Oil and Mineral leases are highly fact dependent (meaning it takes a specific review of your particular contract to determine what your rights are).
Unfortunately, what happens with a lot of land owners that enter into these leases without the assistance of counsel is that the oil or mining company is permitted to extract their minerals or oil without any concern or compensation to the landowner for damage done to the land.
(People can literally sign a mineral lease and the next day have dump trucks and mining equipment tear up their backyard and field, and when the mining is done, they are left with a wasteland).
Regarding your specific lease, you will want to read it very, very carefully. If you do not find the information you are looking for, or if you find the matter to be confusing (these documents are very intricate so I do not mean this to be disrespectful - I truly believe they are written that way on purpose), I would recommend hiring a local attorney for a consultation (most attorneys will give you a consultation for free, or for reduced cost) to review the matter and help you identify your rights.
Even if you did manage to sign these rights away, a local attorney may be able to help you renegotiate your lease agreement with the company under a legal theory of "Waste" and help get you either some compensation, or at least ensure that they do not leave your property in shambles.
You can find local attorneys using the State and local Bar Association directories, or private directories such as www.AVVO.com; www.FindLaw.com; or www.Martindale.com (I personally find www.AVVO.com to be the most user friendly).