# Earth's magnetic field

Earth's magnetic field
Computer simulation of the Earth's field in a normal period between reversals.[1] The tubes represent magnetic field lines, blue when the field points towards the center and yellow when away. The rotation axis of the Earth is centered and vertical. The dense clusters of lines are within the Earth's core.[2]

Earth's magnetic field (also known as the geomagnetic field) is the magnetic field that extends from the Earth's inner core to where it meets the solar wind, a stream of energetic particles emanating from the Sun. It is approximately the field of a magnetic dipole tilted at an angle of 11 degrees with respect to the rotational axis—as if there were a bar magnet placed at that angle at the center of the Earth. However, unlike the field of a bar magnet, Earth's field changes over time because it is really generated by the motion of molten iron alloys in the Earth's outer core (the geodynamo). The Magnetic North Pole wanders, fortunately slowly enough that the compass is useful for navigation. At random intervals (averaging several hundred thousand years) the Earth's field reverses (the north and south geomagnetic poles change places with each other). These reversals leave a record in rocks that allow paleomagnetists to calculate past motions of continents and ocean floors as a result of plate tectonics. The region above the ionosphere, and extending several tens of thousands of kilometers into space, is called the magnetosphere. This region protects the Earth from harmful ultraviolet radiation.

## Importance

Humans have used compasses for direction finding since the 11th century A.D. and for navigation since the 12th century.[3]

The Earth is largely protected from the solar wind, a stream of energetic charged particles emanating from the Sun, by its magnetic field, which deflects most of the charged particles. These particles would strip away the ozone layer, which protects the Earth from harmful ultraviolet rays.[4] Calculations of the loss of carbon dioxide from the atmosphere of Mars, resulting from scavenging of ions by the solar wind, are consistent with a near-total loss of its atmosphere since the magnetic field of Mars turned off.[5]

The Earth's field is recorded in rocks. Reversals of the field have left a series of stripes on the seafloor that made it possible to time seafloor spreading, while the steadiness of the geomagnetic poles in between reversals allow paleomagnetists to track the motion of continents in the past.[6] Reversals also provide the basis for magnetostratigraphy, a way of dating rocks and sediments.[7] The field also magnetizes the crust; magnetic anomalies can be used to search for ores.[8]

## Main characteristics

### Dipolar approximation

The variation between magnetic north (Nm) and "true" north (Ng).

Near the surface of the Earth, its magnetic field can be closely approximated by the field of a magnetic dipole positioned at the center of the Earth and tilted at an angle of about 10° with respect to the rotational axis of the Earth. The dipole is roughly equivalent to a powerful bar magnet, with its south pole pointing towards the geomagnetic North Pole. This may seem surprising, but the north pole of a magnet is so defined because it is attracted towards the Earth's north pole. Since the north pole of a magnet attracts the south poles of other magnets and repels the north poles, it must be attracted to the south pole of Earth's magnet. The dipolar field accounts for 80–90% of the field in most locations.[9]

### Description

At any location, the Earth's magnetic field can be represented by a three-dimensional vector. Suppose a compass needle is suspended from a string so it can rotate in any direction. The direction it points in is the direction of the Earth's field, with the north pole of the compass pointing roughly north (more on that later). The intensity of the field is proportional to the force it exerts on the needle. The inclination or dip is the deviation from vertical. The declination or variation is the angle the needle would make with true north if it were constrained to lie in a horizontal plane (as in an ordinary compass). Another common representation is in X (North), Y (East) and Z (Down) coordinates.[9]

#### Intensity

Intensity of the Earth's magnetic field from the World Magnetic Model for 2010.

The intensity of the field is greatest near the poles and weaker near the Equator. It is generally reported in nanoteslas (nT) or gauss, with 1 gauss = 100,000 nT. It ranges from about 25,000–65,000 nT, or 0.25–0.65 gauss.[10][11] By comparison, a strong refrigerator magnet has a field of about 100 gauss.[12] As can be seen in the figure, the minimum occurs over South America while there are maxima over northern Canada, Siberia, and the coast of Antarctica south of Australia.

#### Inclination

Inclination of the Earth's magnetic field from the World Magnetic Model for 2010.

