Geophysics, Lecture Notes- Physics - Prof Gavin Bell 12

Geophysics, Lecture Notes- Physics - Prof Gavin Bell 12 -...

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Unformatted text preview: 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 v about a rotation pole at a point an angular distance away from the pole. The vector version for velocity v x will not be used in exams but you should be aware of it (see Q. 20) v RE sin 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. Figure (above) – schematic of a pole and plate boundary. Further study Problems 18, 19 and 20. Q18/19 are important – you need to get the hang of the spherical geometry involved in plate motions. Q20 is optional and deals with the full vector approach (which we would not use in a 30 min. exam question). See the web site (Extra Material) for suggested exercises to get your head around rotation poles for a few well known plate boundaries. Note – simplified plate boundaries will normally be used in exam questions. ...
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