Geology Reference
In-Depth Information
plate kinematics. Their importance arises from
the capability to predict both the paleolatitude
and the declination at
any
reference site on a
tectonic plate. Therefore, combining paleopoles
of different age, determined from different
rock units, it is possible to build curves that
describe the variations of paleolatitude and
declination though the geological time at a
common reference site (Van der Voo
1993
;
Schettino and Scotese
2005
). Let
p
and
s
be
the unit vectors associated respectively with a
paleopole
P
and a reference site
S
.TheCartesian
coordinates of these vectors can be calculated
from the corresponding geographic coordinates
predicted paleolatitude at
S
can be determined
promptly by the following formula:
For example, if we wish to determine the
mean paleopole for North America during the
Paleocene, we should select all the paleopoles
obtained from rocks on the cratonic part of this
continent, with an age between 65.5 and 56 Ma,
and satisfying some quality criteria (e.g., Van der
Vo o
1990
,
1993
). To this purpose, we could use
the Global Paleomagnetic Database (GPMDB)
(McElhinny and Lock
1990
), which is a struc-
tured publicly accessible data set of paleopoles
(e.g., Schettino and Scotese
2001
). Most authors
perform a pre-selection of the data according to
more or less subjective data reliability criteria. As
an example, Van der Voo (
1990
,
1993
) proposed
seven reliability criteria that could be satisfied by
a paleopole. In this approach, a “quality factor”
0
Q
7 is assigned to each datum, which in-
dicates the number of criteria that are satisfied.
Va n d e r Vo o (
1990
,
1993
) suggests that
Q
3
is the minimum requirement for a paleopole to
be included in the computation of a representa-
tive mean. Let
p
1
,
p
2
, :::,
p
N
be
N
unit vectors
associated with the selected paleopoles, and let
w
1
,
w
2
, :::,
w
N
be weights assigned to each
paleopole on the basis of their quality parameters.
For example, we could simply set
w
i
D
1/
A
95,
i
for
i
D
1,2, :::,
N
, but other more complex weighting
schemes are possible. In some cases (e.g., Torsvik
et al.
2001
,
2008
), even Van der Voo's quality
factor
Q
has been used as a weighting factor,
although
Q
is all except a physical quantity.
Once a weighting scheme has been selected, the
mean paleopole
p
is calculated by the following
formula:
2
arccos.p
s/
œ
D
(6.54)
Calculating the predicted declination is
likewise simple. We first apply (
6.46
)to
determine “, then the declination can be obtained
by Eq. (
6.42
). Although this technique can be
applied using individual paleopoles of different
ages from the same continent, the large amount
of paleomagnetic data collected during the last
decades and the discrepancy between results
of similar age has led to the development of
statistical techniques for the determination of
the “best” mean paleomagnetic pole from a data
set formed by several paleopoles of similar age.
Similarly, several methods have been proposed
for the determination of best-fit time series
of paleolatitude and declination, and for the
construction of curves on the globe that represent
the migration of the mean paleomagnetic pole
of a continent through the geological time.
The latter curves, which are called
apparent
polar wander paths
(APW paths), represent the
most important result of paleomagnetism for
the study of continental drift. The determination
of mean paleopoles is not much different from
the calculation of individual paleopoles from
data sets of VGPs. However, in this instance
the data are always weighted through their
confidence cones
A
95
and possibly through their
age uncertainties.
X
N
1
w
p
D
w
i
p
i
(6.55)
i
D
1
where
w
is a normalization factor, which ensures
that
j
p
jD
1.
To
determine
the
uncertainty
parameters
of
the
mean
paleopole,
we
can
use
again
Fisher
statistics,
granted
that
the
spatial
distribution
of
the
data
is
conformal
to
a
Fisher
distribution.
This
test
can
be
performed
using
the
technique
described
in
Sect.
6.3
.
Let us consider now the procedure for
constructing APW paths. As mentioned above,
