The%20Earth

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The Earths magnetic field
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The Earths magnetic field
The Earth's magnetic field crudely resembles that
of a central dipole. On the Earth's surface the
field varies from being horizontal and of
magnitude about 30 000 nT near the equator to
vertical and about 60 000 nT near the poles the
root mean square (rms) magnitude of the vector
over the surface is about 45 000 nT. The
internal geomagnetic field also varies in time,
on a time-scale of months and longer, in an as
yet unpredictable manner. This so-called secular
variation (SV) has a complicated spatial pattern,
with a global rms magnitude of about 80 nT/year.
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Secular Variation
Variation of the dipole axis represented by the
location of the North Geomagnetic Pole. (After
Fraser-Smith, 1987)
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Secular Variation
Variation of the dipole moment from successive
spherical harmonic analyses. (After
Fraser-Smith, 1987)
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Secular Variation
Play Shockwave Movies
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The Earths magnetic field
Consequently, any numerical model of the
geomagnetic field has to have coefficients which
vary with time. These coefficients are computed
from observations from geomagnetic observatories
that are distributed throughout the world, and
from satellite observations (Magsat which flew in
1979-80, and the current Ørsted mission). They
are usually updated every 5 years to produce the
International Geomagnetic Reference Field
(IGRF). The IGRF is a series of mathematical
models describing the Earths main field and its
secular variation.
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The Earths magnetic field
Each model comprises a set of spherical harmonic
coefficients (called Gauss coefficients in
recognition of Gausss development of this
technique for geomagnetism), in a truncated
series expansion of a geomagnetic potential
function where ? is the geomagnetic
potential, a is the mean radius of the Earth
(6371.2 km) and r, ?, ?, are the geocentric
spherical coordinates (r is the distance from the
centre of the Earth, ? is the longitude eastward
from Greenwich and ? is the colatitude (90 minus
the latitude). ?0 is the permeability of free
space.
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The Earths magnetic field
The terms are Schmidt
quasi-normalized associated Legendre functions of
degree n and order m (n?1 and m?n). This gives
values for the coefficients in nano-Tesla
(nT). The maximum spherical harmonic degree of
the expansion is N.
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The Earths magnetic field
The IGRF models for the main field are truncated
at N10 (120 coefficients) which represents a
compromise adopted to produce well-determined
main-field models while avoiding most of the
contamination resulting from crustal
sources. The coefficients of the main field are
rounded to the nearest nanoTesla (nT) to reflect
the limit of the resolution of the available
data. The IGRF models for the secular variation
are truncated at N8 (80 coefficients). This
time the coefficients are rounded at the nearest
0.1 nT/year, this time to reduce the effect of
accumulated rounding error.
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The Earths magnetic field
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The Earths magnetic field
Some low-degree Legendre functions. Functions
P0(m) to P6(m) are shown in the interval 1lt m lt
1.
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The Earths magnetic field
Surface projection of the geocentric axial dipole
term. Yellow region indicates a downward pointing
field and green indicates an upward pointing
field.
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The Earths magnetic field
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The Earths magnetic field
Some low-degree Legendre functions. Functions
P0(m) to P6(m) are shown in the interval 1lt m lt
1.
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The Earths magnetic field
Surface projection of the geocentric axial
quadrupole term. Yellow region indicates a
downward pointing field and green indicates an
upward pointing field.
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The Earths magnetic field
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The Earths magnetic field
Some low-degree Legendre functions. Functions
P0(m) to P6(m) are shown in the interval 1lt m lt
1.
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The Earths magnetic field
Surface projection of the geocentric axial
octupole term. Yellow region indicates a downward
pointing field and green indicates an upward
pointing field.
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The Earths magnetic field
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The Earths magnetic field
Surface projection of the equatorial dipole term.
Yellow region indicates a downward pointing field
and green indicates an upward pointing field.
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The Earths magnetic field
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The Earths magnetic field
This variation on timescales of decades to
hundreds or years is known as secular
variation. When averaged over time scaled of
several thousands of years the magnetic field
resembles that of a dipole, where there is a
simple relationship between latitude and the
inclination of the Earths magnetic field Tan I
2 Tan l 
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Generation of the Earths magnetic field
The dynamo theory of the Earths magnetic field
originates from papers by Elasser and Bullard in
the 1940s that the electrically conducting core
of the Earth acts like a self-exciting dynamo,
and produces the electrical currents needed to
sustain the field. The solution of this idea in
an Earth-like scenario has, however, proven to be
very difficult. This is because the Earth has a
homogenous, highly electrically conductive,
rapidly rotating, convecting fluid that forms the
dynamo. Thus the equations needed to provide a
solution to the generation of the field are, of
necessity, fluid dynamical ones. With the advent
of more powerful supercomputers major advances
have been made in recent years.
