Geoscience Reference
In-Depth Information
and the boundary between plates A and C is a transform fault with relative motion
of 3 cm yr
−
1
. The motion at the boundary between plates B and C is unknown
and must be determined by using Eq. (2.2). For this example it is necessary to
draw a vector triangle to determine
C
v
B
(Fig. 2.7(d)). A solution to the problem
is shown in Fig. 2.7(c): plate B undergoes oblique subduction beneath plate C
at 5 cm yr
−
1
. The other possible solution is for plate C to be subducted beneath
plate B at 5 cm yr
−
1
.Inthat case, the boundary between plates C and B would
not remain collinear with the boundary between plates B and C but would move
steadily to the east. (This is an example of the instability of a
triple junction
; see
Section 2.6.)
These examples should give some idea of what can happen when plates move
relative to each other and of the types of plate boundaries that occur in various
situations. Some of the problems at the end of this chapter refer to a flat Earth, such
as we have assumed for these examples. The real Earth, however, is spherical, so
we need to use some spherical geometry.
2.3 Rotation vectors and rotation poles
To describe motions on the surface of a sphere we use Euler's '
fixed-point
' the-
orem, which states that 'The most general displacement of a rigid body with a
fixed point is equivalent to a rotation about an axis through that fixed point.'
Taking a plate as a rigid body and the centre of the Earth as a fixed point, we
can restate this theorem: 'Every displacement from one position to another on
the surface of the Earth can be regarded as a rotation about a suitably chosen axis
passing through the centre of the Earth.'
This restated theorem was first applied by Bullard
et al.
(1965)intheir paper
on continental drift, in which they describe the fitting of the coastlines of South
America and Africa. The 'suitably chosen axis' which passes through the centre
of the Earth is called the
rotation axis
, and it cuts the surface of the Earth at two
points called the
poles of rotation
(Fig. 2.8(a)). These are purely mathematical
points and have no physical reality, but their positions describe the directions
of motion of all points along the plate boundary. The magnitude of the angular
velocity about the axis then defines the magnitude of the relative motion between
the two plates. Because angular velocities behave as vectors, the relative motion
between two plates can be written as
,avector directed along the rotation axis.
The magnitude of
, the angular velocity. The sign convention used is that
a rotation that is clockwise (or right-handed) when viewed from the centre of
the Earth along the rotation axis is positive. Viewed from outside the Earth, a
positive rotation is anticlockwise. Thus, one rotation pole is positive and the other
is negative (Fig. 2.8(b)).
Consider a point X on the surface of the Earth (Fig. 2.8(c)). At X the value of
the relative velocity
v
between the two plates is
is
v
=
ω
R
sin
θ
(2.3)