The inclination is given by an angle that can assume values between -90° (up) to 90° (down). In the northern hemisphere, the field points down. It is straight down at the North Magnetic Pole and rotates upwards as the latitude decreases until it is horizontal () at the magnetic equator. It continues to rotate upwards until it is straight up at the South Magnetic Pole. Inclination can be measured with a dip circle.

#### Declination

Declination of the Earth's magnetic field from the World Magnetic Model for 2010. Isogonic lines give the declination in signed degrees.

Declination is positive for an eastward deviation of the field relative to true north. It can be estimated by comparing the magnetic north/south heading on a compass with the direction of a celestial pole. Maps typically include information on the declination as an angle or a small diagram showing the relationship between magnetic north and true north. Information on declination for a region can be represented by a chart with isogonic lines (contour lines with each line representing a fixed declination).

### Magnetic poles

The movement of Earth's North Magnetic Pole across the Canadian arctic, 1831–2001.

The positions of the magnetic poles can be defined in at least two ways.[13]

Often, a magnetic (dip) pole is viewed as a point on the Earth's surface where the magnetic field is entirely vertical. Another way of saying this is that the inclination of the Earth's field is 90° at the North Magnetic Pole and -90° at the South Magnetic Pole. The two poles wander independently of each other and are not at directly opposite positions on the globe. They can migrate rapidly: movements of up to 40 km per year have been observed for the North Magnetic Pole.[14] The magnetic equator is the line where the inclination is zero (the magnetic field is horizontal).

If a line is drawn parallel to the moment of the best-fitting magnetic dipole, the two positions where it intersects the Earth's surface are called the North and South geomagnetic poles. If the Earth's magnetic field were perfectly dipolar, the geomagnetic and magnetic dip poles would coincide and compasses would point towards them. However, the Earth's field has a significant contribution from non-dipolar terms, so the poles do not coincide and compasses do not generally point at either.

## Magnetosphere

Simulation of the interaction between Earth's magnetic field and the interplanetary magnetic field. The magnetosphere is compressed on the day (Sun) side due to the force of the arriving particles, and extended on the night side.

Some of the charged particles from the solar wind are trapped in the Van Allen radiation belt. A smaller number of particles from the solar wind manage to travel, as though on an electromagnetic energy transmission line, to the Earth's upper atmosphere and ionosphere in the auroral zones. The only time the solar wind is observable on the Earth is when it is strong enough to produce phenomena such as the aurora and geomagnetic storms. Bright auroras strongly heat the ionosphere, causing its plasma to expand into the magnetosphere, increasing the size of the plasma geosphere, and causing escape of atmospheric matter into the solar wind. Geomagnetic storms result when the pressure of plasmas contained inside the magnetosphere is sufficiently large to inflate and thereby distort the geomagnetic field.

The solar wind is responsible for the overall shape of Earth's magnetosphere, and fluctuations in its speed, density, direction, and entrained magnetic field strongly affect Earth's local space environment. For example, the levels of ionizing radiation and radio interference can vary by factors of hundreds to thousands; and the shape and location of the magnetopause and bow shock wave upstream of it can change by several Earth radii, exposing geosynchronous satellites to the direct solar wind. These phenomena are collectively called space weather. The mechanism of atmospheric stripping is caused by gas being caught in bubbles of magnetic field, which are ripped off by solar winds.[15] Variations in the magnetic field strength have been correlated to rainfall variation within the tropics.[16]

## Time dependence

### Short-term variations

Background: a set of traces from magnetic observatories showing a magnetic storm in 2000.
Globe: map showing locations of observatories and contour lines giving horizontal magnetic intensity in μT.

The geomagnetic field changes on time scales from milliseconds to millions of years. Shorter time scales mostly arise from currents in the ionosphere and magnetosphere, and some changes can be traced to geomagnetic storms or daily variations in currents. Changes over time scales of a year or more mostly reflect changes in the Earth's interior, particularly the iron-rich core.[9]

Frequently, the Earth's magnetosphere is hit by solar flares causing geomagnetic storms, provoking displays of aurorae. The short-term instability of the magnetic field is measured with the K-index.

