the only place where magnetic field var-

iations were studied; similar conductivity anomalies were reported

from many other parts of the world. Over the years, some of the largest

conductivity anomalies on Earth were identified with studies relating

vertical magnetic fields to horizontal magnetic fields (see Geomagnetic

deep sounding).

The induction arrow

Wiese (1962) and Parkinson (1962) independently developed graphi-

cal methods to locate the observed “induction effect,” thereby invent-

ing the induction arrow (IA). Both original definitions of the IA are

based on a time-domain approach which is not in use any more. How-

ever, we still draw our IAs in either the Wiese or the Parkinson (q.v.)

convention according to their original designs (see Hobbs, 1992).

Functions that interrelate vertical or horizontal magnetic fields are

known as transfer functions (see Transfer functions). If lateral conduc-

tivity variations exist within the subsurface on length scales equal to or

greater than the penetration depth of the induced horizontal magnetic

fields, a vertical magnetic field component is generated.

The frequency-domain, geomagnetic transfer functions T

ðoÞ; T

ðoÞ

are defined as (dependence on frequency assumed):

¼ T

þ T

(Eq. 1)

x, y,andz denote north, east, and vertical directions, respectively. B is the

magnetic field component in [T]. The IA is a graphical representation of

the complex vertical magnetic field transfer function T. The real and

imaginary parts of T

and T

can be combined to form ðT

; T

and ðT

; T

Þ. The visual display of the IAs in maps is a comprehen-

sive presentation of changes in vertical magnetic field anomalies, both,

as a function of frequency and location. In Parkinson convention the

ðT

; T

Þ is plotted, which tends to point toward regions of higher

conductivity. The IA in the Wiese convention (T

, T

) tends to point

away from areas of higher conductivity. Table I2 gives the definitions

of the IAs in the Wiese and Parkinson conventions.

Figure I1 shows an example. The conductivity contrast associated

with a fault zone can be either due to a juxtaposition of different lithol-

ogies (upper panel of Figure I1) or the damaged rocks within a fault

zone can become conductive to form a conductive channel (bottom

panel of Figure I1). If the conductivity contrast is assumed to extend

indefinitely, both cases resemble a two-dimensional (2D) problem.

Table I2 The definition of induction arrows in Parkinson and

Wiese conventions

Real arrow Imaginary arrow

Convention Length Angle Length Angle

Parkinson

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

þ T

arctan

T



ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

þ T

arctan



Wiese arctan



412 INDUCTION ARROWS

The expected behavior for the real IA is indicated on the left-hand side

of the figure. In 2D, the real and imaginary IAs point parallel or anti-

parallel to each other, and perpendicular to the strike of the structure.

The largest real IAs are observed close to a conductivity contrast, they

become smaller with increasing distance from that boundary. A larger

conductivity contrast will also cause a longer arrow. Although vertical

magnetic field response functions do not contain direct information about

the underlying conductivity structure, they are extremely valuable in

detecting the lateral extension and the strike of conductivity anomalies.

In the absence of lateral resistivity gradients IAs vanish. Real and

imaginary IAs pointing obliquely indicate the influence of off-profile

features of a more complicated three-dimensional Earth. The observed

IAs on the right-hand side of Figure I1 show this influence to some

extend but overall, they are still in good agreement with the simple

2D scenarios on the left. If IAs show great variation, both between

sites and between real and imaginary arrows then a simple interpreta-

tion in terms of geoelectric strike direction is not possible.

Many scientists, including the author, prefer the term induction vec-

tor over IA because we construct and treat IAs like vectors, i.e., their

length and the direction have a physical meaning. They are however,

not vectors in a strict mathematical sense. IAs caused by a superposi-

tion of two different lateral conductivity contrasts which are linked by

inductive coupling will generally not be the same as the vector

constructed by adding the individual IAs. Furthermore, IAs are very

sensitive to electrical anisotropy (q.v.) (Pek and Verner, 1997).

Oliver Ritter

Bibliography

Hobbs, B.A., 1992. Terminology and symbols for use in studies of

electromagnetic induction in the Earth. Surveys of Geophysics,

13: 489–515.

Parkinson, W., 1962. The influence of continents and oceans on geo-

magnetic variations. Geophysical Journal, 2: 441–449.

Pek, J., and Verner, T., 1997. Finite-difference modelling of magneto-

telluric fields in two-dimensional anisotropic media. Geophysical

Journal International, 132: 535–548.

Ritter, O., Hoffmann-Rothe, A., Bedrosian, P.A., Weckmann, U., and

Haak, V., 2005. Electrical conductivity images of active and fossil

fault zones. In Bruhn, D., and Burlini, L., (eds.), High-Strain

Zones: Structure and Physical Properties, Vol. 245. London: Geo-

logical Society of London Special Publications, pp. 165–186.

