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Poles.
Poles.
OCE 661 OCE 661 OCE 661 h Flat Earth Plate Geometry
Simple vector addition can be
used to approximate motion of
plates on a sphere for a local
area. Spherical trig solutions
are needed for global solutions. OCE 661 The east African Rift is
The
part of a RRR triple
junction
junction OCE 661 The motion of a plate can be described by a
The
rotation about a virtual axis which passes through
the center of the sphere (Euler's Theorem).
In terms of the Earth this implies that motions of
plates on a sphere can be described by an angular
velocity vector originating at the center of the globe.
velocity
The most widespread parameterization of such a
vector is using latitude, longitude, describing the
location where the rotation axis cuts the surface of the
Earth, and a rotation rate that corresponds to the
magnitude of the angular velocity (degrees per m.y. or
microradians per year). The latitude and longitude of
the angular velocity vector are called the “Euler
Euler
pole”.
pole
Because angular velocities behave as vectors, the
Because
motion of a plate can be expressed as a rotation w= w
k, where w is the angular velocity, k is a unit vector
along the rotation axis, w the rotation rate.
The motion of individual plates can be described by an
absolute motion angular velocity. The motion
angular
The
between two plates, which have different absolute
motion poles, can be expressed by an angular
velocity of relative motion. Plate tectonic theory was
velocity
developed by determining relative motion between
developed
plates, which  in general  is easier to measure than
their absolute motions.
their
OCE 661 ω= angular velocity, also called Euler vector
angular
Euler
ω = rotation rate at point on sphere, measured in radians/year
(rad/yr)
(rad/yr)
r = vector pointing to a position on sphere. The magnitude of this
vector corresponds to the radius of the sphere, measured in
meters (m).
meters
v = linear velocity vector at r
v = speed at r, measured in millimeter...
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 Winter '14
 Earthquakes, Plate Tectonics, Chris Goldfinger, Sydney School of Geosciences

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