Three-dimensional temperature structure of a ridge-transform-ridge system

We have solved the problem of three-dimensional heat transfer by conduction and material transport within a ridge-transform-ridge system. The boundary conditions are those of a finite plate with temperatures fixed at the top and bottom. We do not solve for the pattern of flow, so must arbitrarily describe the material transport. Within triangular regions beneath the spreading centers, flow is assumed to be vertical and at constant velocity, with the volume of upwelling matching the volume of horizontal transport by the plates. The steady state solution is approached by repeated finite steps in time, each involving two stages. First, to represent material transport, temperatures in the grid of points are shifted horizontally and/or vertically to the point at which the associated particle would arrive given the time period and assumed velocity field. Second, a three-dimensional Fourier Transform technique is used to calculate the cooling which would occur in the static case during the same period.

We find that the geometry of flow in the upwelling region, here parameterized by velocity of upwelling or width of the upwelling zone, is more important than spreading rate in determining the temperature structure. The results indicate that conductive cooling cannot alone account for deepening of the median valley towards the fracture zone. For a 10 m.y. offset on the transform fault, conductive cooling across the fracture zone to the older lithosphere affects the upwelling material only to a distance of about 10 km from the fault, in contrast to the deepening of the median valley over several tens of kilometers observed on the Mid-Atlantic Ridge.