The center is your location at the time the XMP burster is actually fired, which can vary highly depending on your internet connection.
It even happens that you are standing directly on top of a resonator, fire the XMP, but then due to some GPS glitch, you move away and the XMP is fired somewhere else.
In any way, you see the center and damage of your XMP on the screen.
Edit: I was looking for a credible source for my claim, but didn't find one. But I'm a very active Ingress player and there wasn't a single time XMPs behaved differently than I described above.
Since yesterday (version 1.23.1), I've noticed a change in this behaviour. The visuals for firing the XMP now stay at the position the XMP was fired, even if you are moving away. So the correct answer now would be "The center is your location at the time you click on 'Fire'."