I think that one was done after the drummer lost his arm, and he uses mostly electronic drums. IN that case the sound is set through the software in the drum set, and run straight into the PA.
With acoustic drums you can still get a good heavy sound, Phil Collins has done it for a long time. It's partially in the way the drums are tuned, and assisted by the PA. If you know how to tune drums, they can be tuned for a good fat sound to begin with, and many drummers don't really know that involves the bottom head more than the top one. If you don't tune the bottom head so it reverberates against the percussion effect of the top one, you're not getting the sound the drums can produce.
Then you adjust the EQ in the PA. To get rid of the "cardboard" sound of a bass drum, add some treble and mids, and sometimes you have to cut the bass back a little. Ditto for the toms. Every drum has to have a mic, you can't just use two for ambient sound. In many cases that means a dozen mics or more, and you might consider a separate PA just for the drums, and send a line signal to one channel of the main PA. Also add some echo, and play with mic placement. Drums are tricky to adjust, but once you get the hang of it your setup can be reproduced with a little patience. If you use a PA just for drums, use the EQ on that board, run the EQ in that channel of the main board flat, tweak a little if you need to.
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