Schmucker, U., 1959. Erdmagnetische Tiefensondierung in Deutsch-

land 1957/59. Magnetogramme und erste Auswertung. Abh. Akad.

Wiss.Götingen. Math.-Phys. Klasse: Beiträge zum Int. geophys.

Jahr 5.

Wiese, H., 1962. Geomagnetische Tiefentellurik Teil II: die Streichrich-

tung der Untergrundstrukturen des elektrischen Widerstandes,

erschlossen aus geomagnetischen Variationen. Geofisica Pura e

Applicata, 52:83–103.

Cross-references

Anisotropy, Electrical

Geomagnetic Deep Sounding

Natural Sources for EM Induction Studies

Observatories in Germany

Parkinson, Wilfred Dudley (1919–2001)

Transfer Functions

INDUCTION FROM SATELLITE DATA

In addition to sources of internal origin, magnetic satellites record the

variations in Earth’s external magnetic field caused by interaction of

the ionosphere and magnetosphere with the solar wind and radiation,

along with the secondary magnetic fields induced in Earth. The ratio

of the internal to external field may be used to probe the electrical

conductivity structure of the planet. Satellite induction studies date

from Didwall ’s (1984) early work with the POGO satellite data. Olsen

(1999a) and Constable and Constable (2004a) provide reviews of

satellite induction methods. Table I3 presents a list of past, present,

and future magnetic satellite missions that are relevant to induction

studies (see MAGSAT, Ørsted, POGO).

Figure I1 Expected and observed behavior of induction arrows (IA) for two different fault structures. In Wiese convention real (black)

arrows point away from good conductors; imaginary (gray) arrows are parallel or antiparallel to the real arrows, given 2D Earth

structure. Across a conductivity contrast (top panel) real IAs point away from the more conductive side and are largest over the less

conductive side. Measurements from the Dead Sea Transform, locally known as the Arava Fault, are representative of this type of fault

structure. A conductive fault zone sandwiched between more resistive units is characterized by IAs pointing away from the fault on

both sides and small IAs over the fault zone conductor. The West Fault in Chile is representative of this type of fault structure.

(Figure after Ritter et al., 2005.)

INDUCTION FROM SATELLITE DATA 413

Longer period EM variations penetrate deeper into Earth, because

EM fields decay exponentially with a characteristic length given by

the skin depth, or

 500

ﬃﬃﬃﬃﬃﬃﬃﬃﬃ

T=s

where s is electrical conductivity (S m

1

) and T is the period of the

field variations (s). Traditionally, studies of deep Earth conductivity

have relied on either the magnetotelluric (MT) method (q.v.) or the

geomagnetic depth sounding (GDS) method (q.v.). For MT studies,

time series measurements of horizontal magnetic and electric fields

are transformed into frequency domain Earth impedance (see Transfer

functions for EM). In GDS, observatory records of three-component

magnetic fields (or data from portable arrays of instruments), along

with an assumption about the geometry of the inducing field, are trans-

formed into a similar impedance. MT studies have the advantage that

they are largely independent of the geometry of the external fields,

but because induced electric fields decay with increasing period, MT

studies are limited to periods of less than a few days. GDS studies,

on the other hand, have been extended out to the period of the 11-year

sunspot cycle, the longest wherein field variations are external to

Earth’s core.

The usual assumption about the geometry of the external field var-

iations is that it is dominated by the fundamental spherical harmonic

(q.v.) aligned with Earth’s internal dipole field called P

. This is based

both on observations of field geometry (e.g., Banks, 1969) and the

morphology of the equatorial ring current (q.v.), which is composed

mainly of oxygen ions circulating at a distance of 2–9 Earth radii

(a review of the ring current is given by Daglis et al., 1999). Within

the satellite orbit, the magnetic field B can be expressed as the gradient

of a scalar potential F

B ¼m

rF (Eq. 1)

is the magnetic permeability of space) where for P

geometry F is

described by a spherical harmonic representation in radial distance

from Earth’s center r, Earth radius a

, and geomagnetic colatitude y :

ðr; yÞ¼a

ðtÞ



þe

ðtÞ



()

ðcos yÞ: (Eq. 2)

In GDS studies, knowledge of the field geometry allows observatory

time series measurements of vertical and horizontal components of

the magnetic field to be separated into the internal ði

Þ and external

ðe

Þ coefficients, which may be Fourier transformed into the frequency

domain to derive a complex geomagnetic response function of period:

