PX266 Geophysics (2010/11)
Lecture 14 Handout – Rotation Poles and Tectonic Plate Motion
Dr. Gavin Bell
Plate motions on a ‘flat Earth’ are easily described by vector addition of relative
velocities.
On a spherical Earth, the plates are not planar, but segments of the spherical surface.
Since they are constrained to stay on the surface, their (instantaneous) motion can be
uniquely and completely described by rotation about an axis passing through the
centre of the Earth. Formally, this is a consequence of Euler’s ‘fixed point theorem’
for motion of rigid bodies, but it should be fairly obvious from intuition that any
possible motion of a spherical cap segment can be thus expressed.
The intersections of the rotation axis with the Earth’s surface are the Euler poles or
instantaneous rotation poles, one positive and one negative. The sign convention is
that clockwise rotation looking out from the centre of the Earth corresponds to the
positive rotation pole (but don’t worry too much about getting this wrong in an exam).
The relative motion of any two plates can be described by a positive rotation pole
(a latitude and longitude) together with an angular velocity.
This description gives the relative motion at any point on the boundary between the
two plates. The (vector) velocity will, in general, be different at different points on the
boundary. The local relative velocity vector together with the local plate boundary
direction tell you the local nature of the plate boundary (normal constructive, oblique
constructive, conservative, etc.), which changes along the boundary.
Speed vabout a rotation pole at a point
an angular distance away from the
pole. The vector version for velocity
xv
will not be used in exams but
you should be aware of it (see Q. 20)
sin
E
Rv
You should know this equation and understand its application.
Note that ‘instantaneous’ is relative to the geological timescale – a pole may describe
the motion of a plate over many thousands of years, though in general the relative
plate motions have changed over geological history and the rotation poles apply to
present-day motion only.
