The subsidence of the sea floor is generally considered a consequence of its passive cooling and densifying since its formation at the ridge and is therefore regarded as a function of lithospheric age only. However, the lithosphere is defined as the thermal boundary layer of mantle convection, which should thus determine its structure. We examined the evolution of the lithosphere structure and depth along trajectories representative of the underlying mantle flow. We show that along these flow lines, the sea-floor depth varies as the square root of the distance from the ridge (as given by the boundary-layer equation) along the entire plate, without any flattening. Contrary to previous models, no additional heat supply is required at the base of the lithosphere.