1. What is the magnetic potential of a dipole?
Earth as a Dipole M
N (-)
S (+)
Earth’s magnetic field is a potential field, roughly equivalent to a dipole.
What is the magnetic potential of a dipole?
U(r,q) = -
M cos q
4pr2
= colatitude
r = radius
Where: q

2. Earth as a Dipole N (-) q M S (+) H = - U = - r - q H = - r - q
Described in Spherical Coordinates:
U(r,q) = -
M cos q
4pr2
= colatitude
r = radius
Where: q
H = r q
^ ^
2M cos q
4pr3
M sin q
H = U = r q dU dr dq
^ ^ r q ^

3. Position of the Poles

4. Aside – why aren’t roads N-S?

5. Deviations from the Dipole Model
On average ~5% of earth’s field is non-dipole. Some contribution from non-earth sources (the sun), but this is small ~1%
Regional Variation of Inner Core Anisotropy from Seismic Normal Mode Observations’ Science 21 May 2010: vol. 328 no

6. Source of Earth’s Mag. Field
The simple answer: The Dynamo Effect
The Earth’s magnetic field is generated by electrical currents formed by both convection and rotation of the outer core (Fe & Ni).
But, it’s not really a simple problem.
Convection of Earth’s core is very complex!

7. Quantifying Earth’s Magnetic Field
The vector FE, describing Earth’s Magnetic Field, can be divided in to radial and colatitude components (Fr and Fq).

8. Quantifying Earth’s Magnetic Field (HE)
At any point on Earth’s surface, the magnetic field can be represented by
Declination (d) – The angle on the surface between magnetic north and true north.
Inclination (i) – The angle between the horizontal surface and the direction of total magnetic force.
Declination can be looked up for a location. Important to note that it varies through time. So D marked on old maps won’t be 100% accurate!

9. Magnetic Field Strength
Basic Equations Mag. Materials Earth’s Field Magnetic Measurements
Magnetic Field Strength
Total field strength varies from nT at the poles to 25000nT at the equator
Regional Variation of Inner Core Anisotropy from Seismic Normal Mode Observations’ Science 21 May 2010: vol. 328 no

10. Basic Equations Mag. Materials Earth’s Field Magnetic Measurements
Declination

11. Basic Equations Mag. Materials Earth’s Field Magnetic Measurements
Declination

12. N S Inclination FE i tan (i) = 2 tan (lat) Fr Fq tan (i) = = =
2M cos q
4pr3
M sin q Fr Fq
2 cos q
sin q
tan (i) = = =
= 2 cot (q) = 2 tan (lat)

13. N S Inclination FE i tan (i) = 2 tan (lat) Some special cases: Poles
Where lat=90deg; i=90deg
Equator
lat=0deg; i=0deg
St Louis
Lat = 39deg, I = 58 deg

14. Measuring Earth’s Magnetic Field
Directional: Ex. Flux-Gate Magnetometer
Measures the horizontal, vertical, and total field strength.
Full-Field: Ex. Proton-Precession Magnetometer
Measures total field strength
Quick and easy to use
Relatively inexpensive
Most commonly used
Precision to 0.1 nT
Create field to align hydrogen protons. Turn off. Then measure current created by the realigning of nuclei with natural field (Fe+Fa)

15. Interpreting Anomalies in Total Field Strength
The magnetic field generated by a local anomaly will add or subtract from the Earth’s field depending on it’s orientation and your position.
For exploration and environmental purposes, we are interested in the anomaly – the deviations from the Earth’s field!
But, we are typically only measuring the total field – not vertical and horizontal components.
In most exploration cases, FE >>> FA, so we can assume that field FT created by FE + FA is parallel to FE. FE FA
Fobs

16. Interpreting Anomalies in Total Field Strength
Draw this on board
We can only measure total field strength with the magnetometers you will use. But, earth’s field is much, much greater than the anomolies you will be measuring. So, we can typically assume that the vector representing the total field (anomaly + Earth) is parallel to Earth’s field.

17. Corrections: Diurnal Variations
You can compensate for diurnal variations by taking periodic measurements at some “base station” and then removing those observed temporal variations from other measurements.

18. Corrections
Must remove the regional gradient to account for spatial variations of Earth’s dipole field.