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Recipe for Computing Velocity Magnitude

In summary, to calculate the magnitude of the velocity:

  • i)

    Transform lat, lon into x = (x, y, z) unit vector using equation 5.

  • ii)

    Transform pole lat and lon into xp = (xp, yp, zp) unit vector

  • iii)

    cosΔ = x xp

  • iv)

    v = ω a sinΔ

p x = 0.0148

x = -0.375

p y = -0.606

y = -0.862

p z = 0.795

z = -0.342

cosΔ = xxp = (-0.0056 + .522 - .272) = .244

Δ = 75.8˚

v = ω a sinΔ = 142.9 mm/yr

Example: Given the rotation pole between the Pacific and Nazca plates, calculate the spreading rate at –20˚ 113.5˚W. ***One of these calculations will be on the quiz***

52.7

-88.6 1.326 x 10-6 deg/yr

52.7

271.4 2.314 x 10-8 rad/yr

POLE

POINT

20.0˚S 113.5˚W

  • -

    20.0 246.5

9

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