Geomagnetism: Lecture 1 This lecture is based largely on:

The Coulomb (magnetic) force: the definition According to the Coulomb law, the magnetic force, F m, acting between two magnetic monopoles is given by: where:  is a constant of proportionality known as the magnetic permeability. p 1 and p 2 are the charges of the two magnetic monopoles. r is the distance between the two poles.

The Coulomb (magnetic) force: the units The units in SI are: Fn is in Newtons [N]. r is in meters [m]. p 1 and p 2 are in Ampere times meter [Amp m]. In other words, if the force is equal 1 Newton and the two magnetic poles are separated by 1 meter, the poles charge is equal to 1 Ampere meter.

Note the similarities to the gravitational force, i.e., the 1/r 2 dependence. Unlike the gravitational constant, the magnetic permeability, , is a material property. p 1 and p 2 can be either of a positive or a negative sign. If p 1 and p 2 are of the same sign, the Coulomb force is repulsive, otherwise it is attractive. The Coulomb (magnetic) force: related notes

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 positive 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. Note that the arrows come out of the monopole labeled N and into the monopole labeled S. The Coulomb (magnetic) force: magnetic monopoles

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 Coulomb (magnetic) force: field lines

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 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 geomagnetic field

The strength of the geomagnetic field The magnetic field strength, H, is defined as the force per unit pole exerted by a magnetic monopole, p 1 : 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.

While the gravitational force is always attractive, the magnetic force can be either attractive or repulsive. While the gravitational field may be described as a sum of monopoles (single point sources), 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. Differences between geomagnetics and gravity

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, J i, is given by: where , the magnetic susceptibility, is a unitless number, property of the material.

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 values. 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.