Past exam of the physics of the Earth as a Planet course of the University of Cambridge / 2016 / Paper 1 / 1 / d

At the north pole $\mathbf{r}=+R\hat{z}$, so the velocities reverse:The triangle still has side lengths 20, 48 and 52 mm/year. Across AB, A moves toward positive $y$ relative to B; across AC, A moves toward positive $x$ relative to C. Both boundaries therefore open and are spreading ridges, with full opening speeds 20 and 48 mm/year. Together with BC they form a ridge-ridge-transform triple junction.

In the symmetric normal-spreading model, a ridge's normal velocity is the mean normal velocity of its two plates. AB gives $U_y=(0-20)/2=-10$, and AC gives $U_x=(48+0)/2=24$. Their intersection lies on the BC transform velocity line:This northern junction is also instantaneously kinematically stable. The diagrams use the same fixed geocentric tangent axes at both poles; reversing velocities is not the same operation as reflecting a map drawn from an exterior observer's viewpoint.

Not every ridge-ridge-transform geometry works. For pure normal spreading, each ridge velocity line is the perpendicular bisector of the corresponding side of the plate velocity triangle. Their intersection is the triangle's circumcenter. A transform junction must also lie on the third side's line. A nondegenerate triangle's circumcenter lies there only at that side's midpoint, so the opposite angle is a right angle. Equivalently, $({\mathbf{v}}_B-{\mathbf{v}}_A)\cdot ({\mathbf{v}}_C-{\mathbf{v}}_A)=0$. The two ridge directions are then perpendicular, as they are here. RRF junctions are conditionally stable, with the right-angle ridge geometry in this symmetric pure-normal model; they are not all stable. Oblique or asymmetric accretion changes the velocity-line assumptions and must be specified separately.