Gubbins D., Herrero-Bervera E. Encyclopedia of Geomagnetism and Paleomagnetism
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Arthur D. Richmond
NCAR
High Altitude Observatory
POB 3000
Boulder, CO 80307-3000, USA
email: richmond@hao.ucar.edu
Oliver Ritter
GeoForschungsZentrum
Telegrafenberg A45
14473 Potsdam, Germany
email: oritter@gfz-potsdam.de
Andrew P. Roberts
National Oceanography Centre
School of Ocean and Earth Science
University of Southampton
Southampton, SO14 3ZH, UK
email: arob@noc.soton.ac.uk
arob@soc.soton.ac.uk
Paul H. Roberts
Institute of Geophysics and Planetary Physics
UCLA
405 Hilgard Avenue
Los Angeles, CA 90095, USA
email: roberts@math.ucla.edu
Michael G. Rochester
Dept of Earth Sciences
Memorial University of Newfoundland
St. John's, N.L., A1B 3X5, Canada
email: mrochest@mun.ca
Pierre Rochette
CNRS-Université d'Aix-Marseille 3
CEREGE BP80 Europole de l'Arbois
Aix en Provence Cedex 4, 13545, France
email: rochette@cerege.fr
Leonardo Sagnotti
Istituto Nazionale di Geofisica e Vulcanologia
Via di Vigna Murata 605
Roma, 00143, Italy
email: sagnotti@ingv.it
Graeme R. Sarson
School of Mathematics and Statistics
University of Newcastle
Newcastle upon Tyne, NE1 7RU, UK
email: g.r.sarson@ncl.ac.uk
Armin Schmidt
Department of Archaeological Sciences
University of Bradford
BD7 1DP, UK
email: A.Schmidt@Bradford.ac.uk
Jean-Jacques Schott
Ecole et Observatoire des Sciences de la Terre
5, rue Descartes
Strasbourg Cedex, 67084, France
email: jeanJacques.Schott@eost.u-strasbg.fr
Gerald Schubert
Department of Earth & Space Sciences
University of California
2707 Geology Building
Los Angeles, CA 90024-1567, USA
email: gschubert@geovax.ess.ucla.edu
schubert@ucla.edu
Adam Schultz
College of Oceanic and Atmospheric Sciences
Oregon State University
Corvallis, OR 97331-5503, USA
email: adam@coas.oregonstate.edu
Johannes Schweitzer
NORSAR
Instituttveien 25
POB 53
Kjeller, 2027, Norway
email: johannes.schweitzer@norsar.no
Gary R. Scott
Berkeley Geochronology Center
2455 Ridge Road
Berkeley, CA 95709, USA
email: gscott@bgc.org
John Shaw
Department of Earth Sciences
University of Liverpool
Oxford Street, P.O. Box 147
Liverpool, L69 3BX, UK
email: shaw@liverpool.ac.uk
Guoyin Shen
Center for Advanced Radiation Sources
University of Chicago
Chicago, IL 60439, USA
email: shen@cars.uchicago.edu
Manfred Siebert
Institute of Geophysics
University of Göttingen
Friedrich-Hund-Platz 1
37077 Göttingen, Germany
Brad S. Singer
Department of Geology and Geophysics
University of Wisconsin-Madison
1215 West Dayton Street
Madison, WI 53706, USA
email: bsinger@geology.wisc.edu
Alexei V. Smirnov
Department of Earth and Environmental Sciences
University of Rochester
Hutchison Hall 227
Rochester, NY 14627, USA
email: alexei@earth.rochester.edu
Xiaodong Song
Dept. of Geology
University of Illinois
1301 W. Green St. 245NHB
Urbana, IL 61801, USA
email: xsong@uiuc.edu
Annie Souriau
CNRS
Observatoire Midi-Pyrenees
14 Ave. Edouard Belin
Toulouse, 31400, France
email: annie.souriau@cnes.fr
Andrew Soward
School of Mathematical Sciences
University of Exeter
Exeter, EX4 4QE, UK
email: A.M.Soward@exeter.ac.uk
Frank D. Stacey
CSIRO Exploration and Mining
PO Box 883
Kenmore, Queensland 4069, Australia
email: Frank.Stacey@csiro.au
F. Richard Stephenson
Dept. of Physics
University of Durham
South Road
Durham, DH1 3LE, UK
email: frstephenson@durham.ac.uk
xxii CONTRIBUTORS
David J. Stevenson
CALTECH
Div Geology & Planetary Sci, 150-21
Pasadena, CA 91125, USA
email: djs@gps.caltech.edu
John A. Tarduno
Department of Earth and Environmental Sciences
University of Rochester
Hutchison Hall 227
Rochester, NY 14627, USA
email: john@earth.rochester.edu
john@volterra.earth.rochester.edu
Donald D. Tarling
Department of Geological Sciences
Plymouth Polytechnic
Drake Circus
Plymouth, Devon, PL4 8AA, UK
email: d.tarling@plymouth.ac.uk
Patrick T. Taylor
Laboratory for Planetary Geodynamics
NASA/Goddard Space Flight Center
Greenbelt, MD 20771, USA
email: patrick.taylor@nasa.gov
Z.S. Teweldemedhin (no address)
