Download Gary Glatzmaier, Los Alamos and Paul Roberts, UCLA

Geomagnetism: Lecture 1
This lecture is based largely on:
http://www.earthsci.unimelb.edu.au/ES304/
The Coulomb (magnetic) force: the definition
According to the Coulomb law, the magnetic force, Fm, acting
between two magnetic monopoles is given by:
1 p1 p2
Fm 
,
2
 r
where:
•  is a constant of
 proportionality known as the magnetic
permeability.
• p1 and p2 are the charges of the two magnetic monopoles.
• r is the distance between the two poles.
The Coulomb (magnetic) force: the units
Fm 
1 p1 p2
,
2
 r
The units in SI are:
• Fn is in Newtons
[N].
• r is in meters [m].
• p1 and p2 are in Ampere times meter [Amp m].
•  is a unitless constant.
The Coulomb (magnetic) force: related notes
• Note the similarities to the gravitational force, i.e., the 1/r2
dependence.
• Unlike the gravitational constant, the magnetic permeability, , is
a material property.
• p1 and p2 can be either of a positive or a negative sign. If p1 and
p2 are of the same sign, the Coulomb force is repulsive, otherwise
it is attractive.
The Coulomb (magnetic) force: magnetic monopoles
A recipe for calculating a magnetic monopole:
1. Place a negative pole at (-1,0).
2. Take a positive pole and place it at some location (x,z), and
compute the magnetic force.
3. Repeat step-2 by moving the positive pole to a new location.
The Coulomb (magnetic) force: magnetic monopoles
Similarly, one can get a negative monopole:
The Coulomb (magnetic) force: magnetic monopoles
Magnetic monopoles have never actually been observed! Instead,
the fundamental magnetic element is the magnetic dipole, which
consists of two magnetic monopoles.
The dipole is obtained by vector addition of a negative and a
positive monopole.
Note that the arrows come out of the monopole labeled N and into
the monopole labeled S.
The Coulomb (magnetic) force: field lines
A common way to visualize the magnetic force field associated
with a magnetic dipole is to plot the field lines for the force. Field
lines are a set of lines drawn such that they are everywhere
parallel to the direction of the force.
The geomagnetic field
geomagnetic field
= dipole + nondipole.

• A comment on Brunton compass adjustment...
The geomagnetic field
The origin of the dipole field is in the liquid core. This field and its
reversals have been simulated numerically by Glazmaire and
Roberts [1995].
“The following images and animations
show views of a snapshot from a 3D
time dependent computer simulation of
convection and magnetic field
generation in the Earth's liquid core
that spans over 80,000 years. The
simulation took several thousand cpu
hours on the Cray C-90. Magnetic field
lines show the direction and intensity of
the generated magnetic field. Lines are
colored gold where the field is directed
outward and blue where it is directed
inward.” (Gary Glatzmaier, Los Alamos
and Paul Roberts, UCLA)
http://www.psc.edu/research/graphics/gallery/geodynamo.html
The geomagnetic field
The reversal - Earth
The reversal + Earth
http://www.psc.edu/research/graphics/gallery/geodynamo.html
The geomagnetic field
Nondipole field:
Question: what
gives rise to the
nondipole
component?
The geomagnetic field
Two main effects act to produce a nondipole field:
1) Solar wind.
The geomagnetic field
2) Screening by the mantle and the lithosphere.
The strength of the geomagnetic field
The magnetic field strength, H, is defined as the force per unit
pole exerted by a magnetic monopole, p1:
Fm 1 p1
H

.
2
p2  r
• Note that the magnetic field strength is the magnetic analog to
the gravitational acceleration.
• H is measured
 in units of Tesla ,T, where: 1 T = N Amp-1 m-1.
• When describing the magnetic field strength of the earth, it is
more common to use units of nanoTeslas, nT. The average
strength of the Earth's magnetic field is about 50,000 nT.
Similarities between geomagnetics and gravity
• Passive measurement of a naturally occurring field of the earth.
• Potential fields - thus, the mathematics is similar.
• The interpretations are non-unique.
Differences between geomagnetics and gravity
• While the gravitational force is always attractive, the magnetic
force can be either attractive or repulsive.
• While the gravitational field is a
monopole (single point source), the
geomagnetic field is described in
terms of magnetic dipole, i.e., the
sum of a positive and a negative
monopole.
• While the gravitational field does not change significantly with
time, the magnetic field is highly time dependent.
Induced magnetization and magnetic susceptibility
When a magnetic material is placed within a magnetic field, H, the
magnetic material will produce its own magnetization.
The intensity of the induced magnetization, Ji, is given by:
Ji  H,
where , the magnetic susceptibility, is a unitless number, property
of the material.

Induced magnetization and magnetic susceptibility
• The values given here are for SI,
International System Units.
• While the spatial variation in
density are relatively small (between
1 and 3 Kg m-3, magnetic
susceptibility can vary as much as
four to five orders of magnitude.
• Wide variations in susceptibility
occur within a given rock type. Thus,
it will be extremely difficult to
determine rock types based on
magnetic prospecting
Induced magnetization and magnetic susceptibility
The value of the magnetic susceptibility can take on either positive
or negative signs.
Positive value means that the induced magnetic field, I, is in the
same direction as the inducing field, H.
Induced magnetization and magnetic susceptibility
Negative value means that the induced magnetic field is in the
opposite direction as the inducing field.
Remnant magnetization
If the magnetic material has relatively large susceptibilities, or if
the inducing field is strong, the magnetic material will retain a
portion of its induced magnetization even after the induced field
disappears. This remaining magnetization is called remnant
magnetization.
The total magnetic field is a sum
of the main magnetic field
produced in the Earth's core, and
the remnant field within the
material.
remnant
induced
total
Describing the magnetic field at a point
• Declination: The angle between north and the horizontal
projection of the magnetic vector. This value is measured positive
through east and varies from 0 to 360 degrees.
• Inclination: The angle between the surface of the earth and the
magnetic vector. Positive declinations indicate the vector points
downward, negative declinations indicate it points upward.
Declination varies between -90 and 90 degrees.