Balogney. I own the mineral and water rights to my property and I have no technological ability to drill for oil. Nobody may enter my property and drill for oil simply because they own the technology. That would be theft. What you and Piekoff are advocating is a justification for theft which has no basis in property rights but an imagined absence of property rights.
If the owner owns the land for farming, industrial or recreational use, characteristic of real estate ownership in the West, his use of the property will be disrupted by the arrival of oil drilling equipment and such. Thus the common law develops the concept of the real estate as a cone extending from the center of the earth through the boundary and into the outer space, which implies the ownership of the mineral deposits underneath.
When violations of the cone occur in a way that does not disrupt the established use of the land, the common law quickly relaxes the rules of tresspass. Since an airplane at cruising altitude does not interfere with any land use, air travel across property lines does not constitute a tresspass; and conversely, one cannot claim celestial objects by choosing a moment in time when they pass through one's real estate cone and are not claimed by an equally enterpising neighbor.
If oil is discovered under an Arab dwelling, then, of course, in equity the dweller claims the oil regardless of his technological abilities. Unable to exploit the find, he may be willing to sell his oil rights, but that is a different story.
A typical for the Middle East scenario is that oil is discovered in the desert. While a royalty, or a government of the country may have a technical claim on the desert, there is no natural law provision for such claim, because the oil exploration in the desert will not disrupt any activity there.
This is an interesting instance of property rights refracting differently across civilizations.