Michael J. Thompson
Dept. of Applied Mathematics
University of Sheffield
Sheffield, S3 7RH, UK
email: michael.thompson@sheffield.ac.uk
Alan W.P. Thomson
British Geological Survey
West Mains Road
Edinburgh, EH9 3LA, UK
email: a.thomson@bgs.ac.uk
Michael Thorne
Department of Geological Sciences
Arizona State University
Tempe, AZ 85287-1404, USA
Andreas Tilgner
Institute of Geophysics
University of Gottingen
Herzberger Landstr. 180
37075 Göttingen, Germany
email: andreas.tilgner@geo.physik.uni-goettingen.de
Maurice A. Tivey
Dept Geology & Geophysics
WHOI
360 Woods Hole Rd
Woods Hole, MA 02543-1542, USA
email: mtivey@whoi.edu
Steven M. Tobias
Department of Applied Mathematics
University of Leeds
Leeds, LS2 9JT, UK
email: s.m.tobias@leeds.ac.uk
Lester A. Tomlinson
Geoscience, Electronics & Data Services
30 Kirner St.
Christchurch, 8009, New Zealand
email: geoserve@xtra.co.nz
Miquel Torta
Observatori de l'Ebre
Roquetes (Tarragona), 43520, Spain
email: ebre.jmtorta@readysoft.es
John B. Townshend
USGS
Box 25046 MS 966
Golden, CO 80225, USA
Oleg Troshichev
Arctic and Antarctic Research Institute
38 Bering St.
St. Petersburg, 199397, RUSSIA
email: olegtro@aari.nw.ru
Bruce T. Tsurutani
Jet Propulsion Laboratory
California Institute of Technology
4800 Oak Grove Drive
Pasadena, CA 91009, USA
email: BTSURUTANI@jplsp.jpl.nasa.gov
Agustín Udías
Facultad de Ciencias Físicas
Departamento de Geofísica
Universidad Complutense
Ciudad Universitaria
Madrid, 28040, Spain
email: audiasva@fis.ucm.es
Martyn Unsworth
University of Alberta
Edmonton, Alberta, T6G 2J1, Canada
email: unsworth@phys.ualberta.ca
Jaime Urrutia-Fucugauchi
Instituto de Geofisica, Laboratorio de Paleomagnetismo y
Paleoambientes
Universidad Nacional Autonoma de Mexico
Mexico D.F., 04510, Mexico
email: juf@geofisica.unam.mx
Jean-Pierre Valet
Institut de Physique du Globe de Paris
4 place Jussieu
Paris Cedex 05, 75252, France
email: valet@ipgp.jussieu.fr
Lidunka Vočadlo
Dept. Earth Sciences
University College London
Gower St.
London, WC1E 6BT, UK
email: l.vocadlo@ucl.ac.uk
Ingo Wardinski
GeoForschungsZentrum Potsdam
Sektion 2.3 Geomagnetische Felder
Telegrafenberg
14473 Potsdam, Germany
email: ingo@gfz-potsdam.de
Deanis Weaire
Department of Physics
Trinity College
College Green
Dublin 2, Ireland
email: dweaire@tcd.ie
Peter D. Weiler
Baseline Environmental Consulting
5900 Hollis Street
Emeryville, CA 94608, USA
email: peter.weiler@lfr.com
Kathryn A. Whaler
Grant Institute of Earth Science
The University of Edinburgh
West Mains Road
Edinburgh, EH9 3JW, UK
email: kathy.whaler@ed.ac.uk
Quentin Williams
Earth Sciences
UCSC
Santa Cruz, CA 95064, USA
email: qwilliams@es.ucsc.edu
CONTRIBUTORS xxiii
Wyn Williams
Department of Geology & Geophysics
University of Edinburgh
West Mains Road
Edinburgh, EH9 3JW, UK
email: wyn.williams@ed.ac.uk
Ashley P. Willis
Dept of Mathematics
University of Bristol
Bristol, BS8 1TW, UK
email: a.willis@bristol.ac.uk
Denis Winch
School of Mathematics & Statistics F07
University of Sydney
Sydney, NSW 2006, Australia
email: winch-d@maths.su.oz.au
denisw@maths.usyd.edu.au
Dongmei Yang
Institute of Geophysics
China Earthquake Administration, No. 5
Minzudaxuenanlu
Haidan District, Beijing, 100081, China
email: ydmgeomag@263.net
Keke Zhang
Department of Mathematical Sciences
University of Exeter
Exeter, EX4 4QE, UK
email: kzhang@ex.ac.uk
Xixi Zhao
Institute of Geophysics and Planetary Physics
University of California Santa Cruz
1156 High Street
Santa Cruz, CA 95064, USA
email: xzhao@emerald.ucsc.edu
xzhao@es.ucsc.edu
xxiv CONTRIBUTORS
Preface
Geomagnetism is the study of the earth's magnetic field: its
measurement, variation in time and space, origins, and its use in
helping us to understand more about our Earth. Paleomagnetism is the
study of the record left in the rocks; it has contributed much to our
understanding of the geomagnetic field's past behavior and many other
aspects of geology and earth history. Both have applications, pure and
applied: in navigation, in the search for minerals and hydrocarbons, in
dating rock sequences, and in unraveling past geologic movements
such as plate motions. The entire subject is a small subdiscipline of
earth science, and our goal has been to cover it in fine detail at a level
accessible to anyone with a general scientific education. We envisage
the encyclopedia to be of greatest use to those starting in the subject
and those needing to know something of the field for their own
application, but the topic is broad and demanding—as we have become
increasingly aware while editing the huge variety of contributions—
and we also expect it to be of use to experts in geomagnetism or
paleomagnetism who need to stray outside their own area of expertise,
for nobody is an expert in the whole field.
The scope of the encyclopedia is defined by the “GP” section of the
American Geophysical Union: the magnetic field of internal origin.
Over 25% of the membership of GP has contributed to this book.
External sources of magnetic field are included insofar as they are used
in solid earth geomagnetism—for example periodic external fields,
because they induce electric currents in the earth that are useful in
mapping deep electrically conducting regions—and articles are
included on the ionosphere, magnetosphere, Sun, and planets. External
geomagnetism as such is a separate discipline in most research
establishments as well as the AGU, and is therefore not treated.
Geomagnetism is the oldest earth science, having its origins in
simple human curiosity in the lodestone's ability to point north. It
claims what most believe to be the first scientific treatise, William
Gillbert's (q.v.) De Magnete published in 1601, the claim being
founded on its use of deduction from experimental measurement.
These innocent beginnings were soon to give way to the intensely
practical business of finding one's way at sea, and during the European
age of discovery understanding the geomagnetic field and using it for
navigation became a burning challenge for early scientists. A century
after the publication of De Magnete saw Edmond Halley (q.v.)in
charge of a Royal Navy vessel making measurements throughout
the Atlantic Ocean. Halley's plans to fix position more accurately by
using the departures of magnetic north from geographic north were
dashed by the geomagnetic field's rapid changes in time, and the
longitude problem was of course finally solved by Harrison and his
accurate clock, but the compass remains an essential aid to navigation
to this day.
