Because the fall-out from the NK test was so small as to be almost undetectable there is some thought that it was a failure. If so, that would explain NK’s haste to fire off another test.
If NK thought that setting off its nuke would make the world quiver in fear it was wrong. Japan is clearly angry as is China. Japan has first hand knowledge of the meaning or nuclear devastation. NK cannot survive without significant support from China and is seen as a client state of China. At a time when Western companies are doing billions of dollars of business with China the government of China would at least like to appear as a civilized state. NK has embarrassed them before the World. If NK sets off another test China may decide that it is time for “regime change”.
Meanwhile the impotent UN has made a small response attempt and a second NK test might actually tempt it to stand up. Sort of international Viagra.
On the other hand, the US could, without resorting to the more aggressive actions that I have mentioned before, actively and publicly urge Japan to change its Constitution so that they could accept nuclear armaments from the US and could have a standing army. The US could publicly station a submarine off the NK coast in international waters (we could hit them from almost anywhere but this is would a public reminder that they play this game at their own risk).
South Korea is in a difficult position. Seoul is within artillery range of N.K. and NK’s army is about 3 times as large as SKs.