Relative Motion of Two Plates

In looking at the motion of two or more plates, it is helpful to think of the motion in both map view and in velocity space.  You must also remember that plate motions are relative, and that we do not necessarily know the absolute motion.  Any common motion between two plates will be potentially undetectable to someone of one of the plates, who will only see the difference in motion between them.

There are a number of different plate models, and they will have different aboslute motions of the plates depending on the starting assumptions.  However the relative motions between plates should be the same; if they differ significantly, one of the models must have errors.  A likely first assumption would be that one (or both models) simplify reality, and that smaller plates with more complex deformation are involved.  The common models range from 12 to 56 plates.

This is the motion of the African and North American plates, in the NNR-NUVEL-1A plate model, along part of the Mid Atlantic Ridge. 

Both plates have a northward component on motion, but Africa also has a component to the east, and North America has a component to the west.

To graphically find the resultant, you can connect the tips of the two arrows. This resultant vector actually should be drawn on the location corresponding to the tails of the two arrows.  There are two solutions, each holding a different plate stationary.

The motions change along the ridge, because different points are different distances from the Euler pole.
This shows the relative motion of North America, with respect to Africa.  Motion is to the west, and changes in magnitude slightly.

The vectors will normally be perpendicular to the ridge crest.
Relative motion of Africa with respect to North America.  It has the same magnitude, but the opposite direction, compared to the motion keeping Africa fixed.
Velocity diagram for a point on the ridge between Africa and North America.  The axes show the x and y components in mm/yr, with respect to the reference frame of the plate model.

To get the relative motions between the two plates, place yourself on one plate, and consider where the other plate lies in velocity space.  In this case Africa is the point in the lower right; for a person standing on Africa, North America is moving to the northwest.  In the case of a ridge, the two plates will have the same relative position in velocity space as they do on a map.  This will also be the full spreading rate; the half rate will be added to each plate in the general case where the spreading is symmetrical about the ridge.
  This analysis has been done graphically; it could as easily be done with trigonometry in Excel, or using matrix operations in Matlab.

 

Arica/Numbia motion with respect to Europe, in two different reference frames.  In both reference frames, both plates move to the NE at nearly the same rate, but in the model on the right, the absolute rates are about 7 times faster.

The key number is the resultant vector, which shows almost the same slow convergence between the two plates.  The resultant shows the motion of Europe with respect to Africa which is held constant.  If Europe were held constant, the resultant vector would point in the opposite direction.

 

A velocity diagram and four maps which represent possible plate configurations:

  • Map 1 would be a ridge.  The two plates have the relative orientation in velocity space and on the map, and the ridge is oriented perpendicular to two plate velocities.  Spreading is usually orthogonal to the ridge axis, and with the same rate for each plate.
  • Map 2 would be a right-lateral transform fault (as you face the fault plane, the opposite side would be moving to the right).  The motion will be parallel to the plate boundary.  In rare cases, like a leaky transform or a bend like some that occur on the San Andreas fault, the boundary and motion will not be completely parallel, and there will be adjustments to conserve volume.
  • Map 3 will be a trench.  The two plates will have a flipped orientation in velocity space and on the map.  While the trench and volcanic arc are often approximately perpendicular to the plate motion, oblique subduction probably occurs more frequently than oblique spreadking.
  • Map 4 would be a left-lateral transform fault.

 


Last revision 1/18/2018