Data from THEMIS show that the magnetic field, which interacts with the solar wind, is reduced when the magnetic orientation is aligned between Sun and Earth - opposite to the previous hypothesis. During forthcoming solar storms, this could result in blackouts and disruptions in artificial satellites.[17]

### Secular variation

Estimated declination contours by year, 1590 to 1990 (click to see variation).

Changes in Earth's magnetic field on a time scale of a year or more are referred to as secular variation. Over hundreds of years, magnetic declination is observed to vary over tens of degrees.[9] A movie on the right shows how global declinations have changed over the last few centuries.[18]

The direction and intensity of the dipole change over time. Over the last two centuries the dipole strength has been decreasing at a rate of about 6.3% per century.[9] At this rate of decrease, the field would reach zero in about 1600 years.[19] However, this strength is about average for the last 7 thousand years, and the current rate of change is not unusual.[20]

A prominent feature in the non-dipolar part of the secular variation is a westward drift at a rate of about 0.2 degrees per year.[19] This drift is not the same everywhere and has varied over time. The globally averaged drift has been westward since about 1400 AD but eastward between about 1000 AD and 1400 AD.[21]

Changes that predate magnetic observatories are recorded in archaeological and geological materials. Such changes are referred to as paleomagnetic secular variation or paleosecular variation (PSV). The records typically include long periods of small change with occasional large changes reflecting geomagnetic excursions and geomagnetic reversals.[22]

### Magnetic field reversals

Geomagnetic polarity during the late Cenozoic Era. Dark areas denote periods where the polarity matches today's polarity, light areas denote periods where that polarity is reversed.

Although the Earth's field is generally well approximated by a magnetic dipole with its axis near the rotational axis, there are occasional dramatic events where the North and South geomagnetic poles trade places. These events are called geomagnetic reversals. Evidence for these events can be found worldwide in basalts, sediment cores taken from the ocean floors, and seafloor magnetic anomalies. Reversals occur at apparently random intervals ranging from less than 0.1 million years to as much as 50 million years. The most recent such event, called the Brunhes–Matuyama reversal, occurred about 780,000 years ago.[23][24]

The past magnetic field is recorded mostly by iron oxides, such as magnetite, that have some form of ferrimagnetism or other magnetic ordering that allows the Earth's field to magnetize them. This remanent magnetization, or remanence, can be acquired in more than one way. In lava flows, the direction of the field is "frozen" in small magnetic particles as they cool, giving rise to a thermoremanent magnetization. In sediments, the orientation of magnetic particles acquires a slight bias towards the magnetic field as they are deposited on an ocean floor or lake bottom. This is called detrital remanent magnetization.[6]

Thermoremanent magnetization is the form of remanence that gives rise to the magnetic anomalies around ocean ridges. As the seafloor spreads, magma wells up from the mantle and cools to form new basaltic crust. During the cooling, the basalt records the direction of the Earth's field. This new basalt forms on both sides of the ridge and moves away from it. When the Earth's field reverses, new basalt records the reversed direction. The result is a series of stripes that are symmetric about the ridge. A ship towing a magnetometer on the surface of the ocean can detect these stripes and infer the age of the ocean floor below. This provides information on the rate at which seafloor has spread in the past.[6]

Radiometric dating of lava flows has been used to establish a geomagnetic polarity time scale, part of which is shown in the image. This forms the basis of magnetostratigraphy, a geophysical correlation technique that can be used to date both sedimentary and volcanic sequences as well as the seafloor magnetic anomalies.[6]

Studies of lava flows on Steens Mountain, Oregon, indicate that the magnetic field could have shifted at a rate of up to 6 degrees per day at some time in Earth's history, which significantly challenges the popular understanding of how the Earth's magnetic field works.[25]

Temporary dipole tilt variations that take the dipole axis across the equator and then back to the original polarity are known as excursions.

### Earliest appearance

A paleomagnetic study of Australian red dacite and pillow basalt has estimated the magnetic field to have been present since at least 3,450 million years ago.[26][27][28]

## Physical origin

### Earth's core and the geodynamo

A schematic illustrating the relationship between motion of conducting fluid, organized into rolls by the Coriolis force, and the magnetic field the motion generates.

