GG304 Lecture 10 2/15/11 1

Clint Conrad 10-1 University of Hawaii

LECTURE 10: GEOMAGNETISM

The Earth’s magnetic field is produced by the combination of Earth’s rotation

and convection in the Earth’s metallic core. The geomagnetic potential is:

!

W = RR

r

"

# $

%

& '

n+1

m=0

n

( gn

mcosm) + hn

msinm)( )Pn

mcos*( )

n=1

+

( where R is Earth’s radius

This is a multipole expansion. The Gauss coefficients

!

gn

m and

!

hn

m get smaller with

increasing order n. The most important component is the dipole field.

Dipole Field (note reversal of N and S) Quadrupole field

The dipole potential can be written as:

!

W =µ

0mcos"

r2

where

!

m =4"

µ0

R3g1

0

This is the field due to the geocentric axial

magnetic dipole m, which is the strongest

component. The dipole magnetic field can be

broken into radial and tangential components:

!

Br

= "#W

#r=

µ0

4$

2mcos%

r3

!

B" = #1

r

$W

$"=

µ0

4%

msin"

r3

The inclination I is:

!

tanI =B

r

B"

= 2cot" = 2 tan#

GG304 Lecture 10 2/15/11 2

Clint Conrad 10-2 University of Hawaii

Earth’s field is measured in nT

(nanoTeslas), and can be separated

into Inclination (I) and Declination (D).

Deviations from a dipole field are

caused by non-axial dipole

components and higher-order

components. Intensity (nT)

Inclination (degrees) Declination (degrees)

The Earth’s field has several non-dipole complexities, and changes with time:

-- The magnetic poles are not exactly opposite each other.

-- The magnetic field is stronger near high latitudues (weakest over S. Atlantic).

GG304 Lecture 10 2/15/11 3

Clint Conrad 10-3 University of Hawaii

-- Strength of the dipole field is decreasing at 3.2%/century from 1550 to

1900 and then accelerated to 5.8%/century for last 80 years (would be zero in

year 4000 – the beginning of a geomagnetic field reversal?)

-- The location of geomagnetic pole is changing with time.

-- The dipole field drifts westward at 0.044-0.14°/yr (2500-8000 yr period).

-- Non-dipole surface features drift westward 0.2-0.7°/yr (550-1650 yr period).

-- The magnetic field polarity reverses periodically.

Paleomagnetism is the study of geomagnetic

field recorded in rock magnetizations.

Remenant magnetism of rock samples is

measured using an: astatic magnetometer

(rarely), a spinner magnetometer, or a

cryogenic magnetometer (most sensitive).

Dipole and non-dipole components of the

magnetic field average to zero over timescales of 104 yr, thus rocks that

average the field over longer timescales longer

than ~104 yr, and only the average dipole field

remains (axial geocentric dipole hypothesis).

Using the inclination (I), the paleomagnetic pole

can be computed – many observations yield

an average pole near the geographic north pole.

To determine if a set of paleomagnetic poles

is representative of the field at the time of

formation, several tests have been developed:

GG304 Lecture 10 2/15/11 4

Clint Conrad 10-4 University of Hawaii

Fold test: “undo” the fold

to see if orientations align.

Baked contact test: If country

Rock orientations are the same

as those within an intrusion, then field has not changed since intrusion.

Reversals test: If a reversal happens between samples, the paleomagnetic poles

should be exactly opposite each other.

Tectonics can be inferred from

Paleomagnetic data. If a tectonic plate has

moved, since the remanent field was

recorded, then the inclination (I) gives the

distance to the virtual geomagnetic pole

and the declination (D) can be used to

position it. Poles for different ages trace

an apparent polar wander path that can be

linked to plate motions. Each continent has its own polar wander path.

Geomagnetic polarity reversals

(switching of the orientation of

the geomagnetic field) occur

with varying frequencies, take

place over ~3000-5000 yr, and

can be used to calibrate

seafloor age. Plate tectonic

reconstructions can be deduced

from seafloor age maps.