Geology Reference
In-Depth Information
equal to the drag coefficient of the oceanic areas.
Notwithstanding these issues, the NNR condi-
tion ( 2.68 ) has been widely used to build “ab-
solute” plate motions models (e.g., Argus and
Gordon 1991 ), and represents the basis for the
definition of a geocentric reference frame. This
is the International Terrestrial Reference Frame
(ITRF), which is particularly important for the
representation of kinematic data obtained from
geodetic techniques, but it is also linked to an
inertial frame tied to stellar objects, the Celestial
Reference Frame. This NNR reference frame is
periodically updated by the International Earth
Rotation and Reference Systems Service (IERS).
It is realized through the acquisition of time
series of mean station positions at weekly or daily
sampling from a global network of observation
sites equipped with various space geodesy sys-
tems: very long baseline interferometry (VLBI),
satellite laser ranging (SLR), Global Positioning
System (GPS), and Doppler Orbitography Radio-
positioning Integrated by Satellite (DORIS) (Al-
tamimi et al. 2002 ). Then, an assignment of pre-
cise coordinates and linear velocities at reference
epochs is made. These data are used, in con-
junction with Eq. ( 2.17 ), to estimate statistically
the angular velocities of each plate having an
observation site. Finally, a best fit alignment with
the current plates velocity model NNR-NUVEL-
1A is performed, in order to satisfy the condition
( 2.68 ) (Altamimi et al. 2003 ).
We can determine the components of the ten-
sors Q i using a computational method proposed
by Schettino ( 1999b ). Table 2.4 lists the six
independent components of these tensors for the
set of MORVEL plates shown in Fig. 2.38 .This
data set can be used to determine the Euler vector
of the reference plate through Eq. ( 2.68 ). The
instantaneous Euler pole of the Pacific plate,
determined on the basis of the relative Euler
vectors of Table 2.3 and the Q tensor components
of Table 2.4 , is located at 63.5 ı S, 114.4 ı E, and
its angular velocity is ¨ D 0.65 ı /Myr. The NNR
version of MORVEL is listed in Table 2.5 , while
the corresponding velocity fields are shown in
Fig. 2.39 .
An estimation of the errors associated with the
computation of the tensors Q i
as follows. First, it is possible to show that the
area of each plate, A i , can be calculated decom-
posing the corresponding spherical polygon into
a set of spherical triangles, then using the well-
known Girard's formula for calculating the area
of each triangle (Schettino 1999b ).
From ( 2.63 ), we see that these quantities are
related to the diagonal components of Q i
by the
following expression:
Z
1 x j dS D 2A i (2.70)
i D X
j
Tr Q
S i
Therefore, an estimate of the errors associated
with the diagonal components of Q i , which are
listed in the last column of Table 2.4 , can be
obtained by evaluating the expression:
Tr Q
i 2A i
2A i
© i D
(2.71)
It is important to note that the velocity fields
of the NNR version of MORVEL do not really
represent velocities relative to the deep mantle.
In fact, the equations associated with the NNR
condition ( 2.68 ) do not consider the contribution
of slab pull forces to the total torque balance,
and are based upon the implausible assumption
that the drag coefficient is uniform across the
Earth's LAB. However, the method described
above can be considered as a good starting point
for the study of the absolute plate motions. For
example, we can improve the model introduc-
ing in the torque balance equation the torques
associated with the pull exerted by subducting
slabs.
Slab pull is a downward-directed force that
a sinking slab exerts on the unsubducted litho-
sphere along a trench line (Forsyth and Uyeda
1975 ). If T i is the small circle representative of a
trench line, then this force is everywhere normal
to T i . Therefore, if d l is an infinitesimal vector
element tangent to T i , then the torque exerted on
the unsubducted lithosphere is given by:
N i D C i Z
T i
r .dl r/
(2.72)
can be performed
 
Search WWH ::




Custom Search