Geoscience Reference
In-Depth Information
magnetization
is the magnetization of the rock
M
which is induced when the
rock is put into the Earth's magnetic field
B
;itisgivenby
0
M
(
r
)
=
χ
B
(
r
)
(3.18)
where
is the magnetic susceptibility (a dimensionless physical property of the
rock). Values of
χ
for basalts vary from about 10
−
4
to 10
−
1
,sothe induced
magnetization gives rise to a field that is very much weaker than the Earth's
field. Thermoremanent magnetization is generally many times stronger than this
induced magnetization. For any rock sample, the ratio of its remanent magne-
tization to the magnetization induced by the Earth's present field is called the
Konigsberger ratio Q
. Measured values of
Q
for oceanic basalts are in the range
1-160. Thus, an effective susceptibility for TRM of basalt of about 10
−
3
-10
−
1
appears to be reasonable. This permanent TRM therefore produces a local field
of perhaps 1% of the Earth's magnetic field. Effective susceptibilities for sed-
imentary rocks (DRM and CRM) are about two orders of magnitude less than
those for basalt (TRM).
The relationship between the angle of inclination and the magnetic latitude
(Eq. (3.17)) means that a measurement of the angle of inclination of the remanent
magnetization of a suitable lava or sediment laid down on a continent immediately
gives the magnetic palaeolatitude for the particular piece of continent. If the
continent has not moved with respect to the pole since the rock cooled, then the
magnetic latitude determined from the magnetization of the rock is the same
as its present latitude. However, if the continent has moved or if the rock has
been tilted, the magnetic latitude determined from the magnetization of the rock
can be different from its present latitude. Thus, the angle of inclination provides
apowerful method of determining the past latitudes (
palaeolatitudes
)ofthe
continents. Unfortunately, it is not possible to use palaeomagnetic data to make
a determination of palaeolongitude.
If the angles of declination and of inclination of our rock sample are measured,
the position of the palaeomagnetic pole can be calculated. To do this, it is nec-
essary to use spherical geometry, as in the calculations of Chapter 2.Figure 2.11
shows the appropriate spherical triangle if we assume N to be the present north
pole, P the palaeomagnetic north pole and X the location of the rock sample.
The cosine formula for a spherical triangle (e.g., Eq. (2.9)) gives the geographic
latitude of the palaeomagnetic pole P,
χ
λ
p
,as
cos(90
−
λ
p
)
=
cos(90
−
λ
x
) cos(90
−
λ
)
+
sin(90
−
λ
x
) sin(90
−
λ
) cos
D
(3.19)
where
λ
x
is the geographic latitude of the sample location,
D
the measured
remanent declination and
λ
the palaeolatitude (given by Eq. (3.17)). Simplifying
Eq. (3.19)gives
sin
λ
p
=
sin
λ
x
sin
λ
+
cos
λ
x
cos
λ
cos
D
(3.20)