Almost a century after Halley's voyages James Cook was making
even more accurate measurements throughout the oceans, and in the
19th century, Alexander von Humboldt (q.v.) and Carl Friedrich Gauss
(q.v.) set up a network of magnetic observatories, the first example of
international cooperation in a scientific endeavor. The data compilation
continued throughout the 19th century, with typical Victorian tenacity,
led by Edward Sabine (q.v.), and detailed magnetic measurements were
made by James Clark Ross’ expedition to the poles and the voyage of
HMS Challenger. Impressive though these data collections were, with
hindsight they yielded rather little in the way of pure scientific
discovery or useful application. True, Sabine was to identify the source
of magnetic storms with activity on the Sun and they left us a
wonderful record of the geomagnetic field in the 19th century, laying
the foundation for modern surveying, but the real prize of discovering
the geomagnetic field's origin eluded them.
Developments in the early 20th century were to catapult geomagnet-
ism into the limelight yet again, this time in the quest for minerals. Metal
ores, base and noble, are concentrated in rocks rich in magnetites that
are intensely magnetic. Geomagnetism provided a cheap and simple
prospecting tool for exploration, and magnetic surveys proliferated
on land as never befor e. Geo ma gnetism provides the cheapest
geophysical exploration tool, and while it may lack the precision of
seismic methods it continues to produce economic returns—a year's
profit from one of the larger mines would probably pay for all the
mapping in the last century. The discovery of electromagnetic induction
provided yet another technique for exploring the earth's interior and
even more significantly it changed prevailing views on the origin of
geomagnetic fluctuations and the earth's main dipole field. The many
theories for the origin proposed around the turn of the 20th century are
reviewed here by David Stevenson (see Nondynamo theories). The only
one to survive the test of time was
Joseph Larmor's (q.v.) self-exciting
dynamo theory, but even this was to suffer a half-century setback
from Thomas Cowling's (q.v.) proof that no dynamo could sustain a
magnetic field with symmetry about an axis, which the earth's dipole
has to a good approximation.
Spectacular progress was being made at about this time by French
physicists such as Bernard Brunhes and Motonori Matuyama (q.v.)
from Japan trying to understand the magnetic properties of rocks. In
founding the science of paleomagnetism they discovered they were
able to determine the direction of the earth's magnetic field at the time
of the rock's formation, and made the astonishing discovery that the
magnetic field had reversed direction in the past. This discovery, like
the dynamo theory, suffered a setback when, in the late 1950s, Seiya
Uyeda and Takesi Nagata from Japan found that some minerals reverse
spontaneously: this providing an alternative but rather mundane
explanation that appealed to some in a skeptical scientific community.
Evidence for polarity reversals mounted, thanks in great part to the
efforts of Keith Runcorn (q.v.) and colleagues in England, but it
required precise radiometric dating and access to a suite of rocks
younger than 5 million years to establish a complete chronology and
put the question beyond any doubt: this was finally achieved by Allan
Cox (q.v.) and colleagues in the USA in 1960, on the eve of the plate
tectonic revolution.
It is hard to comprehend the rapidity of scientific developments
in earth science in the 1960s and impossible to underestimate the
importance of the role played by paleomagnetism and geomagnetism
in the development of plate tectonics. The establishment of polarity
reversals came together with H. Hess’ ideas on seafloor spreading and
the discovery of magnetic stripes on the ocean floor to provide a means
to map the age of the oceans (see Vine-Matthews-Morley hypothesis)
and confirm once and for all Wegener's ancient ideas of continental
drift. Even today, almost all our quantitative knowledge of plate
movements in the geological past comes from paleomagnetism and
geomagnetism and the development of a reversal timescale (q.v. see
also Bill Lowrie's article Geomagnetic polarity timescales). 1958 saw
at last the removal of Cowling's objection to the dynamo theory
(see Dynamo, Backus and Dynamo, Herzenberg) and work done in
Eastern Europe and the former Soviet Union provided the mathema-
tical foundation and physical insight needed to understand how
the geomagnetic field could be generated in the earth's liquid iron
core (see Dynamos, mean-field and Dynamo, Braginsky). Improve-
ments in instrumentation accelerated magnetic surveys: electromag-
netic surveys became routine, proton magnetometers could be towed
behind ships, and Sputnik ushered in the satellite era with a
magnetometer on board.
So where does geomagnetism and paleomagnetism stand now? The
dynamo theory of the origin of the main field still presents one of the
most difficult challenges to classical physics, but computers are now
fast enough to solve the equations of magnetohydrodynamics (q.v., see
also Geodynamo, numerical simulations) in sufficient complexity to
reproduce many of the observed phenomena; we have just entered a
decade of magnetic observation with two satellites operational at the
time of writing and two more launches planned in the near future; there
are more aircraft devoted to industrial magnetic surveying than ever
before; electromagnetic methods have found application in the search
for hydrocarbon reserves and have moved into the marine environment
(see EM, marine controlled source). Paleomagnetists have begun to
map details of the magnetic field during polarity transition (see
Geomagnetic polarity reversals), discover many examples of excur-
sions (aborted reversals), are mapping systematic departures from the
simple dipole structure, and have automated laboratory techniques to
the point where, in a single day, they can make more measurements of
the absolute paleointensity of magnetic materials such as ceramics and
basaltic rocks than pioneer Emile Thellier (q.v.) could do in a lifetime
(see articles on Absolute paleointensity).
The subject divides naturally into the studies of magnetic fields with
different origins—indeed these differences often make it difficult even
for experts to understand other branches of their own subject! Those
studying the permanent magnetization of the earth's crustal rocks deal
with magnetic fields that owe their origin to permanent magnetism at
the molecular or crystal grain level; those in electromagnetic induction
study magnetic fields caused by electric currents induced in solid rocks
deep inside the Earth; while dynamo theorists deal with induction by a
fluid, and have to deal with the additional complexity of advection by a
moving conductor. Paleomagnetism naturally separates into studies of
the magnetism of rocks, or rock magnetism (q.v.), laboratory methods
for determining the ancient field, and the history of the ancient field
itself. This classification dictated our choice of topics. Special effort
has been made to represent the activities of the global network of
permanent magnetic observatories. These rarely feature in scientific
papers and most practicing scientists are unaware of the meticulous
nature of the work and the dedication of those unsung heroes charged
with maintaining standards over decades—a persistence rarely
experienced in modern science. The observatory section represents,
to our knowledge, the first attempt to draw together into one place this
rather loosely connected international endeavor.
