Paleomagnetism and Earth History - Quantitative Plate Tectonics - page 201

Fig. 6.19 Determination
of a hot-spot Euler pole
( HEP ). In this instance, a
small circle arc about a
HEP, E ,isusedtofita
chain of volcanoes ( red
dots ). H is the location of
present day hot spot
volcanism

arc about a hot spot Euler pole (HEP) to the hot
spot track observed on this plate (Gordon et al.
1984 ). This method is illustrated in Fig. 6.19 .
In this instance, for a set of N plates related by
a circuit C , we can determine the Euler vectors
¨ i describing the motion of each plate in the
global circuit. In fact, if ¨ r is the Euler vector
of the reference plate (with Euler pole in E ,see
Fig. 6.19 )and ¨ ir is the angular velocity of the i -
th plate relative to the root plate, then its absolute
angular velocity will be given by: ¨ i D ¨ ir C ¨ r .
Then, using ( 2.69 ) we see that an Euler vector
describing the rotation of the whole lithosphere
can be written as follows:

component aligned with the spin axis. As noted
by Jurdy and Van der Voo ( 1974 ), only the Equa-
torial component will contribute to TPW, in so far
as it shifts the whole lithosphere from the current
location of the spin axis. Therefore, we can define
TPW as the result of a rotation of the whole
lithosphere about an equatorial Euler pole. Given
that it is unlikely for to be aligned with the spin
axis at any time, we see that TPW is a common
feature of global plate motions, which also affects
at the same time all APW paths. A series of ques-
tions immediately follows (apart from those re-
garding the dynamics associated with TPW). For
example, what is the amount of TPW during the
geologic past? Does it average to zero? Second,
how are APW paths affected by TPW? Third,
what is the kinematic relation between TPW and
hot spots? Although these questions have been
addressed in a number of articles since the 1970s,
no satisfactory answer has been found so far
and TPW is still at the frontier of paleomagnetic
research.

8 X
i

3

i

D Q ¨ i (6.60)

where the components of the tensors Q i are given
by ( 2.63 ) . The vector can be used to establish
the existence of TPW. To this purpose, must be
decomposed into an Equatorial component and a