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Why does the Earth have a magnetic field?
The Earth has, at its centre, a dense liquid
core, of about half the radius of the Earth, with
a solid inner core. This core is though to be
mostly made of molten iron, perhaps mixed with
some lighter elements. The Earth's magnetic field
is generated by fluid motions in the Earth's
core, from circulating flows that help get rid of
heat produced there. The source of this heat is
poorly understood it might come from some of the
iron becoming solid and joining the inner core,
releasing latent heat, or perhaps it is generated
by radioactivity, like the heat of the Earth's
crust. The circulation of the molten iron in the
outer core is very slow, and the energy involved
is just a tiny part of the total heat energy
contained in the core. By moving through the
existing magnetic field, the molten iron creates
a system of electric currents, spread out through
the core. These currents create the magnetic
field.
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Generation of the Earths magnetic field
A number of concepts are central to the
understanding of the geodynamo Frozen-in-field
theorem If a magnetic field exists in a
perfectly conducting medium, the magnetic field
lines be carried along with the fluid medium.
This is a central concept because it means that
the differential motions of the fluid stretch the
field lines and add energy to the field. In the
case of the Earth, however, the fluid is not a
perfect conductor and the magnetic field will
therefore diffuse away with time. To overcome
this diffusion dynamo action is necessary to add
energy back into the system.
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Generation of the Earths magnetic field
Poloidal and Toroidal fields Toroidal fields
have no radial component and cannot, therefore,
be observed at the earths surface whereas
poloidal fields do have a radial component. The
geomagnetic field at the Earths surface is
therefore poloidal.   A central issue in
geodynamo models is how its possible to generate
a toroidal field from a poloidal one and
vice-versa as the feed-backs between the two
provide the necessary energy to maintain the
geodynamo.
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Generation of the Earths magnetic field
Production of a toroidal magnetic field in the
core w-model a) an initial poloidal field
passing through the Earths core is subjected to
an initial cylindrical shear motion of the
fluid. b) The fluid motion drags out the
magnetic field lines, and after one complete
circuit we have generated 2 new toroidal loops of
opposite sign. (After Parker, 1955)
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Generation of the Earths magnetic field
Poloidal and Toroidal fields Toroidal fields
have no radial component and cannot, therefore,
be observed at the earths surface whereas
poloidal fields do have a radial component. The
geomagnetic field at the Earths surface is
therefore poloidal.   A central issue in
geodynamo models is how its possible to generate
a toroidal field from a poloidal one and
vice-versa as the feed-backs between the two
provide the necessary energy to maintain the
geodynamo.
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Generation of the Earths magnetic field
Rotation due to Coriolis force (anticlockwise in
Northern Hemisphere) Helicity
Production of a poloidal magnetic field in the
northern hemisphere a-model A region of fluid
upwelling interacts with the field line. Because
of the Coriolis force the fluid exhibits helicity
(rotating as it moves upwards). The magnetic
field line is carried along and twisted to
produce a poloidal loop. (After Parker, 1955)
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The Alpha Omega Dynamo Cycle
Consider an initial dipolar poloidal field, such
as in (a). The omega-effect consists of (b,c)
differential rotation, wrapping the magnetic
field around the rotational axis, thereby
creating (d) a quadrupolar toroidal field
magnetic field inside the core. A closure of the
dynamo cycle requires a bit of symmetry breaking,
brought about by the alpha-effect, whereby (e)
helical upwelling and downwelling creates loops
of magnetic field. These loops coalesce (f) to
reinforce the original dipolar field.
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Why does the Earth have a magnetic field?
Because the Earth is spinning the convection in
the outer core is influenced by the motion of the
planet. The picture on the right depicts region
where fluid flow is greatest within the outer
core (the core-mantle boundary is the blue mesh
and the inner-outer core boundary is the red
mesh).
The flows form an imaginary tangent cylinder
due to the effects of large rotation, small fluid
viscosity and the presence of a solid inner core
within the spherical shell of the outer core.
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Why does the Earth have a magnetic field?
Because the flow lines within the outer core form
a tangent cylinder the magnetic field lines
generated also tend to wrap around the inner
core. On the left is depicted a snapshot of the
3D magnetic field structure simulated with a
computer generated field model. Magnetic field
lines are blue where the field is directed inward
and yellow where directed outward. The rotation
axis of the model Earth is vertical and through
the centre. A transition occurs at the
core-mantle boundary from the intense,
complicated field structure in the fluid core,
where the field is generated, to the smooth,
potential field structure outside the core. The
field lines are drawn out to two Earth radii.