Our subject relates to many other disciplines, either because the
geomagnetic field is a vital part of our environment and provides a
surprising range of useful techniques to others, from stratigraphy
through navigation to radio communication. Partly because of this, and
partly in an effort to provide a self-contained volume, we have strayed
outside the strict remit of GP. We have included articles on earth
structure, particularly those esoteric regions (see for example articles
on D”) important for geomagnetism, and have covered the fascinating
magnetic fields of other planets and satellites.
Our main thanks must go to our contributors, who have so willingly
and energetically contributed to make this a truly community effort: we
have received very few refusals to our requests to contribute. Alan
Jones and Kathryn Whaler advised on electromagnetic induction, a
difficult subject for both editors. Thanks go to Stella Gubbins for her
unstinting work in organizing the geomagnetism articles and present-
ing them to the publishers in good order.
March 2007
David Gubbins and Emilio Herrero-Bervera
xxvi PREFACE
A
AEROMAGNETIC SURVEYING
Introduction
Magnetic surveying is one of the earliest geophysical methods ever
used, with a magnetic compass survey being used in Sweden in
1640 to detect magnetic iron ores. Once instruments were developed
in the 1880s to measure the magnitude of the Earth’s magnetic field,
magnetic surveys applied to mineral exploration became widespread
(Hanna, 1990). These early surveys, comprising magnetometer mea-
surements taken on or close to the Earth’s surface, were limited in
extent and only small areas could be covered in any great detail. With
the advent of an aircraft-mounted magnetometer system (Muffly,
1946), developed primarily for submarine detection during World
War II, the number and areal coverage of magnetic surveys expanded
rapidly. The first airborne magnetic or aeromagnetic survey for geolo-
gical purposes was flown in 1945 in Alaska by the U.S. Geological
Survey and the U.S. Navy. By the end of the 1940s, aeromagnetic
surveys were being flown worldwide.
Survey objectives
Aeromagnetic surveys are flown for a variety of reasons: geologic
mapping, mineral and oil exploration, and environmental and ground-
water investigations. Since variations in the measured magnetic field
reflect the distribution of magnetic minerals (mainly magnetite) in
the Earth’s crust and human-made objects, surveys can be used to
detect, locate, and characterize these magnetic sources. Most surveys
are flown to aid in surface geologic mapping, where the magnetic
effects of geologic bodies and structures can be detected even in areas
where rock outcrop is scarce or absent, and bedrock is covered by gla-
cial overburden, bodies of water, sand, or vegetation. Magnetic sur-
veys can also detect magnetic sources at great depth (tens of
kilometers) within the Earth ’s crust, being limited only by the depth
at which magnetic minerals reach their Curie point and cease to be fer-
rimagnetic. Broad correlations can be made between rock type and
magnetic properties, but the relationship is often complicated by tem-
perature, pressure, and chemical changes that rocks are exposed to
(Grant, 1985). Nevertheless, determining the location, shape, and atti-
tude of magnetic sources and combining this with available geologic
information can result in a meaningful geological interpretation of a
given area. Certain kinds of ore bodies may produce magnetic anoma-
lies that are desirable targets for mineral exploration surveys. Although
hydrocarbon reservoirs are not directly detectable by aeromagnetic
surveys, magnetic data can be used to locate geologic structures that
provide favorable conditions for oil/gas production and accumulation
(Gibson and Millegan, 1998). Similarly, mapping the magnetic signa-
tures of faults and fractures within water-bearing sedimentary rocks
provides valuable constraints on the geometry of aquifers and the
framework of groundwater systems.
Survey design
Aeromagnetic surveys are usually flown in a regular pattern of equally
spaced parallel lines (flightlines). A series of control or tie-lines is also
flown perpendicular to the flightline direction to assist in the proces-
sing of the magnetic field data set. The ratio of control to flightline
spacing generally ranges from 3 to 10 depending on the desired data
quality. Flightline spacing is dependent on the primary aim of the sur-
vey and governs the amount of detail in the measured magnetic field.
For reconnaissance mapping of large regions (e.g., states, countries),
where little or no knowledge of the magnetic field to be mapped is
available, typical line spacings are 1.5 km in Australia and 0.8 km in
Canada. Reconnaissance survey lines are usually oriented north-south
or east-west. For smaller areas with similar financial resources avail-
able, these spacings can be reduced (e.g., 0.2 km in Sweden and
Finland). For smaller regions, the line spacing is governed by the size
of the target (geological structure, oil prospect, ore body) being
investigated. For example, mineral exploration surveys generally have
spacings in the range 50–200 m and are flown perpendicular to the
dominant geologic strike direction, although directions no more than
45
o
from magnetic north are preferred because N-S wavelengths are
shorter than E-W wavelengths at low and intermediate latitudes. For
areas with distinct regions of differing geologic strike, costs may
permit splitting the survey into several flight directions or a single
compromise direction must be assigned.
The survey flying height is intimately related to flightline spacing
with lower heights being more appropriate for closer line spacings.
This is due to the rapid decrease in magnetic field intensity and
increase in wavelength as a function of the distance from a magnetic
source. Theoretical arguments suggest a line spacing to height ratio
of 2 or less is desirable to accurately sample variations in the magnetic
field (Reid, 1980). The majority of surveys, however, have ratios
higher than this, i.e., 2.5 to 8. The minimum flight height is limited
by government restrictions, safety considerations, and ruggedness of
the terrain. Topographic variations also affect the mode of flying used
in a survey. For geologic mapping and mineral exploration surveys,
measurements are desirable at levels as close to the magnetic sources
as possible, hence surveys are flown at a constant height (mean terrain
clearance) above the ground surface. Prior to the availability of
real-time global positioning system (GPS) navigation, surveys over
mountainous regions were flown at a constant altitude. Postsurvey pro-
cessing of the collected magnetic field data could then be applied to
artificially “drape” the measurements onto a surface at some specified
mean terrain clearance. This can improve the resolution of magnetic
anomalies that is degraded by flying at the higher constant altitude.
