following a brief bit of googling around, derby.log appears to be a generic log file name used by Java for web apps, and is invoked by specific apps on-demand. So some page you are accessing has a java applet (more than likely) that has decided to make a java log file, and that's where it is going to go. If it just started after you made a web browser change, it's possible that the applet is taking a different route in its logic in response, causing the logos to appear. Or there's an error message in them because the browser change broke something in the applet. (what's in your derby.log file?)
That being the case, the only way to prevent it from appearing then would be to fix whatever's causing the error in the applet, (which may not be possible for you to do) or to avoid visiting the page with the applet on it.
I work for the Department of Redundancy Department