= Solution
\b[Cooling makes the <oceanic lithosphere> denser and contracts it; <isostatic adjustment> therefore lowers the seafloor.] The cooling layer includes substantial <mantle>, not just the approximately fixed-thickness igneous <oceanic crust>.
New plate near a <spreading ridge> is hot and relatively buoyant. As it moves away, conductive cooling penetrates more deeply, and material formerly in the hot <asthenosphere> becomes part of the colder <thermal boundary layer>. To first order,
$$
\delta\rho(z,t)=\rho_m\alpha\,[T_m-T(z,t)],
$$
where $\alpha$ is the volumetric <thermal expansion coefficient>, $\rho_m$ a reference mantle <density>, $T_m$ the hot reference <temperature>, and $t$ plate age. A positive depth-integrated <density> anomaly makes the column negatively buoyant relative to the ridge column. <Isostasy> is restored by downward displacement and mantle redistribution; cold <rock> also occupies less <volume>.
At a fixed sufficiently deep datum, deepening the seafloor by $\Delta d$ removes an equivalent thickness of <rock> from the column and replaces it with less dense <seawater>. In the usual constant-property approximation this gives
$$
(\rho_m-\rho_w)\Delta d\simeq
\int_0^{z_c}\delta\rho(z,t)\,dz,
$$
where $\rho_w$ is <seawater> <density> and $z_c$ lies below the relevant thermal anomaly. This explains why contraction alone and water-loaded seafloor subsidence are not identical numerical quantities.
For a <half-space cooling model>,
$$
T(z,t)=T_s+(T_m-T_s)\operatorname{erf}\!\left(\frac{z}{2\sqrt{\kappa t}}\right),
$$
so <integration> yields
$$
\boxed{\Delta d(t)=\frac{2\rho_m\alpha(T_m-T_s)}{\rho_m-\rho_w}\sqrt{\frac{\kappa t}{\pi}}.}
$$
Here $\kappa$ is <thermal diffusivity> and $z$ is measured downward from the surface of the thermal model. The leading <oceanic thermal subsidence> is proportional to $\sqrt t$. A finite <oceanic plate cooling model> limits this growth at old ages. <Sediment loading>, <dynamic topography>, anomalous <crust> thickness and hydrothermal heat transport can produce departures from the simple relation.<An analysis of the variation of ocean floor bathymetry and heat flow with age by Barry Parsons and John G. Sclater>{ref}
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