However, current usage of more accurate navigational systems (GPS)
now permits fixed-wing surveys to be flown along a preplanned artifi-
cial drape surface in regions of rugged topography. The drape sur-
face is set to a constant height above ground level but is modified to
take into consideration the climb and descent rate of the survey air-
craft. Helicopters can also offer an alternative (usually costlier) to
fixed-wing aircraft in mountainous areas.
Survey data acquisition
Along with measurements of the magnetic field, information relating
to the accurate location and time of these recorded values is gathered.
A modern data acquisition system (usually computer-based) records
and archives magnetic, navigational, temporal, altitude, and perhaps
aircraft attitude data. In addition, video recordings of the flight-path
of the aircraft are made that may be used later to identify magnetic
effects of human-made sources and to provide checks on navigation.
Accurate synchronization of all the data streams is crucial for subse-
quent processing of the raw magnetometer data. Magnetometer mea-
suring rates of 10 samples per second and navigational information
at one sample per second are current norms.
Magnetometers
Compared to the first magnetometers used in the 1940s, the resolution
and accuracy of magnetic field measurements have increased signifi-
cantly. The early fluxgate magnetometers had resolutions of about
1 nT and noise envelopes of 2 nT (Horsfall, 1997). These instruments
only produced relative measurements of the field and suffered from
appreciable drift, possibly 10 nT/hr. Proton precession magnetometers
followed with a resolution of 0.1 nT and noise envelope of 1 nT. These
instruments measured the magnetic field intensity and had minimal
drift. These have been superseded by the optically pumped, generally
caesium-vapor magnetometers which have a resolution of 0.001 nT
and a noise envelope of 0.005 nT. Such levels of measurement accu-
racy are not met in practice since errors arise through unremoved
aircraft magnetic effects, navigation effects, and postsurvey data pro-
cessing. Standard sampling rates of 10 samples per second coupled
with aircraft speeds of 220–280 km/hr result in measurements at an
interval of 6–8 meters.
Single magnetometer aircraft configurations simply produce mea-
surements of the magnetic field intensity in the direction of the Earth’s
magnetic field. By adding extra sensors, various other quantities can
be measured. Two vertically separated sensors can provide vertical
magnetic gradient information while two wing-tip sensors allow mea-
surement of the transverse horizontal magnetic gradient. Vertical gradi-
ent measurements have the advantage in effectively suppressing longer
wavelength magnetic anomalies and providing a higher resolution
definition of shorter wavelength features. This is crucial in surveys
flown for mapping of near-surface geology where the longer wave-
length effects of deep sources are of secondary interest. In theory,
having two sensors also implies that a simple subtraction of the two
measurements removes any temporal effects in the data. However, in
practical applications, temporal effects may still be present in the data.
Transverse (perpendicular to the flight path) gradient measurements
are not generally used as a final interpretation product but can be
exploited when the magnetic data are interpolated between the flight
lines to produce a regular grid of magnetic field values (Hogg, 1989).
Aircraft noise
Magnetic noise caused by the survey aircraft arises from permanent
and induced magnetization effects and from the flow of electrical
currents. The permanent magnetization of the aircraft results in a head-
ing error which is a function of the flightline direction. Induced mag-
netizations occur due to the motion of the aircraft in the Earth’s
magnetic field. These effects are partially reduced by mounting the
magnetometer as far away as possible from the source of the noise,
either on a boom mounted on the aircraft’s tail or in a towed “bird”
attached by a cable. Although the bird can be located several tens of
meters below the aircraft, this may introduce orientation and positional
errors if the sensor does not maintain a fixed location relative to the
aircraft. For magnetometers mounted on the aircraft, a technique called
compensation is needed to reduce remaining magnetic noise effects to
an acceptable level. Modern aircraft are compensated by establishing
and modeling the magnetic response of the aircraft to changes in its
orientation. This is usually done prior to surveying by flying lines in
each of the four local survey directions in an area of low magnetic
field gradient and at high altitude, while carrying out several roll,
pitch, and yaw maneuvers. The compensation may be done digitally
in real time through the data acquisition system, or later as part of data
processing. Information on the aircraft’s orientation and direction is
used to predict the resultant magnetic effect, which is then removed
as the survey is flown, or later. The figure of merit, consisting of the
sum of the absolute values of the magnetic effects of the roll, pitch,
and yaw maneuvers for each of the four headings (12 values in all),
can be as low as one nanotesla. Once a survey is started, the aircraft’s
noise level should be assessed repeatedly to ensure that the same level
of data quality is maintained.
Positioning
No matter what accuracies are achieved in the magnetic field measure-
ments, the value of the final survey data is dependent on accurate loca-
tion of the measurement points. Traditional methods of navigation
relied heavily on visual tracking using aerial photographs. The actual
location of the flight path would be recovered manually by comparing
these photographs with images from onboard video cameras. Synchro-
nizing the data recording with the cameras would allow positioning of
the magnetic field data. Electronic navigation systems were also used
either to interpolate between visually located points or provide posi-
tioning information for offshore surveys. Positional errors of the order
of hundreds of meters would not be unexpected. These techniques
have been superseded by the introduction in the 1990s of GPS.
Navigation using GPS relies on the information sent from an array
of satellites whose locations are known precisely. Signals from a num-
ber of satellites are used to triangulate the position of the receiver in
the aircraft so that its position is known for navigational purposes
and to locate the magnetic field measurements. GPS systems also pro-
vide highly accurate time information that forms the basis for synchro-
nizing each component of the data acquisition system. Positional
accuracies of 5 m horizontally and 10 m vertically can be achieved
with a single GPS receiver. These values can be improved upon by
using another receiver and refining positions by making differential
corrections. The added receiver is set up at the survey base and simul-
taneously collects data from the satellites as the survey is flown. Post-
survey processing of all the positional data reduces errors in
information provided by the satellites and accuracies of 2–4 m can
be achieved. Current surveys generally use real-time differential GPS
navigation where the raw positional information is corrected as the
data is being collected. The GPS location and altitude are also used
to calculate (and subtract) the expected normal field for the location,
as predicted by the International Geomagnetic Reference Field (IGRF).
This generally removes an unhelpful regional component arising from
the Earth’s core field.
