<P> To first approximation, sea floor global topography in areas without significant subduction can be estimated by the half - space model . In this model, the seabed height is determined by the oceanic lithosphere temperature, due to thermal expansion . 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. 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 . Thus at x = 0 the temperature is the Heaviside step function T 1 ⋅ Θ (− z) (\ displaystyle T_ (1) \ cdot \ Theta (- z)). Finally, we assume the system is at a quasi-steady state, so that the temperature distribution is constant in time, i.e. T = T (x, z). </P> <P> By calculating in the frame of reference of the moving lithosphere (velocity v), which have spatial coordinate x' = x-vt, we may write T = T (x', z, t) and use the heat equation: ∂ T ∂ t = κ ∇ 2 T = κ ∂ 2 T ∂ 2 z + κ ∂ 2 T ∂ 2 x ′ (\ displaystyle (\ frac (\ partial T) (\ partial t)) = \ kappa \ nabla ^ (2) T = \ kappa (\ frac (\ partial ^ (2) T) (\ partial ^ (2) z)) + \ kappa (\ frac (\ partial ^ (2) T) (\ partial ^ (2) x'))) where κ (\ displaystyle \ kappa) is the thermal diffusivity of the mantle lithosphere . </P> <P> Since T depends on x' and t only through the combination x = x ′ + v t (\ displaystyle x = x'+ vt), we have: ∂ T ∂ x ′ = 1 v ⋅ ∂ T ∂ t (\ displaystyle (\ frac (\ partial T) (\ partial x')) = (\ frac (1) (v)) \ cdot (\ frac (\ partial T) (\ partial t))) </P> <P> Thus: ∂ T ∂ t = κ ∇ 2 T = κ ∂ 2 T ∂ 2 z + κ v 2 ∂ 2 T ∂ 2 t (\ displaystyle (\ frac (\ partial T) (\ partial t)) = \ kappa \ nabla ^ (2) T = \ kappa (\ frac (\ partial ^ (2) T) (\ partial ^ (2) z)) + (\ frac (\ kappa) (v ^ (2))) (\ frac (\ partial ^ (2) T) (\ partial ^ (2) t))) </P>

Where would you go for a great example of initiation of sea floor spreading