I had the same issue when i used my Z800. I noticed the same with the Z820 but not as much as with the Z800. Once i removed all spinning HDD´s in the Z800 the problem got better but not solved. (I had three spinning HDD´s and one SSD.) If you put your hand on the top of the Z800 you can feel how it "vibrates". I then replaced all chassi fans with the quieter ones from the Z820 and the result was much better, but not good.
The chassi fans in the Z800 are/were really bad and each one sounded like a propeller airplane. The two front fans were easy to get but the combined rear chassi fans were harder to get since HP did not like sell me Z820 fans for use in a Z800, but i eventually got them to sell me the Z820 fans.It should not be a problem today.
(Part numer, Z820 rear fans: 683764-001)
(Part number, Z820 front fans: 684576-001 or even cheaper order two of these: 684025-001)
Replacing the fans will help for the "airplane-propeller-issue", but it will not remove the low level noise.
I bought a Z440 (G1X59EA) a year ago and was positively shocked by two things:
1. The Z440 is dead quiet when i use it.
2. It outperformed the Z800 in all applications i use but Adobe After Effects. But since i only use Adobe After Effects for short compositions a couple of seconds slower per render was not an issue for me.
I had two processors in the Z800, watercooling, original chassi fans. The watercooling unit made some low level noise and i remember how it vibrated when i put my hand on it when it was running. I never took out the power supply and tested how much sound it made when it is on. I think it is a combination of power supply, cooling fans, processor cooling, a big chassi that allowes all those sounds to resonate freely.
If you remove the two plastic covers inside the issue gets somewhat better but it will not solve the issue.