This sounds like an acoustic engineering problem, though the builder should take steps to reduce such extreme acoustic problems. Using infrared to determine what I think you called, bat number of the insulation has nothing to do with the sound blocking issues. Fiberglass and most other common insulation fill do little to absorb and control unwanted resonance through walls. Blown cellulose is an exception but that's not likely to be in your walls.

I’ve worked many years as a recording engineer, and have a studio. I’m not an acoustic engineer. I do know things like bass from a sub are very hard problems to stop. Because your wall seems to be nailed to a concrete separator, your neighbor’s sheetrock is acting like a microphone of sorts. Any resonance that vibrates their wall will be transferred through the hard connection made by the brick wall, and through the studs.

The only way to stop low and ambient frequency transfer is to have acoustic traps in the wall and /or sound absorbing material between the walls. For a subwoofer, which is hardest to block, the separator walls can’t be hard fastened together as one wall section.

There are a variety of materials that can greatly reduce the sound transfer and other unwanted resonances. You would have to apply them to the existing walls and sheetrock over the sound dampening material, or remove the sheet rock and use the correct materials with better installation methods. I chose the first method to reduce the problems just  to be tolerable, though the issue was not totally fixed.  The extra wall is hard fastened with a rubber-like material in between called sheetblok. Some sub frequencies still get through, but nothing else does. 

A link that could help (there are many( http://www.soundproofing101.com/

Good luck!
Ron