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Euler's "fixed point" theorem ... can be stated as:

The most general displacement of a rigid body over the surface of a sphere can be regarded as a rotation about a suitable axis which passes through the centre of that sphere.

Thus all plate motions can be described by a rotation axis, which passes through the centre of the Earth and cuts the surface at two points, called the poles of rotation. The relative motion of two plates then needs a pole of rotation and an angular velocity to be defined.

So where are those poles located? Is there any map or resource indicating where those are 'poles' are?

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Up to now, we constrained the (relative) plate movements mostly with seismic slip measurments.

Since 10-20 years, with the diffusion of GPS measurments, it has been possible to have a more granular distribution of movements and a more precise estimation of the rotation pole for a given plate.

Roughly speaking, then, you should look for the work of authors like these: https://meetingorganizer.copernicus.org/EGU2017/EGU2017-14816-1.pdf (just a random "scientific" google result for the search)

The end product (an accurate determination of rotation poles) should help in estabilishing the seismic hazard, by observing gaps and differential displacements, possibly representing loading of the fault, in a very primitive Reid (1910) way of thinking:

https://earthquake.usgs.gov/earthquakes/events/1906calif/18april/reid.php USGS image https://earthquake.usgs.gov/earthquakes/events/1906calif/18april/images/ElasticRebound.gif

I have no right on the image, it comes from the USGS site.

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  • $\begingroup$ Rotation poles aren't fixed in space or time. They are a construct relative to something else (e.g. neighbour plates or the whole earth) and depend on modelling. They can be roughly determined for a single plate in relation to the rest for a time interval, but not for more plates at the same time because the geometry of the whole earth can't change. usna.edu/Users/oceano/pguth/md_help/geology_course/… $\endgroup$ – a_donda Apr 2 at 13:27
  • $\begingroup$ @a_donda The page you posted is old and referring to some specific "models". Since plate tectonics is a recent theory, I do not expect everyone can fully grasp the resolution power of GPS measurments and the possibility of identifying the many, individual, "splitted" plate, with the final idea of getting a detailed picture of the relative movement of plates (i.e. earthquakes number and magnitudes, if the movement is expressed seismically) ... or to confute the whole idea that earthquake are happening only at the plate boundaries :) $\endgroup$ – EarlGrey Apr 2 at 18:35
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    $\begingroup$ Last revison date is Feb 2020. Plate tectonics builds on continental drift which is ~100 years old, first ideas of fitting continental outlines reach back to the Rennaissance (F. Bacon ?). I wanted to say that calculation depends on modelling and time frame. So the Euler point for e.g. North America can be in Northeastern Canada or off the coast of Costa Rica. A concept of rigid plates rotating without mutual dependence and deformation is probably not applicable sciencedirect.com/science/article/abs/pii/S106879711600050X. I fear the question can't be answered easily ... $\endgroup$ – a_donda Apr 2 at 19:32
  • $\begingroup$ Prsent day Eurasian Plate for example seems to be too complex to describe with GPS data. sciencedirect.com/science/article/pii/S1674984715301774 and academic.oup.com/gji/article/169/3/1180/625340. But I am not an expert at this, i admit. $\endgroup$ – a_donda Apr 2 at 19:36
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    $\begingroup$ I don't know, the first paper states "It may be seen from Figure 2, Figure 4, Figure 5 that the directions and velocities vary gradually from western Europe to eastern Asia" while what I see in the picture is just geodetic trajectory, so that changes in velocity are only apparent (like airplane routes). Then, I don't know, it is a peer reviewed publication, I hope they did all right. I agree " A concept of rigid plates rotating [...] is probably not applicable" but I feel you need euler pole to define rotation and (AND!) also to compute the deformation correctly. Neither alone is enough $\endgroup$ – EarlGrey Apr 2 at 19:44

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