EARTH
In the literature: open
How much water is stored in Earth's mantle and core?
In plain words
The oceans hold only part of Earth's water; more is locked in minerals deep inside, and hydrogen may also be dissolved in the iron core. Estimates of the hidden amount vary from less than one ocean to many.
Precise statement
Determine the bulk-Earth hydrogen inventory expressed in ocean masses (1 ocean is about $1.4e24\,\mathrm{g}$ of water), split among oceans, mantle and core. Mantle estimates range from below one to a few oceans and core estimates up to tens of oceans equivalent depending on metal-silicate partitioning. An answer is each reservoir's content with uncertainty below a factor of two.
What would settle it
Experimental hydrogen partitioning at core-formation conditions plus mantle water mapping from electrical conductivity and seismic attenuation.