= Solution
\b[I would not assign the <lunar mare> an automatic terrestrial 100–125 km compensation level. For present-day mare basins, a local equal-column-mass model may have no physically valid <compensation depth>; first test whether <lithospheric flexure> supports the load.] For ancient thermally driven subsidence that did relax, choose a common datum beneath the cooling layer in deformable <lunar mantle> appropriate to that epoch.
The <Moon> is smaller than <Earth> and has lost a larger fraction of its original heat. Its cold, mechanically strong outer shell can be much thicker relative to its radius than the terrestrial oceanic <lithosphere>. <Lunar mare> <basalts> filled pre-existing impact basins: their loading, basin excavation, mantle uplift, cooling and the evolving strength of the lithosphere all matter. A thick <elastic lithosphere> can support lateral <stress> differences, so equal column <mass> need not hold even after a long time. The strong <gravity anomalies> of lunar <mascons>, measured by <GRAIL>, are evidence that the present mare-basin system is not everywhere locally compensated.<NASA's GRAIL Mission Solves Mystery of Moon's Surface Gravity by National Aeronautics and Space Administration>{ref}
For an explicitly assumed ancient relaxed thermal model, estimate its thermal penetration depth from <thermal diffusivity> and the elapsed cooling time, infer the contemporaneous mechanical lid from <gravity-topography admittance> or basin deformation, and place $z_c$ below that layer where lateral <pressure> anomalies relax. For example, a hypothetical several-hundred-kilometre-thick lid requires a deeper datum than that lid, not the shallow <crust-mantle boundary>. The paper supplies neither an epoch-specific thermal model nor a load wavelength, so a unique kilometre value is not determined. If the chosen datum is a substantial fraction of the lunar radius, spherical geometry and radial variation in <gravity> must replace the flat, constant-gravity column approximation.
\b[Does the Moon have an <asthenosphere>? Not a demonstrated shallow, globally connected Earth-like layer underlying mobile plates; but “no weak or partially molten mantle anywhere, ever” is too strong.] <Apollo lunar seismology> indicates a cold outer interior and more attenuating deep regions. Reanalyses support a deep low-velocity or partially molten region near the <lunar core>, while <lunar laser ranging> and tidal <Love numbers> constrain deep deformability and <tidal dissipation>. Such a deep weak region is sometimes called a lunar <asthenosphere>; it is not automatically the correct local compensation surface for a mare load.<Seismic detection of the layers of the lunar core by Renee C. Weber and colleagues>{ref}
The inferred melt fraction and distribution remain model dependent: <Dissipation at tidal and seismic frequencies in a melt-free Moon by Francis Nimmo and others> demonstrates that much of the dissipation can also be explained by hot solid-state <anelasticity>, although its model does not reproduce every frequency-dependent constraint. The <Moon> was hotter during mare emplacement and could relax loads differently then. \b[Choose the datum from the relevant thermal and mechanical history, or use a flexural model when local <isostasy> fails.]
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