The Earth's magnetic field is mostly caused by electric currents in the liquid outer core, which is composed of highly conductive molten iron. A magnetic field is generated by a feedback loop: current loops generate magnetic fields (Ampère's circuital law); a changing magnetic field generates an electric field (Faraday's law); and the electric and magnetic fields exert a force on the charges that are flowing in currents (the Lorentz force). These effects can be combined in an equation for the magnetic field only called the magnetic induction equation:

$\frac{\partial \mathbf{B}}{\partial t} = \eta \nabla^2 \mathbf{B} + \nabla \times (\mathbf{u} \times \mathbf{B})$

where u is the velocity of the fluid, B is the magnetic B-field; and η=1/σμ is the magnetic diffusivity with σ electrical conductivity and μ permeability.[29] This is a partial differential equation. The term B/∂t is the time derivative of the field; 2 is the Laplacian and ∇× is the curl.

The first term on the right hand side of the induction equation is a diffusion term. In a stationary fluid, the magnetic field declines and any concentrations of field spread out. If the Earth's dynamo shut off, the dipole part would disappear in a few tens of thousands of years.[29]

In a perfect conductor (σ=∞), there would be no diffusion. By Lenz's law, any change in the magnetic field would be immediately opposed by currents, so the flux through a given volume of fluid could not change. As the fluid moved, the magnetic field would go with it. The theorem describing this effect is called the frozen-in-field theorem. Even in a fluid with a finite conductivity, new field is generated by stretching field lines as the fluid moves in ways that deform it. This process could go on generating new field indefinitely, were it not that as the magnetic field increases in strength, it resists fluid motion.[29]

The motion of the fluid is sustained by convection, motion driven by buoyancy. The temperature increases towards the center of the Earth, and the higher temperature of the fluid lower down makes it buoyant. This buoyancy is enhanced by chemical separation: As the core cools, some of the molten iron solidifies and is plated to the inner core. In the process, lighter elements are left behind in the fluid, making it lighter. This is called compositional convection. A Coriolis effect, caused by the overall planetary rotation, tends to organize the flow into rolls aligned along the north-south polar axis.[29][30]

The average magnetic field in the Earth's outer core was calculated to be 25 Gauss, 50 times stronger than the field at the surface.[31][32]

#### Numerical models

The equations for the geodynamo are enormously difficult to solve, and the realism of the solutions is limited mainly by computer power. For decades, theorists were confined to creating kinematic dynamos in which the fluid motion is chosen in advance and the effect on the magnetic field calculated. Kinematic dynamo theory was mainly a matter of trying different flow geometries and seeing whether they could sustain a dynamo.[33]

The first self-consistent dynamo models, ones that determine both the fluid motions and the magnetic field, were developed by two groups in 1995, one in Japan [34] and one in the United States.[35][1] The latter received a lot of attention because it sucessfully reproduced some of the characteristics of the Earth's field, including geomagnetic reversals.[33]

### Currents in the ionosphere and magnetosphere

Electric currents induced in the ionosphere generate magnetic fields. Such a field is always generated near where the atmosphere is closest to the Sun, causing daily alterations that can deflect surface magnetic fields by as much as one degree. Typical daily variations of field strength are about 25 nanoteslas (nT) (i.e. ~ 1:2,000), with variations over a few seconds of typically around 1 nT (i.e. ~ 1:50,000).[36]

### Crustal magnetic anomalies

A model of short-wavelength features of Earth's magnetic field, attributed to lithospheric anomalies.[37]

Magnetometers detect minute deviations in the Earth's magnetic field caused by iron artifacts, kilns, some types of stone structures, and even ditches and middens in archaeological geophysics. Using magnetic instruments adapted from airborne magnetic anomaly detectors developed during World War II to detect submarines, the magnetic variations across the ocean floor have been mapped. Basalt — the iron-rich, volcanic rock making up the ocean floor — contains a strongly magnetic mineral (magnetite) and can locally distort compass readings. The distortion was recognized by Icelandic mariners as early as the late 18th century. More important, because the presence of magnetite gives the basalt measurable magnetic properties, these magnetic variations have provided another means to study the deep ocean floor. When newly formed rock cools, such magnetic materials record the Earth's magnetic field.

