The most important thing that saved the tanks from breaking was the fact that the fact that the tanks were properly installed so as not to crash to the floor in case of an earthquake. The biggest concern one should have about possible earthquakes is that the typical aquarium on a typical stand is a system with a high center of gravity. Such setup, unless properly secured, will tip over even at significantly smaller earthquake than the one that hit Japan. In other words the whole thing will just tip over and crash to the floor. No mat will ever make any difference in such situation.
Of course, there's no way to absolutely prevent this from happening in a sufficiently strong earthquake. However, once the reasonable measures have been taken to ensure the vertical stability of the tank/stand combination, one can start thinking about mats. How important the mat itself is in such situation will depend on may factors.
I'd say that the main purpose of the mat is the prevention/reduction of continuous everyday static stresses on tank structure from surface imperfections, not protection against earthquakes.
Agreed. As said above, "Now do the mats relieve stress from the tank, of course it does. It also serves as a buffer if you will between the vibrating equipment like filters and such from transferring to the tank. It's like a sound dampening mat. It absorbs sound, vibrations from getting to the tank and relieves pressure points as well".
Also the stand on which it sits upon makes a world of difference. One doesn't need an earthquake or vibrations to bring a tank crashing down that's sitting on a crappy stand.