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

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 ^ 1 ^ r q ^

Position of the Poles http://roma2.rm.ingv.it/

Aside – why aren’t roads N-S?

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. 5981 1018-1020

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!

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).

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!

Magnetic Field Strength Basic Equations Mag. Materials Earth’s Field Magnetic Measurements Magnetic Field Strength Total field strength varies from 690000nT 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. 5981 1018-1020

Basic Equations Mag. Materials Earth’s Field Magnetic Measurements Declination http://www.solarpathfinder.com/images/spf/magdec-world-big.jpg

Basic Equations Mag. Materials Earth’s Field Magnetic Measurements Declination http://www.solarpathfinder.com/images/spf/magdec-us-big.gif

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)

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 http://roma2.rm.ingv.it/

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)

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

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.

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.

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