## Measurement and analysis

### Detection

The Earth's magnetic field strength was measured by Carl Friedrich Gauss in 1835 and has been repeatedly measured since then, showing a relative decay of about 10% over the last 150 years.[38] The Magsat satellite and later satellites have used 3-axis vector magnetometers to probe the 3-D structure of the Earth's magnetic field. The later Ørsted satellite allowed a comparison indicating a dynamic geodynamo in action that appears to be giving rise to an alternate pole under the Atlantic Ocean west of S. Africa.[39]

Governments sometimes operate units that specialize in measurement of the Earth's magnetic field. These are geomagnetic observatories, typically part of a national Geological Survey, for example the British Geological Survey's Eskdalemuir Observatory. Such observatories can measure and forecast magnetic conditions that sometimes affect communications, electric power, and other human activities. (See magnetic storm.)

The International Real-time Magnetic Observatory Network, with over 100 interlinked geomagnetic observatories around the world has been recording the earths magnetic field since 1991.

The military determines local geomagnetic field characteristics, in order to detect anomalies in the natural background that might be caused by a significant metallic object such as a submerged submarine. Typically, these magnetic anomaly detectors are flown in aircraft like the UK's Nimrod or towed as an instrument or an array of instruments from surface ships.

Commercially, geophysical prospecting companies also use magnetic detectors to identify naturally occurring anomalies from ore bodies, such as the Kursk Magnetic Anomaly.

### Statistical models

Each measurement of the magnetic field is at a particular place and time. If an accurate estimate of the field at some other place and time is needed, the measurements must be converted to a model and the model used to make predictions.

#### Spherical harmonics

Schematic representation of spherical harmonics on a sphere and their nodal lines. Pm is equal to 0 along m great circles passing through the poles, and along ℓ-m circles of equal latitude. The function changes sign each ℓtime it crosses one of these lines.
Example of a quadrupole field. This could also be constructed by moving two dipoles together. If this arrangement were placed at the center of the Earth, then a magnetic survey at the surface would find two magnetic north poles (at the geographic poles) and two south poles at the equator.

The most common way of analyzing the global variations in the Earth's magnetic field is to fit the measurements to a set of spherical harmonics. This was first done by Carl Friedrich Gauss. Spherical harmonics are functions that oscillate over the surface of a sphere. They are the product of two functions, one that depends on latitude and one on longitude. The function of longitude is zero along zero or more great circles passing through the North and South Poles; the number of such nodal lines is the absolute value of the order m. The function of latitude is zero along zero or more latitude circles; this plus the order is equal to the degree ℓ. Each harmonic is equivalent to a particular arrangement of magnetic charges at the center of the Earth. A monopole is an isolated magnetic charge, which has never been observed. A dipole is equivalent to two opposing charges brought close together and a quadrupole to two dipoles brought together. A quadrupole field is shown in the lower figure on the right.[9]

Spherical harmonics can represent any scalar field (function of position) that satisfies certain properties. A magnetic field is a vector field, but if it is expressed in Cartesian components X, Y, Z, each component is the derivative of the same scalar function called the magnetic potential. Analyses of the Earth's magnetic field use a modified version of the usual spherical harmonics that differ by a multiplicative factor. A least-squares fit to the magnetic field measurements gives the Earth's field as the sum of spherical harmonics, each multiplied by the best-fitting Gauss coefficient gm or hm.[9]

The lowest-degree Gauss coefficient, g00, gives the contribution of an isolated magnetic charge, so it is zero. The next three coefficients – g10, g11, and h11 – determine the direction and magnitude of the dipole contribution. The best fitting dipole is tilted at an angle of about 10° with respect to the rotational axis, as described earlier.[9]

Spherical harmonic analysis can be used to distinguish internal from external sources if measurements are available at more than one height (for example, ground observatories and satellites). In that case, each term with coefficient gm or hm can be split into two terms: one that decreases with radius as 1/rℓ+1 and one that increases with radius as r. The increasing terms fit the external sources (currents in the ionosphere and magnetosphere). However, averaged over a few years the external contributions average to zero.[9]

