Earth is permanently under gravitational influence of Sun and Moon. As Moon orbits Earth, the gravitational pull is "modulated", causing not only the oceans water tide, but also permanently deforming the Earth's crust. The amplitude of this deformation is peaking at full Moon and also at new Moon, so triggering of the earthquake is more probable this time. The earthquake is a consequence of the material tensions inside the Earth's crust that is suddenly released. In my opinion, Moon is providing permanent "massage" of the Earth crust and thus releasing the tensions before they will grow to enormous values. Without Moon and its influence, the earthquakes would be more seldom, but much stronger.