Temporal effects
Since the Earth’s magnetic field varies temporally as well as spatially,
time variations that occur over the period of surveying must be deter-
mined and removed from the raw measurements. The dominant effect
2 AEROMAGNETIC SURVEYING
for airborne surveys is the diurnal variation, which generally has an
amplitude of tens of nanotesla. Shorter time-period variations due to
magnetic storms can be much larger (hundreds of nanotesla) and
severe enough to prevent survey data collection. Data can also be
degraded my micropulsations with short periods and amplitudes of
several nanotesla. Monitoring of the Earth’s field is an essential com-
ponent of a survey in order to mitigate these time-varying effects. One
or more base station magnetometers is used to track changes in the
field during survey operations. When variations are unacceptably
large, surveying is suspended and any flightlines recording during dis-
turbed periods are reflown. The smoothly changing diurnal variation
is removed from the data using tie-line leveling. Simply subtracting
this variation from the measured data is not sufficient since diurnal
changes may vary significantly over the survey area. Nonetheless,
the recorded diurnal can be used as a guide in the leveling process.
Tie-line leveling is based on the differences in the measured field at the
intersection of flightlines and tie-lines. If the distance and hence the
time taken to fly between these intersection points is small enough
then it can be assumed that the diurnal varies approximately linearly
and can be corrected for (Luyendyk, 1997).
Data display and interpretation
The final product resulting from an aeromagnetic survey is a set of
leveled flightline data that are interpolated onto a regular grid of mag-
netic field intensity values covering the survey region. These values
can be displayed in a variety of ways, the most common being a color
map or image, where the magnetic field values, based on their magni-
tude, are assigned a specific color. Similarly, the values can be repre-
sented as a simple line contour map. Both kinds of representation
can be used in a qualitative fashion to divide the survey area into sub-
regions of high and low magnetizations. Since the data are available
digitally, it is straightforward to use computer-based algorithms to
modify and enhance the magnetic field image for the specific purpose
of the survey. Transformation and filtering allows certain attributes of
the data to be enhanced, such as the effects due to magnetic sources
at shallow or deep levels, or occurring along a specified strike direc-
tion. More sophisticated methods may estimate the depths, locations,
attitudes, and the magnetic properties of magnetic sources.
Mark Pilkington
Bibliography
Gibson, R.I., and Millegan, P.S. (eds.), 1998. Geologic Applications of
Gravity and Magnetics: Case Histories. Tulsa, OK, U.S.A.: Society
of Exploration Geophysicists and American Association of Petro-
leum Geologists.
Grant, F.S., 1985. Aeromagnetics, geology and ore environments,
I. Magnetite in igneous, sedimentary and metamorphic rocks: An
overview. Geoexploration, 23: 303–333.
Hanna, W.F., 1990. Some historical notes on early magnetic surveying
in the U.S. Geological Survey. In Hanna, W.F., (ed.), Geologic
Applications of Modern Aeromagnetic Surveys. United States Geo-
logical Survey Bulletin 1924, pp. 63–73.
Hogg, R.L.S., 1989. Recent advances in high sensitivity and high reso-
lution aeromagnetics. In Garland, G.D. (ed.), Proceedings of
Exploration ’87, Third Decennial International Conference on
Geophysical and Geochemical Exploration for Minerals and
Groundwater. Ontario Geological Survey, Special Volume 3, pp.
153–169.
Horsfall, K.R., 1997. Airborne magnetic and gamma-ray data acquisi-
tion. Australian Geological Survey Organization Journal of Aus-
tralian Geology and Geophysics, 17:23–30.
Luyendyk, A.P.J., 1997. Processing of airborne magnetic data. Austra-
lian Geological Survey Organization Journal of Australian Geol-
ogy and Geophysics, 17:31–38.
Muffly, G., 1946. The airborne magnetometer. Geophysics, 11:321–334.
Reid, A.B., 1980. Aeromagnetic surveydesign.Geophysics,45:973–976.
Cross-references
Compass
Crustal Magnetic Field
Depth to Curie Temperature
IGRF, International Geomagnetic Reference Field
Magnetic Anomalies for Geology and Resources
Magnetic Anomalies, Modeling
AGRICOLA, GEORGIUS (1494–1555)
Agricola, which seems to have been the classical academic pen-name
for Georg Bauer, was born at Glauchau, Germany, on March 24, 1494
as the son of a dyer and draper. He studied at Leipzig University and
trained as a doctor, and became Town Physician to the Saxon mining
community of Chemnitz. His significance derives from his great treatise
on metal mining, De Re Metallica (1556), or “On Things of Metal.” This
sumptuously illustrated work was a masterly study of all aspects of
mining, including geology, stratigraphy, pictures of mineshafts, machin-
ery, smelting foundries, and even the diseases suffered by miners.
Book III of De Re Metallica contains a description and details of
how to use the miner’s compass which, by 1556, seems to have been
a well-established technical aid to the industry. Agricola drew a parallel
between the miner’s and the mariner’s compass, saying that the direction
cards of both were divided into equidistant divisions in accordance with
a system of “winds.” Agricola’s compass is divided into four quadrants,
with each quadrant subdivided into six: 24 equidistant divisions around
the circle. And just as a mariner named the “quarters” of his compass
from the prevailing winds, such as “Septentrio” for north and “Auster”
for south, so the miner likewise named his underground metal veins,
depending on the directions in which they ran.
Agricola also tells us that when prospecting for ore, a mining engi-
neer would use his compass to detect the veins of metal underground
and use it to plot their direction and the likely location of their strata
across the landscape.
Agricola, it was said, always enjoyed robust health and vigor. He
served as Burgomaster of Chemnitz on several occasions and worked
tirelessly for the sick during the Bubonic Plague epidemic that ravaged
Saxony during 1552–1553. Then, on November 21, 1555, he suddenly
died from a “four days” fever.
Allan Chapman
Bibliography
Agricola, G., De Re Metallica (Basilae, 1556), translated by Hoover,
H.C., and Hoover, L.H. (1912; Dover Edition, New York, 1950).