The remaining terms predict that the potential of a dipole source (ℓ=1) drops off as 1/r2. The magnetic field, being a derivative of the potential, drops off as 1/r3. Quadrupole terms drop off as 1/r4, and higher order terms drop off increasingly rapidly with the radius. The radius of the outer core is about half of the radius of the Earth. If the field at the core-mantle boundary is fit to spherical harmonics, the dipole part is smaller by a factor of about at the surface, the quadrupole part 1⁄16, and so on. Thus, only the components with large wavelengths can be noticeable at the surface. From a variety of arguments, it is usually assumed that only terms up to degree 14 or less have their origin in the core. These have wavelengths of about 2000 km or less. Smaller features are attributed to crustal anomalies.[9]

#### Global models

The International Association of Geomagnetism and Aeronomy maintains a standard global field model called the International Geomagnetic Reference Field. It is updated every 5 years. The 11th-generation model, IGRF11, was developed using data from satellites (Ørsted, CHAMP and SAC-C) and a world network of geomagnetic observatories.[40] The spherical harmonic expansion was truncated at degree 10, with 120 coefficients, until 2000. Subsequent models are truncated at degree 13 (195 coefficients).[41]

Another global field model is produced jointly by the National Geophysical Data Center and the British Geological Survey. This model truncates at degree 12 (168 coefficients). It is the model used by the United States Department of Defense, the Ministry of Defence (United Kingdom), the North Atlantic Treaty Organization, and the International Hydrographic Office as well as in many civilian navigation systems.[42]

A third model, produced by the Goddard Space Flight Center (NASA and GSFC) and the Danish Space Research Institute, uses a "comprehensive modeling" approach that attempts to reconcile data with greatly varying temporal and spatial resolution from ground and satellite sources.[43]

## Biomagnetism

Animals including birds and turtles can detect the Earth's magnetic field, and use the field to navigate during migration.[44] Cows and wild deer tend to align their bodies north-south while relaxing, but not when the animals are under high voltage power lines, leading researchers to believe magnetism is responsible.[45][46]

Magnetic survey ships:

Portals:

## Notes

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• Dipole model of the Earth's magnetic field — Plot showing field lines (which, in three dimensions would describe shells ) for L values 1.5, 2, 3, 4 and 5 using a dipole model of the Earth s magnetic field The dipole model of the Earth s magnetic field is a first order approximation of the… …   Wikipedia

• Magnetic field — This article is about a scientific description of the magnetic influence of an electric current or magnetic material. For the physics of magnetic materials, see magnetism. For information about objects that create magnetic fields, see magnet. For …   Wikipedia

• Magnetic field of celestial bodies — See also Earth s magnetic field The magnetic field of a rotating body of conductive gas or liquid develops self amplifying electric currents, and thus a self generated magnetic field, due to a combination of differential rotation (different… …   Wikipedia

• Magnetic field (disambiguation) — A magnetic field is the physical phenomenon produced by moving electric charges and exhibited by ferrous materials. Magnetic field or magnetic fields may also refer to: Directly related to primary meaning: Earth s magnetic field Magnetic field of …   Wikipedia

• magnetic field — mag.netic field n an area around an object that has magnetic power ▪ the Earth s magnetic field …   Dictionary of contemporary English

• Magnetic field — Field Field (f[=e]ld), n. [OE. feld, fild, AS. feld; akin to D. veld, G. feld, Sw. f[ a]lt, Dan. felt, Icel. fold field of grass, AS. folde earth, land, ground, OS. folda.] 1. Cleared land; land suitable for tillage or pasture; cultivated ground; …   The Collaborative International Dictionary of English

• Mercury's magnetic field — Magnetosphere of Mercury Graph showing relative strength of Mercury s magnetic field. Discovery[1] …   Wikipedia

• magnetic field — 1. a region of space near a magnet, electric current, or moving charged particle in which a magnetic force acts on any other magnet, electric current, or moving charged particle. 2. See magnetic intensity. [1835 45] * * * Region around a magnet,… …   Universalium

• Magnetic field of the Moon — Total magnetic field strength at the surface of the Moon as derived from the Lunar Prospector electron reflectometer experiment. The external magnetic field of the Moon is very weak in comparison to that of the Earth. Other major differences are… …   Wikipedia

• Magnetic field imaging — Patient during an MFI acquisition Schematic visualization of an MFI acquisition …   Wikipedia