If the Law of the Sea says all on our continental shelf is ours, then all on that shelf is ours regardless of whether we have troops there or not. Inversely, all that is not on our shelf isn't ours, no matter how many troops we have there.
Which is why a survey is being done so bluster does dominate over quiet Canada. Exactly what a contienntal shelf is not always clearly defined O saw on one TV show, it can get hazy. Science can do a great deal, but claiming land is a political act.
We always seem to be responding to Russian "bombers", howome they are never "fighters"? Without a presence up north, we look meek, and a presence means bases of the coast guard variety for a start.