Simple measures first
Unfortunately, arguments between neighbours are given coverage on the media when they result in horrendous situations involving court cases and even bodily harm. Most are dealt with much more simply and perhaps the easiest thing is just to tap on the door and mention that the noise is not acceptable. Make a joke of it if you can and certainly don't go in all guns blazing. If you live below someone in a flat and they seem to have a herd of elephant up there, why not treat them to a thick modern rug for the lounge or a hall runner if that is the problem area. Choose a neutral rug so it will go with any decor and they should be suitably grateful. Don't make trouble in the first instance should be your watchword.
Don't try tit for tat
If friendly approaches haven’t worked or if you feel it has got worse after your first attempt, don't try and drown the noise with some of your own. This can be used against you if things escalate so it is best to just behave as normal and don't start DIY projects at three in the morning just to get even. Without making an undue fuss about it, visit other neighbours to see if they are affected. If a group of you makes an approach, it might have more impact. If you did try buying your heavy footed neighbour a shaggy rug to try and minimise the noise, don't ask for it back if it doesn’t work – that will only make things worse.
There may be a reason
Find out first whether there is a reason for the noise. There may be problems on the domestic front or perhaps a child who is going through a phase. Although this won't stop the noise, a little understanding makes it all a little easier to bear.