(Land prices go up, as other taxes go down, as you can see on the Swiss/German border. Taxing land rents has no economic deadweight loss, since the supply of land is fixed.)
At the most crude, you could separate natural resources from the rest of the land rights, people already do that.
By the way if memory serves right Germany, which doesn't have general land taxes, already doesn't let you own mineral resources below your land by default. Would be interesting to see what effect that regulation already has on people prospecting.