Like others have said, I think you are better off using a thin (3/8" - 1/2") plywood top before installing a rigid foam base (3/4" or 1") from a big box store w/o a foil backing.
The foam does not dramatically reduce noise, but it does seem quieter than plain plywood. In addition, it provides a nice medium for simply gluing and pressing in scenics like telephone poles and trees on your layout rather than having to drill through plywood.
I have always used a construction tube adhesive (like Liquid N**ls) to adhere the foam to the plywood and placed heavy items (books, tools, etc.) on top to weigh it down overnight. I use a utility knife and a very sharp 10" commercial chef's knife to cut and trim the foam. I also tape any seams with duct tape which seems to hold up very well. You could also use a flexible joint compound or similar product to fill in the seams, but I haven't found it necessary.
Depending on what you are looking for, I typically paint the foam with an earth brown latex paint in sections and sprinkle with green and yellow fine turf while still wet to hold the turf in place and, when dry, brush very lightly with a dry utility paint brush to spread the turf around and remove any blotchiness and then spray with a high hold hair spray to keep the turf in place.
Pic of latest project attached.
