Unlike many natural phenomena, earthquakes are not especially mysterious. National Geographic explains the physics behind earthquakes, and the catastrophic effects they can cause, in this short video:
One of the things we know about earthquakes is that they operate as low-frequency acoustic waves passing through solid media. And four French geologists have discovered that the acoustic waves that cause earthquakes, like most waves, are subject to refraction—they can potentially be distorted, blurred, and misdirected. So can they be distorted, blurred, and misdirected in such a way that they pass harmlessly (or, at least, less harmfully) through a city by use of a seismic cloak?
The science behind acoustic cloaking is remarkably similar to the science behind visible light spectrum cloaking, and poses many of the same practical problems—but there are key differences that make seismic cloaking easier in terms of scope, and harder in terms of scale. A seismic cloak doesn't need to make a city acoustically invisible—just less of a seismic obstacle. The world rumbles harmlessly under our feet every day; it's only severe seismic waves that pose a problem. On the other hand, it's simply not practicable to cloak all of the ground beneath a city in acoustic metamaterials.
That said, we now know that it is theoretically possible to cloak a city from an earthquake—and that's a very good place to start.