Earth quake occur as a result of shakes with the earth crust which is usually accompany by the release of large amount of energy.Heavy rain fall could cause earth quake but this is depend on the nature of the area in focus, cos it isn't an effect that occurred suddenly. It occurred as a result of accumulated faults over a long period of time.
Generally there are three types of faults that occurred below the earth crust which are normal, reverse and strip like fault. The normal occurs majorly in a areas where there is extended boundary while the reverse occur in a area where the crust is shortened while the strip like fault occurs between two faults the slip on each other horizontally.
Huge rain fall will cause immediate earth quake on areas that are weak as a result faults, these effect is mostly felt in areas where there lots of continuous mining and other extractive activities that causes uneven expansion and contractions in the layers of the earth crust