ALFVE
´
N WAVES
Introduction and historical details
Alfvén waves are transverse magnetic tension waves that travel along
magnetic field lines and can be excited in any electrically conducting
fluid permeated by a magnetic field. Hannes Alfvén (q.v.) deduced their
existence from the equations of electromagnetism and hydrodynamics
(Alfvén, 1942). Experimental confirmation of his prediction was found
seven years later in studies of waves in liquid mercury (Lundquist,
1949). Alfvén waves are now known to be an important mechanism
AGRICOLA, GEORGIUS (1494–1555) 3
for transporting energy and momentum in many geophysical and astro-
physical hydromagnetic systems. They have been observed in Earth’s
magnetosphere (Voigt, 2002), in interplanetary plasmas (Tsurutani and
Ho, 1999), and in the solar photosphere (Nakariakov et al., 1999).
The ubiquitous nature of Alfvén waves and their role in communicating
the effects of changes in electric currents and magnetic fields has
ensured that they remain the focus of increasingly detailed laboratory
investigations (Gekelman, 1999). In the context of geomagnetism, it
has been suggested that Alfvén waves could be a crucial aspect of the
dynamics of Earth’s liquid outer core and they have been proposed as
the origin of geomagnetic jerks (q.v.)(Bloxhamet al., 2002). In this ar-
ticle a description is given of the Alfvén wave mechanism, the Alfvén
wave equation is derived and the consequences of Alfvén waves for
geomagnetic observations are discussed. Alternative introductory per-
spectives on Alfvén waves can be found in the books by Alfvén and
Fälthammar (1963), Moffatt (1978), or Davidson (2001). More technical
details concerning Alfvén waves in Earth’scorecanbefoundinthe
review article of Jault (2003).
The Alfve
´
n wave mechanism
The restoring force responsible for Alfvén waves follows from two
simple physical principles:
1. Lenz’s law applied to conducting fluids: “Electrical currents induced
by the motion of a conducting fluid through a magnetic field give
rise to electromagnetic forces acting to oppose that fluid motion.”
2. Newton’s second law for fluids: “A force applied to a fluid will
result in a change in the momentum of the fluid proportional to
the magnitude of the force and in the same direction.”
The oscillation underlying Alfvén waves is best understood via a sim-
ple thought experiment (Davidson, 2001). Imagine a uniform magnetic
field permeating a perfectly conducting fluid, with a uniform flow
initially normal to the magnetic field lines. The fluid flow will distort
the magnetic field lines (see Alfvén’s theorem and the frozen flux approx-
imation) so they become curved as shown in Figure A1 (part (b)). The
curvature of magnetic field lines produces a magnetic (Lorentz) force
on the fluid, which opposes further curvature as predicted by Lenz’s
law. By Newton’s second law, the Lorentz force changes the momentum
of the fluid, pushing it (and consequently the magnetic field lines) in
an attempt to minimize field line distortion and restore the system toward
its equilibrium state. This restoring force provides the basis for trans-
verse oscillations of magnetic fields in conducting fluids and therefore
for Alfvén waves. As the curvature of the magnetic field lines increases,
so does the strength of the restoring force. Eventually the Lorentz
force becomes strong enough to reverse the direction of the fluid flow.
Magnetic field lines are pushed back to their undistorted configuration
and the Lorentz force associated with their curvature weakens until
the field lines become straight again. The sequence of flow causing field
line distortion and field line distortion exerting a force on the fluid
now repeats, but with the initial flow (a consequence of fluid inertia)
now in the opposite direction. In the absence of dissipation this cycle will
continue indefinitely. Figure A1 shows one complete cycle resulting
from the push and pull between inertial acceleration and acceleration
due to the Lorentz force.
Consideration of typical scales of physical quantities involved in
this inertial-magnetic (Alfvén) oscillation shows that the strength of
the magnetic field will determine the frequency of Alfvén waves.
Balancing inertial accelerations and accelerations caused by magnetic
field curvature, we find that U =T
A
¼ B
2
=L
A
rm where U is a typical
scale of the fluid velocity, T
A
is the time scale of the inertial-magnetic
(Alfvén) oscillation, L
A
is the length scale associated with the oscilla-
tion, B is the scale of the magnetic field strength, r is the fluid density,
and m is the magnetic permeability of the medium. For highly electri-
cally conducting fluids, magnetic field changes occur primarily through
advection (see Alfvén’s theorem and the frozen flux approximation)so
we have the additional constraint that B=T
A
¼ UB=L
A
or U ¼ L
A
=T
A
.
Consequently L
2
A
=T
2
A
¼ B
2
=rm or v
A
¼ B=ðrmÞ
1=2
.Thisisacharacteristic
velocity scale associated with Alfvén waves and is referred to as the
Alfvén velocity. The Alfvén velocity will be derived in a more rigorous
manner and its implications discussed further in the next section.
Physical intuition concerning Alfvén waves can be obtained through an
analogy between the response of a magnetic field line distorted by fluid
flow across it and the response of an elastic string when plucked. Both
rely on tension as a restoring force, elastic tension in the case of the string
and magnetic tension in the case of the magnetic field line and both result
in transverse waves propagating in directions perpendicular to their dis-
placement. When visualizing Alfvén waves it can be helpful to think of
a fluid being endowed with a pseudoelastic nature by the presence of a
magnetic field, and consequently supporting transverse waves. Nonuni-
form magnetic fields have similar consequences for Alfvén waves as non-
uniform elasticity of solids has for elastic shear waves.
The Alfve
´
n wave equation
To determine the properties of Alfvén waves in a quantitative manner,
we employ the classical technique of deriving a wave equation and
then proceed to find the relationship between frequency and wave-
length necessary for plane waves to be solutions. Consider a uniform,
steady, magnetic field B
0
in an infinite, homogeneous, incompressible,
electrically conducting fluid of density r, kinematic viscosity n, and
magnetic diffusivity ¼ 1=sm where s is the electrical conductivity.
Figure A1 The Alfve
´
n wave mechanism. In (a) an initial fluid velocity normal to the uniform field lines distorts them into the curved
lines shown in (b) giving rise to a Lorentz force which retards and eventually reverses the fluid velocity, returning the field lines to their
undisturbed position as shown in (c). The process of field line distortion is then reversed in (d) until the cycle is completed with the
return to the initial configuration in (e).
