The popular conception of international waters is that there is no owner of them, so anyone can take advantage of them. Some propose that instead international waters are to be seen as owned by all the people of the planet. Hence, any particular person exploiting the natural resources of international waters should be taxed by the United Nations, any proxy of it, or some other international agency.
At present, property laws govern this issue. Natural resources are bound to the land and offshore natural resources are deemed to be owned by the state. Generally speaking, there is no tax on the consumption of natural resources. It might be difficult to implement such a tax.
The stumpage fee can also be deemed as a kind of natural resources consumption tax.