If I was obscenely wealthy I'd do the same for the seas and oceans, there's got to be so many fascinating wrecks out there as well as natural formations we know nothing about yet that sonar could pick up. Shipwrecks often have a limited lifespan for things to be preserved too, for example there's very little left of Lusitania's wreck that resembles a ship any more just a rusty debris field.
Saw Sarah Parcak speak on this at her book launch @ The Explorer's Club (https://www.amazon.com/Archaeology-Space-Future-Shapes-Past/...). The current, viable remote observation approach for shipwrecks is to use satellite photos of sand plume disturbances near beaches to hint at underwater features worth further exploration.
> If you were to discover an alien spaceship laying under the ice in Antartica
A fair few things this could reference, but I'll use it as an opportunity to recommend reading the least likely option which is the book Ice Station by Matthew Reilly.
One way to sort of do it would be to poke at how much 3dep has cost so far and extrapolate from there. Hard to figure that though, with it being an aggregation of a bunch of other programs.
The amount of stuff that seems to be hidden beneath forest and snow and mud and ocean is absurd.