# Geocentric Axial Dipole Hypothesis (GAD)

Paleomagnetic data are collected globally and over geological timescales. The temporal and spatial variability of the data and the difficulties relating these between different studies mean that it is often easier to work with the time-averaged paleomagnetic field. The geocentric axial dipole hypothesis (GAD) was first proposed by Jan Hospers in 1954[1] as way of describing the time-averaged field. The hypothesis states that if the paleomagnetic field is averaged over sufficient time the field will be equivalent to that expected from a geocentric axial dipole.

The geometry of the GAD model is such that the geographic and geomagnetic poles and equators coincide (i.e., geographic latitude,
λ, is equal to the time-averaged paleomagnetic latitude). The horizontal (H) and vertical (Z) components of the GAD field at a given latitude can be described by:

SHOW FIGURE OF GEOMETRY

$H=\frac{\mu_0m\cos{\lambda}}{4\pi a^2}, Z=\frac{2\mu_0m\sin{\lambda}}{4\pi a^2}$

where:
μ0 is the permeability of free space,
m is the magnetic moment of the time-averaged field,
a is the radius of the Earth.

The total field (F) is given by:

$F=(H^2+Z^2)^{\frac{1}{2}}$

Since the tanget of the magnetic inclination, I, is Z/H, it can be shown that:

$\tan{I}=2\tan{\lambda}$

and by the definition the GAD the declination D=0 (geographic and geomagnetic poles coincide). The colatitude, p (p=90-λ) can be determined by:
$\tan{I}=2\cot{p}, ~ ~~0\leq p\leq 180.$

The inclination-latitude relation allows paleolatitude to be determined from the mean inclinations, which is fundamental plate tectonic reconstructions and paleosecular variation studies.

The magnetic field intensity (F) of the GAD varies as a function of latitude according to:

$F=F_0(1+3\sin^2\lambda)^{\frac{1}{2}}$

where:
F0 is the field intensity at the equator.
SHOW FIGURE OF INTENSITY

Given the importance of the GAD hypothesis to paleomagnetic studies it is essential that the hypothesis is tested.

## References

1. ^ Hospers, J. (1954), Rock magnetism and polar wandering, Nature, 173, 1183–1184, doi: 10.1038/1731183a0.