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in the construction of an APW path are mean
paleopoles. In this instance, a smoothed APW
path must have the property to be a best fitting
regression curve on the sphere in the least-squares
sense, and there is no necessity to have best
fitting paleolatitude or declination plots. Con-
versely, in the approach of Schettino and Scotese
( 2005 ) declination and inclination represent the
primary physical observables, from which it is
possible to calculate a paleomagnetic pole using
some assumptions (e.g., the GAD hypothesis). In
this view, the data are paleomagnetic directions
determined at sampling sites, and the utility of
paleopoles resides exclusively in their capability
to predict inclination and declination at any other
site, as well as in the possibility to determine total
reconstruction poles for the continent.
Therefore, in the view of these authors, the im-
portant time series to be analyzed, and for which
best fitting regression curves were searched, were
the sequences of paleolatitude and declination at
representative reference sites and not the pale-
opole time series.
The importance of these variables was also
stressed observing that the declination D and the
paleolatitude œ at a reference site are kinematic
quantities that completely describe the motion of
a tectonic plate with respect to a paleomagnetic
reference frame. In fact, it is easy to show that any
motion on the sphere can be resolved into three
elementary Euler rotations, namely: ( a ) A pure
N - S rotation, associated with an Equatorial Euler
pole and variations of latitude of the reference
site S ;( b ) A pure rotation about the vertical
axis at the reference site, which is responsible
for changes in declination, and ( c ) A rotation
about the spin axis ( z axis), which only changes
the site longitude. Figure 6.16 illustrates these
independent rotations, which can be performed
in any order without affecting the final result.
Therefore, assuming a paleomagnetic reference
frame where the longitude of the site S is fixed
(see Sect. 2.3 ) , we have that the pair (œ, D )com-
pletely describes the kinematics of the tectonic
plate to which S belongs. Another reason to
prefer declination and paleolatitude regressions
sacrificing paleopole fitting is that declination
and inclination (hence paleolatitude) are influ-
enced differently by tectonic processes after the
acquisition of NRM, which also contributes to
their physical independence. For example, the
site of a paleopole could be located on a second-
order tectonic element that experienced a small
amount of vertical axis rotation with respect to
the main continent. This process could affect
significantly the site declination, although its pa-
leolatitude would remain unchanged. On the con-
trary, a process known as sedimentary inclination
shallowing (e.g., Arason and Levi 1990 ) could
modify the magnetic inclination of deep-sea sed-
iments during the process of compaction without
affecting their declination. As a consequence,
paleopoles having either a wrong declination or
a wrong paleolatitude have a negative effect on
a spherical regression curve, whereas they would
be easily detected as outliers on either paleolati-
tude or declination plots. Therefore, an essential
aspect of the approach of Schettino and Scotese
( 2005 ) was the detection of anomalous values of
the predicted declination or paleolatitude at the
reference sites. These outliers were filtered away
during the process of construction of a smoothed
paleolatitude or declination plot, although the
corresponding paleopoles could still contribute
to the other curve (respectively declination or
paleolatitude). Finally, the resulting spline regres-
sion curves were combined to generate spherical
smoothed (but not necessarily best fitting in the
spherical sense) APW paths.
6.5
Paleomagnetic Reference
Frames
In Chap. 2 , when we have described the general
structure and the process of construction of plate
circuits, we omitted to specify how the finite
rotations of the root plate are determined. We
have learnt that rotation models are listings of
finite reconstruction poles and rotation angles for
each identified pair of conjugate plates. How-
ever, the finite rotations of the plate associated
with the circuit root node cannot be referred to
any other plate, so that in a rotation table like
that illustrated in Fig. 2.29 the reference plate
field of the corresponding entries will be set to
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