Triple junction stability
Encyclopedia
Triple junction stability is a term used in geology
Geology
Geology is the science comprising the study of solid Earth, the rocks of which it is composed, and the processes by which it evolves. Geology gives insight into the history of the Earth, as it provides the primary evidence for plate tectonics, the evolutionary history of life, and past climates...

. A triple junction
Triple junction
A triple junction is the point where the boundaries of three tectonic plates meet. At the triple junction a boundary will be one of 3 types - a ridge, trench or transform fault - and triple junctions can be described according to the types of plate margin that meet at them...

 is the point at which three plate boundaries
Plate tectonics
Plate tectonics is a scientific theory that describes the large scale motions of Earth's lithosphere...

 meet. These boundaries can either be ridges
Mid-ocean ridge
A mid-ocean ridge is a general term for an underwater mountain system that consists of various mountain ranges , typically having a valley known as a rift running along its spine, formed by plate tectonics. This type of oceanic ridge is characteristic of what is known as an oceanic spreading...

 (R), trenches
Oceanic trench
The oceanic trenches are hemispheric-scale long but narrow topographic depressions of the sea floor. They are also the deepest parts of the ocean floor....

 (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
Aulacogen
In geology, an aulacogen is a failed arm of a triple junction of a plate tectonics rift system. A triple junction beneath a continental plate initiates a three way breakup of the continental plate. As the continental break-up develops one of the three spreading ridges typically fails or stops...

) 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.

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
Mid-ocean ridge
A mid-ocean ridge is a general term for an underwater mountain system that consists of various mountain ranges , typically having a valley known as a rift running along its spine, formed by plate tectonics. This type of oceanic ridge is characteristic of what is known as an oceanic spreading...

, trenches
Oceanic trench
The oceanic trenches are hemispheric-scale long but narrow topographic depressions of the sea floor. They are also the deepest parts of the ocean floor....

 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
Leonhard Euler
Leonhard Euler was a pioneering Swiss mathematician and physicist. He made important discoveries in fields as diverse as infinitesimal calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion...

’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
Oceanic crust
Oceanic crust is the part of Earth's lithosphere that surfaces in the ocean basins. Oceanic crust is primarily composed of mafic rocks, or sima, which is rich in iron and magnesium...

, 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
W. Jason Morgan
William Jason Morgan is an American geophysicist who has made seminal contributions to the theory of plate tectonics and geodynamics...

 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
    Lithosphere
    The lithosphere is the rigid outermost shell of a rocky planet. On Earth, it comprises the crust and the portion of the upper mantle that behaves elastically on time scales of thousands of years or greater.- Earth's 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
    Gulf of Aden
    The Gulf of Aden is located in the Arabian Sea between Yemen, on the south coast of the Arabian Peninsula, and Somalia in the Horn of Africa. In the northwest, it connects with the Red Sea through the Bab-el-Mandeb strait, which is about 20 miles wide....

    ).
  • 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
Plate tectonics
Plate tectonics is a scientific theory that describes the large scale motions of Earth's lithosphere...

 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 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:

AvB + BvC + CvA = 0

where AvB 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 AvB, BvC and CvA 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
    Mid-ocean ridge
    A mid-ocean ridge is a general term for an underwater mountain system that consists of various mountain ranges , typically having a valley known as a rift running along its spine, formed by plate tectonics. This type of oceanic ridge is characteristic of what is known as an oceanic spreading...

     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
    Transform fault
    A transform fault or transform boundary, also known as conservative plate boundary since these faults neither create nor destroy lithosphere, is a type of fault whose relative motion is predominantly horizontal in either sinistral or dextral direction. Furthermore, transform faults end abruptly...

     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
    Oceanic trench
    The oceanic trenches are hemispheric-scale long but narrow topographic depressions of the sea floor. They are also the deepest parts of the ocean floor....

     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

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
Rift
In geology, a rift or chasm is a place where the Earth's crust and lithosphere are being pulled apart and is an example of extensional tectonics....

 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
Mid-Atlantic Ridge
The Mid-Atlantic Ridge is a mid-ocean ridge, a divergent tectonic plate boundary located along the floor of the Atlantic Ocean, and part of the longest mountain range in the world. It separates the Eurasian Plate and North American Plate in the North Atlantic, and the African Plate from the South...

