= Solution
\b[Choose a common horizontal <compensation depth> beneath the deepest cooling-induced <density> anomaly, within <mantle> that can relax pressure differences over the timescale considered.] In a normal oceanic plate model, this means below the old plate's thermal <lithosphere>, not at the base of the approximately 7 km thick <oceanic crust>.
The reason is that cooling changes <density> through both <crust> and <lithospheric mantle>. A datum at the <Mohorovičić discontinuity> would omit most of the changing column <mass>. A different datum for each age would also compare unlike columns. Once the common datum is sufficiently deep, extending it farther into laterally uniform <mantle> adds the same <mass> per unit area to each column and does not change the predicted relative subsidence.
There is no unique number fixed by the question. For an illustrative <oceanic plate cooling model> with a thermal thickness about 100–125 km, a common datum beneath that layer, of order 150–200 km below sea level, is a defensible choice provided the model has no substantial lateral <density> anomaly there. These are model choices, not measured universal boundaries. In a <half-space cooling model>, use the oldest age $t_{\max}$ to choose a practical cutoff: $z_c\gtrsim4\sqrt{\kappa t_{\max}}$ makes the remaining <temperature> anomaly less than about 0.5% of its surface contrast. For $\kappa=10^{-6}\,\mathrm{m^2\,s^{-1}}$ and $t_{\max}=100$ million years, this is about 225 km. A half-space model has no mathematically sharp finite thermal base.
Finally, equal column <mass> is the local, approximately constant-<gravitational acceleration> representation of equal <pressure> at the datum. A weak <asthenosphere> permits pressure relaxation through slow solid-state <material creep>; it need not be liquid. Short-wavelength loads, <lithospheric flexure> or <dynamic topography> can violate local column-by-column <isostasy>, requiring a more complete mechanical model.
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