Paleomagnetism and Earth History - Quantitative Plate Tectonics - page 187

Fig. 6.7 Transformation of a paleomagnetic field at an Euler rotation that moves P to N . In this example, the

Euler axis of rotation, a , has pole at (0 ı ,¥ P C t 140 Ma (early Cretaceous), with pole at P in the

reference frame of Africa (present day coordinates), into
a GAD field. The transformation is performed applying

D 90 ı )andthe

rotation angle is -™ P

Therefore, solving for ¥ P gives: graphic North Pole N , as shown in Fig. 6.7 ,and

the continent has been restored to its original ori-
entation with respect to the spin axis. However, as
a GAD field is symmetric with respect to the spin
axis, there is no way to establish a paleolongitude
of the site S relative to the present day location.
In other words, there are infinitely many rotations
that moves P to N , which determine infinitely
many longitudinal displacements of the site S .All
these reconstructions are admissible, and there
is no way to determine the correct longitude
variation of S from the present day location to
its reconstructed position. A common method to
perform paleomagnetic reconstructions is illus-
trated in Fig. 6.7 . In this approach, the paleopole
is moved to the North Pole along its own meridian
of longitude through an Euler rotation about an
equatorial pole at (0,¥ P C 90 ı ) by an angle -™ P
(e.g., Ziegler et al. 1983 ; Schettino and Scotese
2005 ). We shall come back to this point in the
next section.
Once that we have determined the paleopole
corresponding to a paleomagnetic direction ( D , I ),
the next step is assigning uncertainty parameters
to the location (™ P ,¥ P ). To this purpose, let us
first consider the uncertainty of a paleomagnetic

¥ S C “
¥ S C “

for cos ™ cos™ P cos ™ S
for cos ™<cos™ P cos ™ S
(6.47)

¥ P D

Differently from a mean paleomagnetic direc-
tion ( D , I ), which is a site-dependent quantity,
a paleomagnetic pole of age t (the mean age
attributed to the rock unit) is a global quantity
that represents the apparent location of the geo-
graphic North Pole at time t in a reference frame
fixed to the continent to which the site S belongs
(Fig. 6.7 ). This is clearly a consequence of the
GAD hypothesis (see Sect. 4.3 ) , which states that
a time-averaged geomagnetic field approximately
coincides with a GAD field not only in the present
epoch but also in the geologic past. Therefore,
any Euler rotation that brings a paleopole to
the geographic North Pole will also transform
the time-averaged paleomagnetic field associated
with the paleopole into a GAD field. This rotation
coincides with a transformation from a reference
frame where the continent is at rest in the present
day position to a geocentric reference frame in
which the paleopole P coincides with the geo-