, and an associated aulacogen
Aulacogen
In geology, an aulacogen is a failed arm of a triple junction of a plate tectonics rift system. A triple junction beneath a continental plate initiates a three way breakup of the continental plate. As the continental break-up develops one of the three spreading ridges typically fails or stops...

 in the Niger Delta
Niger Delta
The Niger Delta, the delta of the Niger River in Nigeria, is a densely populated region sometimes called the Oil Rivers because it was once a major producer of palm oil...

 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
Hotspot (geology)
The places known as hotspots or hot spots in geology are volcanic regions thought to be fed by underlying mantle that is anomalously hot compared with the mantle elsewhere. They may be on, near to, or far from tectonic plate boundaries. There are two hypotheses to explain them...

 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
Gulf of California
The Gulf of California is a body of water that separates the Baja California Peninsula from the Mexican mainland...

 where the East Pacific Rise
East Pacific Rise
The East Pacific Rise is a mid-oceanic ridge, a divergent tectonic plate boundary located along the floor of the Pacific Ocean. It separates the Pacific Plate to the west from the North American Plate, the Rivera Plate, the Cocos Plate, the Nazca Plate, and the Antarctic Plate...

 currently meets the San Andreas Fault
San Andreas Fault
The San Andreas Fault is a continental strike-slip fault that runs a length of roughly through California in the United States. The fault's motion is right-lateral strike-slip...

 zone. The Guadeloupe and Fallaron microplates were previously being subducted under the North American Plate
North American Plate
The North American Plate is a tectonic plate covering most of North America, Greenland, Cuba, Bahamas, and parts of Siberia, Japan and Iceland. It extends eastward to the Mid-Atlantic Ridge and westward to the Chersky Range in eastern Siberia. The plate includes both continental and oceanic crust...

 and the northern end of this boundary met the San Andreas Fault
San Andreas Fault
The San Andreas Fault is a continental strike-slip fault that runs a length of roughly through California in the United States. The fault's motion is right-lateral strike-slip...

. Material for this subduction was provided by a ridge equivalent to the modern East Pacific Rise
East Pacific Rise
The East Pacific Rise is a mid-oceanic ridge, a divergent tectonic plate boundary located along the floor of the Pacific Ocean. It separates the Pacific Plate to the west from the North American Plate, the Rivera Plate, the Cocos Plate, the Nazca Plate, and the Antarctic Plate...

 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
Slab pull
The Slab pull force is a tectonic plate force due to subduction. Plate motion is partly driven by the weight of cold, dense plates sinking into the mantle at trenches. This force and the slab suction force account for most of the overall force acting on plate tectonics, and the ridge push force...

 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
Eurasian Plate
The Eurasian Plate is a tectonic plate which includes most of the continent of Eurasia , with the notable exceptions of the Indian subcontinent, the Arabian subcontinent, and the area east of the Chersky Range in East Siberia...

 overrides the Philippine
Philippine Plate
The Philippine Sea Plate is a tectonic plate comprising oceanic lithosphere that lies beneath the Philippine Sea, to the east of the Philippines...

 and Pacific plate
Pacific Plate
The Pacific Plate is an oceanic tectonic plate that lies beneath the Pacific Ocean. At 103 million square kilometres, it is the largest tectonic plate....

s, with the Philippine plate also overriding the Pacific. Here the Japan Trench
Japan Trench
__notoc__The Japan Trench is an oceanic trench, a part of the Pacific Ring of Fire, in the floor of the northern Pacific Ocean off northeast Japan. It extends from the Kuril Islands to the Bonin Islands and is at its deepest. It is an extension of the Kuril-Kamchatka Trench to the north and the...

 effectively branches to form the Ryuku and Bonia arcs
Volcanic arc
A volcanic arc is a chain of volcanoes positioned in an arc shape as seen from above. Offshore volcanoes form islands, resulting in a volcanic island arc. Generally they result from the subduction of an oceanic tectonic plate under another tectonic plate, and often parallel an oceanic trench...

. The stability criteria for this type of junction are either ab and ac form a straight line or that BC is parallel to CA.
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