The magnetic field is wrapped around the tangent
cylinder due to the shear of the zonal fluid
flow.
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Reversals of the field
The Earths magnetic field is known to have
reversed its polarity in the past that is the
magnetic field has flipped to flow from North
to South. These reversals are not periodic and
episodes of constant polarity vary greatly in
length. The history of reversals of the Earths
magnetic field is very well known for the past
200 million years. Magnetostratigraphy involves
measuring the pattern of reversals in a sequence
of rocks. This yields a unique fingerprint, or
barcode, of reversals that can be matched to
known reversal records elsewhere. This
fingerprint can be used to date rocks and in
correlating different rock sequences.
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Why does it reverse?
Because the field is generated by fluid flow the
geometry of the field is affected by any
instabilities within the flow. The field is time
varying, but polarity is stabilised by the
presence of an inner core. Any field reversal
must reverse the field in the inner core and the
inner core therefore damps the effect of any
turbulence in flow in the outer core. If
instabilities build up for a long enough period
of time the flow can induce the opposite polarity
and hence we have a reversal.
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How does it reverse?
A full understanding of how the field reverses
has yet to be achieved. Two main approaches are
currently being used to study how the field
reverses. The first is the study of the behaviour
of the field through the magnetic records
preserved in rock sequences. However to get a
full 3-d picture of what happens multiple studies
of the same reversal are required from multiple
sites spread out around the globe. This will
take some time to achieve. The second approach is
the use of supercomputers to model the behaviour
of the field through time. The model on the left
depicts a reversal in the computer model of
Glatzmaier Roberts (1995). Note that the field
lines become chaotic during the reversal but
revert to a dipole geometry once the reversal is
complete.
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How does it reverse?
A snapshot of the 3D magnetic field structure
simulated with the Glatzmaier-Roberts geodynamo
model. Magnetic field lines are blue where the
field is directed inward and yellow where
directed outward. The rotation axis of the model
Earth is vertical and through the centre. A
transition occurs at the core-mantle boundary
from the intense, complicated field structure in
the fluid core, where the field is generated, to
the smooth, potential field structure outside the
core. The field lines are drawn out to two Earth
radii. Magnetic field is wrapped around the
tangent cylinder due to the shear of the zonal
fluid flow.
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How does it reverse?
500 years before the middle of a magnetic
reversal.
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How does it reverse?
During the middle of a magnetic reversal
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How does it reverse?
500 years after the middle of a magnetic reversal
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How does it reverse?
A snapshot of the simulated magnetic field
structure within the core. Lines are blue where
outside the inner core and orange within the
inner core. The rotation axis is vertical.
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Preferred Reversal Paths?
Transitional VGP paths for the upper Olduvai
transition in the Cristolo sediment.
362 transitional VGPs from 121 volcanic record of
reversals younger than 16 Ma.
After Tric et al., 1991 Prevot Camps, 1993
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Preferred Reversal Paths?
Equator crossings for sedimentary VGP transition
paths up to 1995.
After McFadden Merrill, (1995)
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What triggers reversals?
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Polarity Lengths and Superchrons
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Non-Dipole Fields in the Past?
A fundamental assumption in all plate
reconstructions based on magnetic data is that we
are dealing with a time-averaged geocentric axial
dipole. (Kent Smethurst 1998)
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Non-Dipole Fields in the Past?
The addition of varying proportions of non-dipole
fields will have the effect of changing the
inclination vs latitude relationship Tan I 2
Tan l. Here the addition of quadrupole fields is
modelled. (Kent Smethurst 1998)
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Non-Dipole Fields in the Past?
The addition of varying proportions of non-dipole
fields will have the effect of changing the
inclination vs latitude relationship Tan I 2
Tan l. Here the addition of octupole fields is
modelled. After Kent Smethurst 1998.
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Non-Dipole Fields in the Past?

• The Frequency vs Inclination distribution for
  Palaeozoic Rocks is far from dipolar.
• This could indicate
• Non-dipole fields
• Shallowing of inclinations in sedimentary
  sequences
• Inadequate global sampling (i.e. we just happen
  to have sampled the low-latitude continents)
• After Kent Smethurst 1998.

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Non-Dipole Fields in the Past?
It is possible to model the distributions in
terms of non-dipole contributions to the main
field. After Kent Smethurst 1998.