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Earth and Space Sciences · 术语表

什么是 Euler pole; Euler vector？

又称： Euler pole · Euler vector

Definition 12.3 University Earth and Space Sciences — Year 1 · 第 12 章 — Plate Kinematics on a Sphere

The motion of a plate B relative to a plate A is a rotation about an axis through the centre of the Earth. The Euler pole of the pair is the point where this axis meets the surface, chosen so that the rotation is anticlockwise seen from above it; the antipodal point is the opposite pole. The Euler vector $\vec\omega_{BA}$ is the angular velocity of B relative to A: it points from the centre of the Earth towards the Euler pole, and its length $\omega$ is the rate of rotation.

示例

Example 12.8 (Eurasia moves away from North America in Iceland)

Take the middle of Iceland at $64.5{}^{\circ}$ N, $18{}^{\circ}$ W, and the Euler vector of Eurasia relative to North America above. Then $\omega R = 3.665 \times 10^{-9}\times6.371 \times 10^{9}\,\mathrm{mm} = 23.35\,\mathrm{mm}\,\mathrm{yr}^{-1}$ , and

\cos\Delta = \sin61.8{}^{\circ}\sin64.5{}^{\circ} + \cos61.8{}^{\circ}\cos64.5{}^{\circ}\cos(-18{}^{\circ} - 139.6{}^{\circ}) = 0.60736,

so $\Delta = 52.60{}^{\circ}$ and $v = 23.35\sin52.60{}^{\circ} = 18.55\,\mathrm{mm}\,\mathrm{yr}^{-1}$ . The pole is seen at the azimuth $\beta = 13.1{}^{\circ}$ , a little east of north, over the Arctic; Eurasia moves towards $103.1{}^{\circ}$ , east-south-east, that is $18.07\,\mathrm{mm}\,\mathrm{yr}^{-1}$ to the east and $4.20\,\mathrm{mm}\,\mathrm{yr}^{-1}$ to the south.

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