4 ALFVE
´
N WAVES
We imagine that the fluid is perturbed by an infinitesimally small
flow u inducing a perturbation magnetic field b. Ignoring terms that
are quadratic in small quantities, the equations describing Newton’s
second law for fluids and the evolution of the magnetic fields encom-
passing Lenz’s law are
]u
]t
|{z}
Inertial
acceleration
¼
1
r
rp
|fflfflffl{zfflfflffl}
Combined mechanical
and magnetic
pressure gradient
þ
1
rm
ðB
0
rÞb
|fflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflffl}
Lorentz acceleration
due to magnetic tension
þ nr
2
u
|fflffl{zfflffl}
Viscous
diffusion
;
(Eq. 1)
]b
]t
|{z}
Change in the
magnetic field
¼ðB
0
rÞu
|fflfflfflfflfflffl{zfflfflfflfflfflffl}
Stretching of magnetic
field by fluid motion
þ r
2
b
|fflffl{zfflffl}
Magnetic
diffusion
(Eq. 2)
Taking the curl ðrÞ of equation 1, we obtain an equation describing
how the fluid vorticity x ¼ru evolves
]x
]t
¼
1
rm
ðB
0
rÞðr bÞþnr
2
x: (Eq. 3)
r equation 2 gives
r
]b
]t
¼ðB
0
rÞx þ r
2
ðr bÞ: (Eq. 4)
To find the wave equation, we take a further time derivative of equa-
tion 3 so that
]
2
x
]t
2
¼
1
rm
ðB
0
rÞ r
]b
]t
þ n r
2
]x
]t
; (Eq. 5)
and then eliminate b using an expression for
1
rm
ðB
0
rÞðr ]b=]tÞ in
terms of x obtained by operating with
1
rm
ðB
0
rÞon (4) and substitut-
ing for
1
rm
ðB
0
rÞðr bÞ from equation 3 which gives
1
rm
ðB
0
rÞ r
]b
]t
¼
1
rm
ðB
0
rÞ
2
x nr
4
x þðn þÞr
2
]x
]t
;
(Eq. 6)
which when substituted into equation 5 leaves the Alfvén wave
equation
]
2
x
]t
2
¼
1
rm
ðB
0
rÞ
2
x nr
4
x þðn þ Þr
2
]x
]t
: (Eq. 7)
The first term on the right hand side is the restoring force which arises
from the stretching of magnetic field lines. The second term is the cor-
rection to the restoring force caused by the presence of viscous and
ohmic diffusion, while the final term expresses the dissipation of
energy from the system due to these finite diffusivities.
Dispersion relation and properties of Alfve
´
n waves
Substituting a simple plane wave solution of the form x ¼ Ref
^
xe
iðkrotÞ
g
where k ¼ k
x
^
x þ k
y
^
y þ k
z
^
z and r ¼ x
^
x þ y
^
y þ z
^
z into the Alfvén wave
equation 7, we find that valid solutions are possible provided that
o
2
¼
B
2
0
ðk
^
B
0
Þ
2
rm
nk
4
!
iðn þ Þk
2
o: (Eq. 8)
where
^
B
0
¼ B
0
=jB
0
j.
Equation 8 is the dispersion relation, which specifies the relation-
ship between the angular frequency o and the wavenumber k of
Alfvén waves. It is a complex quadratic equation in o, so we can
use the well known formula to find explicit solutions for o, which are
o ¼
iðn þ Þk
2
2
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
B
2
0
ðk
^
B
0
Þ
2
rm
ðn Þ
2
k
4
4
s
: (Eq. 9)
In an idealized medium with n ¼ ¼ 0 there is no dissipation and the
dispersion relation simplifies to
o ¼v
A
ðk
^
B
0
Þ; (Eq. 10)
where v
A
is the Alfvén velocity
v
A
¼
B
0
ðrmÞ
1=2
: (Eq. 11)
This derivation illustrates that the Alfvén velocity is the speed at which
an Alfvén wave propagates along magnetic field lines. Alfvén waves are
nondispersive because their angular frequency is independent of jkj and
the phase velocity and the group velocity (at which energy and informa-
tion are transported by the wave) are equal. Alfvén waves are however
anisotropic, with their properties dependent on the angle between the
applied magnetic field and the wave propagation direction.
An idea of Alfvén wave speeds in Earth ’s core can be obtained by
inserting into equation 11 the seismologically determined density of
the outer core fluid r ¼ 1 10
4
kg, the magnetic permeability for a
metal above its Curie temperature m ¼ 4p 10
7
T
2
mkg
1
s
2
and a
plausible value for the strength of the magnetic field in the core (which
we take to be the typical amplitude of the radial field strength observed
at the core surface B
0
¼ 5 10
4
T) giving an Alfvén velocity of
v
A
¼ 0:004 m s
1
or 140 km yr
1
. The time taken for such a wave to
travel a distance of order of the core radius is around 25 years.
It should also be noted that Alfvén waves in the magnetosphere (where
they also play an important role in dynamics) travel much faster because
the density of the electrically conducting is very much smaller.
Considering Alfvén waves in Earth’s core, Ohmic dissipation is
expected to dominate viscous dissipation but for large scale waves will
still be a small effect so that nk
2
k
2
v
2
A
. Given this assumption
the dispersion relation reduces to
o ¼
ik
2
2
v
A
ðk
^
B
0
Þ (Eq. 12)
and the wave solutions have the form of simple Alfvén waves, damped
on the Ohmic diffusion timescale of T
ohm
¼ 2=k
2
x ¼ Re
^
xe
iðkr v
A
ðk
^
B
0
ÞtÞe
t=T
ohm
no
(Eq. 13)
Smaller scale waves are rapidly damped out by Ohmic diffusion, while
large scale waves will be the longer lived, so we expect these to have
the most important impact on both dynamics of the core and the obser-
vable magnetic field.
Observations of Alfve
´
n waves and their relevance
to geomagnetism
The theory of Alfvén waves outlined above is attractive in its simpli-
city, but can we really expect such waves to be present in Earth’s core?
In the outer core, rotation will have a strong influence on the fluid
dynamics (see Proudmann-Taylor theorem). Alfvén waves cannot
exist when the Coriolis force plays an important role in the force balance;
in this case, more complex wave motions arise (see Magnetohydrody-
namic waves). In addition convection is occurring (see Core convection)
ALFVE
´
N WAVES 5