In the mantle half-space model, the seabed height is determined by the oceanic lithosphere and mantle temperature, due to thermal expansion. The simple result is that the ridge height or ocean depth is proportional to the square root of its age. Oceanic lithosphere is continuously formed at a constant rate at the mid-ocean ridges. The source of the lithosphere has a half-plane shape ("x" = 0, "z" < 0) and a constant temperature "T"1. Due to its continuous creation, the lithosphere at "x" > 0 is moving away from the ridge at a constant velocity "v", which is assumed large compared to other typical scales in the problem. The temperature at the upper boundary of the lithosphere ("z" = 0) is a constant "T"0 = 0. Thus at "x" = 0 the temperature is the Heaviside step function formula_1. The system is assumed to be at a quasi-steady state, so that the temperature distribution is constant in time, i.e. formula_2