Triple junction stability

Triple junction stability is a term used in geology. A triple junction is the point at which three plate boundaries meet. These boundaries can either be ridges (R), trenches (T) or transform faults (F). Triple junctions were once defined simply as the meeting point of three spreading ridges. This is because this sort of triple junction is very common, usually with one of the ridges failing (forming an aulacogen) and the other two continuing to open a new ocean. The meeting of 4 or more plates is also theoretically possible but junctions will only exist instantaneously.^[1]

Assessing stability

Definitions and assumptions

Triple junctions may be described and their stability assessed without use of the geological details but simply by defining the properties of the ridges, 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 situation.

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).

By assuming that plates are rigid and that the earth is spherical, Leonhard Euler’s theorem of 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.

McKenzie and Morgan^[2] 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 faults parallel to the slip vector.

Classification

McKenzie and Morgan determined that there were 16 types of triple junction theoretically possible, though several of these are speculative and have not necessarily been seen on earth. These junctions were classified firstly by the types of plate boundaries meeting - for example RRR, TTR, RRT, FFT etc. - and secondly by the relative motion directions of the plates involved. Some configurations such as RRR can only have one set of relative motions whereas TTT junctions may be classified into TTT(a) and TTT(b). These differences in motion direction affect the stability criteria.

McKenzie and Morgan claimed that of these 14 were stable with FFF and RRF configurations unstable, however, York^[3] later showed that the RRF configuration could be stable under certain conditions.

Stability criteria

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

_Av_B + _Bv_C + _Cv_A = 0

where _Av_B 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 _Av_B, _Bv_C and _Cv_A 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.

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 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 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.

Ridge-Ridge-Ridge junctions

A map of the Afar triangle, showing the East of Africa and the three ridges passing through the Red Sea, the Gulf of Aden and the East African Rift Valley.

A map of the Afar triangle in East Africa, another example of an RRR junction and the only triple junction on earth that can be seen above sea level.

An RRR junction is always stable using these definitions and therefore very common on earth, though in a geological sense ridge spreading is usually discontinued in one direction leaving failed rift zone. There are many examples of these present both now and in the geological past such as the South Atlantic opening with ridges spreading North and South to form the Mid-Atlantic Ridge, and an associated aulacogen in the Niger Delta region of Africa. RRR junctions are also common as rifting along three fractures at 120° is the best way to relieve stresses from uplift at the surface of a sphere; on earth stresses similar to these are believed to be caused by the mantle hotspots thought to initiate rifting in continents.

The stability of RRR junctions is demonstrated below - as the perpendicular bisectors of the sides of a triangle always meet at a single point, the lines ab, bc and ca can always be made to meet regardless of relative velocities.

Ridge-Trench-Fault junctions

RTF junctions are less common, an unstable junction of this type (an RTF(a)) is thought to have existed at roughly 12Ma at the mouth of the Gulf of California where the East Pacific Rise currently meets the San Andreas Fault zone.^[4] The Guadeloupe and Fallaron microplates were previously being subducted under the North American Plate and the northern end of this boundary met the San Andreas Fault. Material for this subduction was provided by a ridge equivalent to the modern East Pacific Rise slightly displaced to the west of the trench. As the ridge itself was subducted an RTF triple junction momentarily existed but subduction of the ridge caused the subducted lithosphere to weaken and ‘tear’ from the point of the triple junction. The loss of slab pull caused by the detachment of this lithosphere ended the RTF junction giving the present day ridge – fault system. An RTF(a) is stable if ab goes through the point in velocity space C, or if ac and bc are colinear.

Trench-Trench-Trench junctions

A TTT(a) junction can be found in central Japan where the Eurasian plate overrides the Philippine and Pacific plates, with the Philippine plate also overriding the Pacific. Here the Japan Trench effectively branches to form the Ryukyu and Bonia arcs. The stability criteria for this type of junction are either ab and ac form a straight line or that BC is parallel to CA.

References

↑ The Solid Earth, An Introduction to Global Geophysics, C.M.R Fowler
↑ Evolution of Triple Junctions, McKenzie, D. P., and Morgan, W. J., Nature, 224, 125 (1969)
↑ Evolution of Triple Junctions, Letters to Nature, Nature 244, 341 - 342 (10 August 1973)
↑ http://www.orfeus-eu.org/Announcements/workshop_utrecht/presentations/zhang.pdf

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