PLATES I: Euler poles

After sober reflection, aided by several bottles of my favorite beer and a long patch of gloomy weather, I have decided to finish off my account of being in on – although contributing little to –  the plate tectonics revolution,  by attempting to describe some of its more esoteric and certainly least intuitive aspects.  Today I am going to describe something called an Euler pole. 

That’s Euler, as in someone who applies oil to things – not “Youler”, as its spelling seems to imply.  It is named after a famous 18^th century Swiss mathematician who first described it, Leonhard Euler.

In passing, this is not really a proper part of my history as a student watching the birth of plate theory with open-mouthed amazement.  I learned about Euler poles long after my college years; by that time I was with the USGS or maybe already at WWU.  But, still …..

Seems that Dr. Euler once showed that any motion on a sphere could be described as a rotation about a fixed point located somewhere else on the same sphere.  Thus, the opening of the northern Atlantic Ocean can be modeled as rotations, in opposite directions, of the North American and Eurasian plates about a pole located in the artic region. This explains why (at one time a puzzle) the spreading rate on the Mid Atlantic ridge is not constant, but rather increases from negligible in the Arctic region (where the Euler pole is located) to a maximum of several cm/year near the equator, then decreases as the plate boundary is traced further south.  As another example, the San Andreas Fault, which is the boundary between the Pacific and North American plates,  mathematically can be described  rotation about an Euler pole located in the north Pacific, off Labrador.  Every moving chunk of crust has its own Euler pole and, believe it or not, all that confusion turns out to be useful!

Don’t fall into the trap of regarding Euler poles as in any way active geodynamic elements; they are passive - merely useful descriptions.  Plates move in response to the sum of forces acting on them – not because of something an Euler pole somehow tell them to do!

As if this little essay were not confusing enough already, let me dump one more non-intuitive concept on you.  It transpires that Euler poles can be treated as vectors!  Hence the, Pacific-North American relative motion can be described thusly:

                                   _LatR_Long

where Lat and Long describe the location of the pole and R represents the relevant angular velocity (say, in degrees/million years).  This turns out to be handy:  if, for some reason you wished to know the relative motion between North America and Antarctica you could calculate it as the sum of the NA/Africa and Africa/Antarctica Euler vectors.

Sorry.  There is a bit more of this kind of stuff.  If I should quit now, please let me know!