Editing Triple junction (section)

==Stability==
[[File:Points triples entre plaques continentales.svg|thumb|upright=1.85|Main [[list of tectonic plates|tectonic plate]] boundaries – ridge (red), trench (green), transform fault (black) – and corresponding triple junctions (yellow dots)]]
Triple junctions may be described and their stability assessed without use of the geological details but simply by defining the properties of the [[Mid-ocean ridge|ridges]], [[oceanic trench|trenches]] and [[transform faults]] involved, making some simplifying assumptions and applying simple velocity calculations. This assessment can generalise to most actual triple junction settings provided the assumptions and definitions broadly apply to the real Earth.

A stable junction is one at which the geometry of the junction is retained with time as the plates involved move. This places restrictions on relative velocities and plate boundary orientation. An unstable triple junction will change with time, either to become another form of triple junction (RRF junctions easily evolve to FFR junctions), will change geometry or are simply not feasible (as in the case of FFF junctions). The inherent instability of an FFF junction is believed to have caused the formation of the [[Pacific plate]] about 190 million years ago.<ref>{{Cite journal|last1=Boschman|first1=Lydian M.|last2=Hinsbergen|first2=Douwe J. J. van|date=2016-07-01|title=On the enigmatic birth of the Pacific plate within the Panthalassa Ocean|journal=Science Advances|volume=2|issue=7|pages=e1600022|doi=10.1126/sciadv.1600022|pmid=29713683|pmc=5919776|bibcode=2016SciA....2E0022B|issn=2375-2548|doi-access=free}}</ref>

By assuming that plates are rigid and that the Earth is spherical, [[Leonhard Euler]]'s theorem of [[Euler's rotation theorem|motion on a sphere]] can be used to reduce the stability assessment to determining boundaries and relative motions of the interacting plates. The rigid assumption holds very well in the case of [[oceanic crust]], and the radius of the Earth at the equator and poles only varies by a factor of roughly one part in 300 so the Earth approximates very well to a sphere.

[[Dan McKenzie (geophysicist)|McKenzie]] and [[W. Jason Morgan|Morgan]]<ref name="auto">Evolution of Triple Junctions, McKenzie, D. P., and Morgan, W. J., Nature, 224, 125 (1969)</ref> first analysed the stability of triple junctions using these assumptions with the additional assumption that the Euler poles describing the motions of the plates were such that they approximated to straight line motion on a flat surface. This simplification applies when the Euler poles are distant from the triple junction concerned. The definitions they used for R, T and F are as follows:

* R – structures that produce [[lithosphere]] symmetrically and perpendicular to the relative velocity of the plates on either side (this does not always apply, for example in the [[Gulf of Aden]]).
* T – structures that consume lithosphere from one side only. The relative velocity vector can be oblique to the plate boundary.
* F – [[active fault]]s parallel to the slip vector.

=== Stability criteria ===
{{Unreferenced section|date=August 2021}}

For a triple junction between the plates A, B and C to exist, the following condition must be satisfied:

:<sub>A</sub>v<sub>B</sub> + <sub>B</sub>v<sub>C</sub> + <sub>C</sub>v<sub>A</sub> = 0

where <sub>A</sub>v<sub>B</sub> is the relative motion of B with respect to A.

This condition can be represented in velocity space by constructing a velocity triangle ABC where the lengths AB, BC and CA are proportional to the velocities <sub>A</sub>v<sub>B</sub>, <sub>B</sub>v<sub>C</sub> and <sub>C</sub>v<sub>A</sub> respectively.

Further conditions must also be met for the triple junction to exist stably – the plates must move in a way that leaves their individual geometries unchanged. Alternatively the triple junction must move in such a way that it remains on all three of the plate boundaries involved.

[[Dan McKenzie (geophysicist)|McKenzie]] and [[W. Jason Morgan|Morgan]]<ref name="auto"/> demonstrated that these criteria can be represented on the same velocity space diagrams in the following way. The lines ab, bc and ca join points in velocity space which will leave the geometry of AB, BC and CA unchanged. These lines are the same as those that join points in velocity space at which an observer could move at the given velocity and still remain on the plate boundary. When these are drawn onto the diagram containing the velocity triangle these lines must be able to meet at a single point, for the triple junction to exist stably.

These lines necessarily are parallel to the plate boundaries as to remain on the plate boundaries the observer must either move along the plate boundary or remain stationary on it.

* For a [[Mid-ocean ridge|ridge]] the line constructed must be the perpendicular bisector of the relative motion vector as to remain in the middle of the ridge an observer would have to move at half the relative speeds of the plates either side but could also move in a perpendicular direction along the plate boundary.
* For a [[transform fault]] the line must be parallel to the relative motion vector as all of the motion is parallel to the boundary direction and so the line ab must lie along AB for a transform fault separating the plates A and B.
* For an observer to remain on a [[oceanic trench|trench]] boundary they must walk along the strike of the trench but remaining on the overriding plate. Therefore, the line constructed will lie parallel to the plate boundary but passing through the point in velocity space occupied by the overriding plate.

The point at which these lines meet, J, gives the overall motion of the triple junction with respect to the Earth.

Using these criteria it can easily be shown why the FFF triple junction is not stable: the only case in which three lines lying along the sides of a triangle can meet at a point is the trivial case in which the triangle has sides lengths zero, corresponding to zero relative motion between the plates. As faults are required to be active for the purpose of this assessment, an FFF junction can never be stable.