Search for info on insulated concrete form. Really cool stuff, it's essentially styrofoam lego bricks that are filled with concrete. Tons of insulation, and wit

Search for info on insulated concrete form. Really cool stuff, it's essentially styrofoam lego bricks that are filled with concrete. Tons of insulation, and with 6" of concrete in all the outer walls as long as the windows are high quality it does a shockingly good job for noise insulation. No need to deal with the other issues of an underground house if all you want is noise insulation.