Geos 322 Introduction to Geophysics
SPRING 2003
Vector Rules for Plate Kinematics
A. A vector is an arrow showing direction and magnitude (in this case, the magnitude is plate
velocity in cm/yr).
B. To add two vectors, place the tail of one vector at the head of the other vector. The sum of
these two vectors is the vector from the tail of the first to the head of the second. To do
subtraction, reverse the direction of the negative vector and add as before.
Numerically, this process is the same as adding the x-components of the two vectors to get
the new x-component of the sum and similarly for the y-components, e.g., v1 = [2, 3], v2 =
[4, 1], then v1 + v2 = v3 = [6, 4].
C. In plate kinematics, the relative motion of plate A with respect to plate B is represented by
BvA and plate B with respect to A by AvB. When adding plate velocity vectors, the inside
subscripts should match and the sum represents the relative motion of the outside subscript.
e.g., AvB + BvC = AvC
also, the following should be obvious, AvB + BvA = AvA = 0. Why?
Plotting Plates in Velocity-Space Diagrams
Step 1: Put a point on the plot for plate A. Everything is relative, so you have to start
somewhere (do this in pencil; you may have to move things later).
Step 2: Assuming plate A is stationary, determine the relative motion of plate B with respect to
plate A and plot the point in the same relative direction. For example, consider a case where
plate A on the left is separated by a ridge from plate B on the right. For a fixed plate A, plate B is
moving to the right at twice the spreading rate, (e.g., 4 cm/yr). So, place a point B on the graph 4
units to the right of point A. In this example, if plate A and B are separated by a trench, then for
fixed plate A, plate B is moving at the convergence velocity (e.g., 3 cm/yr) to the left. In this
case, place point B on the graph 3 units to the left of point A.
IMPORTANT NOTE: In velocity space, the relative positions of the points representing the
plates may or may not reflect the relative geographic positions of the plates. In both examples
above, plate A is to the left of plate B. In the first (ridge) case, point B is plotted right of point A,
but in the second (trench) case, point B is plotted to the left of point A.
Step 3: Draw a line between points A and B. Verify the relative plate motion vectors by
drawing an arrow parallel to the line AB. Then BvA should have its arrowhead at point A and AvB
should have its head at B.
Plate Boundary Rules
Rule #1: Ridges
Mid-ocean ridges are represented in velocity space by the perpendicular bisector of the line
between the two points representing the two plates.
Rule #2: Transforms
Transform faults are represented in vector space by a line going through both points representing
the two plates. The line is parallel to the map view of the transform.
Rule #3: Trenches
Subduction zones (trenches) are represented by a line parallel to the strike of the trench that goes
through the point representing the upper plate (trench teeth point towards the upper plate).
Triple Junctions
A triple junction is where three plates meet at a point, and many combinations are possible, but
not all are “stable”. Stability refers to a three-plate system geometry that can operate for an
interval of time without changing the current geometry.
Rule #1: The velocity triangle of three plates must close (the three vectors form a closed
triangle).
i.e., AvB + BvC + CvA = AvA = 0
Rule #2: For an RRR (ridge-ridge-ridge) triple junction the lines representing the three ridges
must intersect at a point for the triple junction to be stable. The intersection point represents the
triple junction, and the vectors from that point to the points representing the plates show the
motion of the plates with respect to the triple junction, or vice versa.
Rule #3: This is a generalization of rule #2. For any combination of plate boundaries involved
in a triple junction, the lines representing those boundaries on a vector-space diagram must
intersect at a point for that triple junction to be stable. The intersection point represents the triple
junction in the diagram, and vectors between the triple junction point and the points representing
the plates give the relative motion between the plates and the triple junction.
Plotting Steps for Triple Junctions
When plotting three plates on a velocity-space diagram, start with two plates and plot them using
the rules presented earlier. Usually plates separated by a ridge or transform are the easiest to
visualize. Assume one is fixed (A) and plot the other (B) with respect to A. Next, choose
another pair of plates (B and C). Assume B is fixed, and plot C with respect to B. Finally,
choose the last pair (A and C) and repeat the process. Does the triangle close? If so, this is a
plausible (but perhaps unstable) configuration.
NOTE: In some cases, only two relative velocities will be given, in that case, plot the two plates
that are involved and close the triangle and get the velocity information on the third plate
boundary from the graph.
Next, draw the lines ab, bc, and ac representing the three plate boundaries on the diagram. Don’t
forget to use the appropriate rule for ridges, transforms, and trenches. If the three lines intersect
in a point, then this configuration is stable.
NOTE: Unstable triple junctions can exist, but only for a moment in geologic time.