[Anthony]

That depends a bit on what you know about the mysteries, and what actual oddities you run into.

Step one is probably aerial surveying -- ordinary geological surveying for the natural causes of the shapes of the land, and an archeology team for evidence of human (or inhuman) activity. As an oilman, you can probably handle the geological survey with people who already work for you, but you'll probably need to recruit archeologists. This is unlikely to be hard.

Step two depends on what you find, but unless something really stands out, it's probably just repeating the same types of surveys on the ground.

Step three is calling in specialists for the weird stuff you find. What that will be depends on what weird stuff you find.