Paleomagnetism and Earth History - Quantitative Plate Tectonics - page 202

trajectories of reference sites on four continents
since 230 Ma (late Ladinian). An important fea-
ture that these paths have in common is that they
are chains of small circle arcs .Furthermore,it
is possible to show that the velocity along each
small circle arc is approximately constant, which
suggests us that the motion of any point can be
described by a sequence of rotations about fixed
Euler axes.
It is not difficult to prove that this is in part
a consequence of the fact that the relative motion
between two neighbor plates in a circuit is always
a sequence of stage rotations (see Sect. 2.7 ) . The
technique to calculate the path of relative motion
travelled by a reference point has been described
in Sect. 2.8 . Extending the method to absolute
motions is an elementary task: we simply sub-
stitute the relative linear velocity appearing in
( 2.56 ) , which could not be associated with a stage
rotation, by an absolute velocity v :

6.7 Velocity Fields

and Acceleration Fields
During the Cenozoic
and the Mesozoic

Now we are going to describe some insightful
features of global plate motions since the late Tri-
assic through an unconventional approach, based
on an analysis of velocity and acceleration fields.
To this end, we will use the techniques described
in Sect. 2.8 to determine the absolute linear ve-
locity of a point (Eq. 2.51 ) and its acceleration.
For simplicity, plate motions will be represented
in the paleomagnetic reference frame of Schet-
tino and Scotese ( 2005 ), but the validity of the
results extends to more sophisticated coordinate
systems. Our starting point is the observation that
the absolute motion of a reference point on any
given plate, which can be determined using the
methods described in Sect. 2.7 , is far from being a
random walk. Figure 6.20 illustrates the absolute

r .T C •T/ D r.T/ C v .r/•T (6.61)

Fig. 6.20 Trajectories of reference points in N. America, S. America, Eurasia, and India during the last 230 Myrs in
the paleomagnetic reference frame of Schettino and Scotese ( 2005 ). Numbers represent ages along the paths