Since your screenshot references
java where the app name usually is written, it suggests that it's the command-line version of Java that a given app is trying to run.
If it appears at specific intervals, it either an app that you have open or a periodical job running automatically in the background (Which, ironically, could be the Java Updater itself).
A quick way to check out which of your installed applications use Java is to run this command in Terminal (
find /Applications -type f -name *.jar
This isn't 100 % accurate but it can give you a rough idea. Dreamweaver and Flash from Adobe, for instance, uses Java.
To get a list of currently running automated background scripts use this command in Terminal — You should run in as close as possible to the moment when the Java popup appears:
(Credit to this thread on Apple Support, it's also useful in understanding
This will, sadly, only give you a list of processes running and not why or what they're running.
Finally, you might want to take a look at the files in
~/Library/LaunchAgents (In Finder use Cmd+Shift+G and paste in the path. This directory shows the periodical jobs that you've setup as a user (sometimes indirectly through an install). Maybe one of these use Java.