The cooling mantle model explains the age-depth observations for seafloor younger than 80 million years.
The cooling plate model explains the age-depth observations best for seafloor older that 20 million years.
In addition, the cooling plate model explains the almost constant depth and heat flow observed in very old seafloor and lithosphere.
In practice it is convenient to use the solution for the cooling mantle model for an age-depth relationship younger than 20 million years.
The first theories for seafloor spreading in the early and mid twentieth century explained the elevations of the mid-ocean ridges as upwellings above convection currents in Earth's mantle.
[1][2] The next idea connected seafloor spreading and continental drift in a model of plate tectonics.
In 1969, the elevations of ridges was explained as thermal expansion of a lithospheric plate at the spreading center.
[5] These observations could not be explained by the earlier 'cooling mantle model' which predicted increasing depth and decreasing heat flow at very old ages.
Depth is measured to the top of the ocean crust, below any overlying sediment.
The age-depth relation can be modeled by the cooling of a lithosphere plate[3][6][7][8][5] or mantle half-space in areas without significant subduction.
The result of the cooling mantle model is that seafloor depth is predicted to be proportional to the square root of its age.
The simple result is that the ridge height or seabed depth is proportional to the square root of its age.
[4] In all models, oceanic lithosphere is continuously formed at a constant rate at the mid-ocean ridges.
Due to its continuous creation, the lithosphere at x > 0 is moving away from the ridge at a constant velocity
The system is assumed to be at a quasi-steady state, so that the temperature distribution is constant in time, i.e.
is given by the error function: Due to the large velocity, the temperature dependence on the horizontal direction is negligible, and the height at time t (i.e. of sea floor of age t) can be calculated by integrating the thermal expansion over z: where
is the effective volumetric thermal expansion coefficient, and h0 is the mid-ocean ridge height (compared to some reference).
due to isostasic effect of the change in water column height above the lithosphere as it expands or contracts.
By substituting the parameters by their rough estimates into the solution for the height of the ocean floor
measured from the ocean surface) we can find that: The depth predicted by the square root of seafloor age found by the 1974 cooling mantle derivation[4] is too deep for seafloor older than 80 million years.
The difference is in requiring a thermal boundary at the base of a cooling plate.
Analysis of depth versus age and depth versus square root of age data allowed Parsons and Sclater[5] to estimate model parameters (for the North Pacific): Assuming isostatic equilibrium everywhere beneath the cooling plate yields a revised age-depth relationship for older sea floor that is approximately correct for ages as young as 20 million years: Thus older seafloor deepens more slowly than younger and in fact can be assumed almost constant at ~6400 m depth.
Their plate model also allowed an expression for conductive heat flow, q(t) from the ocean floor, which is approximately constant at
beyond 120 million years: Parsons and Sclater concluded that some style of mantle convection must apply heat to the base of the plate everywhere to prevent cooling down below 125 km and lithosphere contraction (seafloor deepening) at older ages.
[5] Morgan and Smith[10][11] showed that the flattening of the older seafloor depth can be explained by flow in the asthenosphere below the lithosphere.
The age-depth-heat flow relationship continued to be studied with refinements in the physical parameters that define ocean lithospheric plates.
[12][13][14] The usual method for estimating the age of the seafloor is from marine magnetic anomaly data and applying the Vine-Matthews-Morley hypothesis.
Other ways include expensive deep sea drilling and dating of core material.
This results in global eustatic sea level rise (fall) because the Earth is not expanding.
Two main drivers of sea level variation over geologic time are then changes in the volume of continental ice on the land, and the changes over time in ocean basin average depth (basin volume) depending on its average age.