ðTÞ¼i

ðTÞ=e

ðTÞ: (Eq. 3)

Table I3 Satellite missions relevant to magnetic induction studies, as of July, 2005

Satellite Type Launch date Data to Inclination Altitude (km)

POGO 2 Scalar October 14, 1965 October 2, 1967 87.3



410–1510

POGO 4 Scalar July 28, 1967 January 19, 1969 86.0



410–910

POGO 6 Scalar June 5, 1969 April 26, 1971 82.0



400–1100

MAGSAT Vector October 30, 1979 May 6, 1980 96.8 352–561

Ørsted Vector February 23, 1999 Present 96.6



500–850

SAC-C Vector November 18, 2000 Present 98.2



702

CHAMP Vector July 15, 2000 Present 87.3



200–454

SWARM Three vector sats Proposed 2008 450–550

Figure I2 The equatorial ring current generates an external

magnetic field of uniform P

geometry (grey arrows). The external

field variations induce an internal field (black arrows) which is

also described by P

geometry but that decays with altitude. The

different altitude dependence and different directional behavior

with latitude allows a separation of the internal and external fields

using satellite measurements made during pole to pole passes.

Figure I3 Amplitude spectrum taken from 13 years of the hourly

Dst geomagnetic index. A broad peak in energy is seen around

the 27-day solar rotation period, and narrow peaks at periods of

1 day and harmonics. The daily variations are generated mainly in

the ionosphere, and are not P

geometry. Power at frequencies

lower than 10

7

Hz is probably dominated by secular variation

in the internal magnetic field.

414 INDUCTION FROM SATELLITE DATA

The more familiar MT apparent resistivity and phase can be derived

from the real and imaginary components of Q

ðTÞ, as can the induc-

tive scale length C-response (see transfer functions for EM).

Magnetic satellites, collecting either scalar (total field magnitude

only) or vector (three component) data, offer an opportunity to take

GDS induction studies beyond the global observatory network. There

are numerous advantages to using satellites for these types of studies:

1. Global coverage can be achieved using satellites, while the mag-

netic observatory network is sparse, nonuniform, and restricted to

land.

2. During each mission magnetic measurements are made using a

single, high-quality instrument having a single calibration and

which is removed from the distorting effects of crustal magnetic

anomalies. Satellite magnetic sensors include scalar proton preces-

sion magnetometers, which are often augmented by vector fluxgate

magnetometers oriented by star cameras (see Magnetometers).

3. Extensive spatial coverage means that the geometry of the inducing

magnetic fields can be estimated, instead of being assumed.

Point (3) is illustrated in Figure I2. As a satellite makes a pass

across the equator from pole to pole, the geometry of the magnetic

field variations is different for the internal and external components.

Variations in satellite altitude provide additional discrimination to fit

the separate geometries of the internal and external fields.

Induction is powered by variations in the ring current intensity

caused by interactions with the solar wind. During magnetic storms

(q.v.), these may amount to a few hundred nanoteslas. A proxy for ring

current intensity is provided by the Dst (disturbed storm time) mag-

netic index, a weighted average of horizontal fields at four low latitude

magnetic observatories. Ring current variations are observed at periods

of a few hours to many months or years, but are strongest at about

1 month because the solar wind is modulated by solar rotation.

Figure I3 shows an amplitude spectrum of the Dst index; power at

the daily harmonics is caused by contamination from the daily varia-

tion in the magnetic field, generated in the ionosphere and by the

Chapman-Ferraro current s outside the magnetosphere, and is more

complicated than simple P

geometry. Power at periods greater than

1 month is contaminated by secular variation of the main magnetic

field (q.v.), of internal origin and unsuitable for induction studies.

For GDS observatory studies, it is difficult to reject these contamina-

tions and these periods have to be avoided, but satellite data have some

power to reject non-P

geometries.

The above discussion ignores the contributions to the magnetic field

that come from the main (internal) field and the crustal field (q.v.).

These parts of the field must be removed before an induction analysis

can be carried out, and therein lies one of the great difficulties of satel-

lite induction. Without additional information, it is impossible to

Figure I5 Satellite responses from the MAGSAT (circles, from Constable and Constable, 2004b) and Ørsted (triangles, from Olsen

et al., 2003) missions, compared with Olsen’s (1999b) long period observatory response for Europe (squares). The real components

of C are positive, the imaginary are negative; error bars are one standard deviation.

Figure I4 Without additional information, it is impossible to

distinguish between temporal variations in the external magnetic

field and spatial variations in the internal magnetic field sampled

as the magnetic satellite flies though its orbit.

INDUCTION FROM SATELLITE DATA 415