Paleomagnetism:
Chapter 7
121
PALEOMAGNETIC
POLES
Figure 7.1
Determination of magnetic pole position from a magnetic field direction.
Site location is at
S
(
λ
s
,
φ
s
); sitemean magnetic field direction is
I
m
,
D
m
;
M
is the geocentric dipole that can account
for the observed magnetic field direction;
P
is the magnetic pole at (
λ
p
,
φ
p
);
p
is the magnetic
colatitude (angular distance from
S
to
P
); North Pole is the north geographic pole;
β
is the
difference in longitude between the magnetic pole and the site.
The basic procedure for calculating a magnetic pole position is introduced here.
Definitions of types of magnetic
poles are then presented, leading to a discussion of paleomagnetic sampling of geomagnetic secular variation.
Here you acquire methods for judging the next level of paleomagnetic analysis: the data set of sitemean
directions and the paleomagnetic pole determined from those directions.
Examples of paleomagnetic poles
and some commonsense criteria for judging reliability of paleomagnetic poles are offered.
PROCEDURE FOR POLE DETERMINATION
The inclination and declination of a dipolar magnetic field change with position on the globe.
But the position
of the
magnetic pole
of a geocentric dipole is independent of observing locality.
For many purposes, com
parison of results between various observing localities is facilitated by determining a
pole position
.
This pole
position is simply the geographic location of the projection of the negative end of the dipole onto the Earth’s
surface, as shown in Figure 7.1.
Equator
North Pole
ß
(λ
s
,
Φ
s
)
S
P
p
D
m
I
m
M
λ
s
λ
p
Φ
p
Φ
s
p
(λ
p
,
Φ
p
)
G
r
e
e
n
w
i
c
h
M
e
r
i
d
i
a
n
Meridian
Greenwich
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Paleomagnetism:
Chapter 7
122
Calculation of a pole position is a navigational problem in spherical trigonometry that uses the dipole
formula (Equation (1.15)) to determine the distance traveled from observing locality to pole position.
Details
of the derivation of a magnetic pole position from a magnetic field direction are given in the Appendix.
Sign
conventions for geographic locations are as follows:
1.
Latitudes increase from –90
°
at south geographic pole to 0
°
at equator and to +90
°
at the north
geographic pole.
2.
Longitudes east of the Greenwich meridian are positive, while westerly longitudes are negative.
Figure 7.1 illustrates how a pole position (
λ
p
,
φ
p
) is calculated from a sitemean direction (
I
m
,
D
m
) mea
sured at a particular site (
λ
s
,
φ
s
).
The first step is to determine the magnetic
colatitude
,
p
,
which is the great
circle distance from site to pole.
From the dipole formula (Equation (1.15)),
p
I
I
m
m
=
=


cot
2
tan
2
1
1
tan
tan
(7.1)
Pole latitude is given by
λ
λ
λ
p
s
s
m
p
p
D
=
+
(
29

sin
sin
cos
cos
sin
cos
1
(7.2)
The longitudinal difference between pole and site is denoted by
β
, is positive toward the east, and is given by
β
=
sin

1
sin
p
sin
D
m
cos
λ
p
(7.3)
At this point in the calculation, there are two possibilities for pole longitude.
If
cos
p
≥
sin
λ
s
sin
λ
p
(7.4)
then
φ
p
=
φ
s
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 Fall '07
 ANANDAKRISHNAN
 Earth's magnetic field, Secular Variation, VGPs, geomagnetic secular variation, paleomagnetic pole

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