The stability of the boundaries between plates is dependent upon their relative velocity vectors. If a boundary is unstable it will exist only instantaneously and will immediately devolve into a stable configuration.
Figure 5.19a shows an unstable boundary between two plates where plate X is underthrusting plate Y at bc in a northeasterly direction and plate Y is underthrust-ing plate X at ab in a southwesterly direction. The boundary is unstable because a trench can only consume in one direction, so to accommodate these movements a dextral transform fault develops at b (Fig. 5.19b). This sequence of events may have occurred in the develop ment of the Alpine Fault of New Zealand (Fig. 5.19c), which is a dextral transform fault linking the Tonga-Kermadec Trench, beneath which Pacific lithosphere is underthrusting in a southwesterly direction, to a trench to the south of New Zealand where the Tasman Sea is being consumed in a northeasterly direction (McKenzie & Morgan, 1969).
A more complex and potentially unstable situation arises when three plates come into contact at a triple junction. Quadruple junctions are always unstable, and immediately devolve into a pair of stable triple junctions, as will be shown later.
The Earth's surface is covered by more than two plates, therefore there must be points at which three plates come together to form triple junctions. In a similar fashion to a boundary between two plates, the stability of triple junctions depends upon the relative directions of the velocity vectors of the plates in contact. Figure 5.20 shows a triple junction between a ridge (R), trench (T), and transform fault (F). From this figure it can be appreciated that, in order to be stable, the triple junction must be capable of migrating up or
down the three boundaries between pairs of plates. It is easier to visualize the conditions for stability of the triple junction if each boundary is first considered individually.
Figure 5.21a shows the trench, at which plate A is underthrusting plate B in a northeasterly direction. Figure 5.21b shows the relative movement between A and B in velocity space (Cox & Hart, 1986), that is, on a figure in which the velocity of any single point is represented by its north and east components, and lines joining two points represent velocity vectors. Thus, the direction of line AB represents the direction of relative movement between A and B, and its length is proportional to the magnitude of their relative velocity. Line ab must represent the locus of a point that travels up and down the trench. This line, then, is the locus of a stable triple junction. B must lie on ab because there is no motion of the overriding plate B with respect to the trench.
Now consider the transform boundary (Fig. 5.22a) between plates B and C, and its representation in velocity space (Fig. 5.22b). Again, line BC represents the relative velocity vector between the plates, but the locus of a point traveling up and down the fault, bc, is now in the same sense as vector BC, because the relative motion direction of B and C is along their boundary.
Finally, consider the ridge separating two plates A and C (Fig. 5.23a), and its representation in velocity space (Fig. 5.23b). The relative velocity vector AC is now orthogonal to the plate margin, and so the line ac now represents the locus of a point traveling along the ridge. The ridge crest must pass through the midpoint
of velocity vector CA if the accretion process is symmetric with plates A and C each moving at half the rate of accretion.
By combining the velocity space representations (Fig. 5.24), the stability of the triple junction can be determined from the relative positions of the velocity lines representing the boundaries. If they intersect at one point, it implies that a stable triple junction exists because that point has the property of being able to travel up and down all three plate margins. In the case of the RTF triple junction, it can be appreciated that a stable triple junction exists only if velocity line ac passes through B, or if ab is the same as bc, that is, the trench and transform fault have the same trend, as shown here. If the velocity lines do not all intersect at a single point the triple junction is unstable. The more general case of an RTF triple junction, which is unstable, is shown in Fig. 5.25.
Figure 5.26 illustrates how an unstable triple junction can evolve into a stable system, and how this evolution can produce a change in direction of motion. The TTT triple junction shown in Fig. 5.26a is unstable, as the velocity lines representing the trenches do not intersect at a single point (Fig. 5.26b). In time the system evolves into a stable configuration (Fig. 5.26c) in which the new triple junction moves northwards along trench AB. The dashed lines show where plates B and C would have been if they had not been subducted. The point X (Fig. 5.26a,c) undergoes an abrupt change in relative motion as the triple junction passes. This apparent change in underthrusting direction can be distinguished from a global change as it occurs at
different times and locations along the plate boundary. In order to be stable, the plate configuration shown in Fig. 5.26a must be as in Fig. 5.26d. When plotted in velocity space (Fig. 5.26e) the velocity lines then intersect at a single point.
McKenzie & Morgan (1969) have determined the geometry and stability of the 16 possible combina tions of trench, ridge, and transform fault (Fig. 5.27), taking into account the two possible polarities of trenches, but not transform faults. Of these, only the RRR triple junction is stable for any orientation of the ridges. This comes about because the associated velocity lines are the perpendicular bisectors of the triangle of velocity vectors, and these always intersect at a
Figure 5.26 (a) Triple junction between three trenches separating plates A, B, and C. (b) Its representation in velocity space, illustrating its instability. (c) The positions plates B and C would have reached if they had not been consumed are shown as dashed lines. (d) Stable configuration of a trench-trench-trench triple junction. (e) Its representation in velocity space. ((a) and (c) redrawn from McKenzie & Morgan, 1969, with permission from Nature 224,125-33. Copyright © 1969 Macmillan Publishers Ltd).
Figure 5.26 (a) Triple junction between three trenches separating plates A, B, and C. (b) Its representation in velocity space, illustrating its instability. (c) The positions plates B and C would have reached if they had not been consumed are shown as dashed lines. (d) Stable configuration of a trench-trench-trench triple junction. (e) Its representation in velocity space. ((a) and (c) redrawn from McKenzie & Morgan, 1969, with permission from Nature 224,125-33. Copyright © 1969 Macmillan Publishers Ltd).
single point (the circumcenter of the triangle). The FFF triple junction is never stable, as the velocity lines coincide with the vector triangle, and, of course, the sides of a triangle never meet in a single point. The other possible triple junctions are only stable for certain particular orientations of the juxtaposed plate margins.
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