This myth may be so common because we want it to be true. Several recent damaging earthquakes have been in the early morning, so many people believe that all big earthquakes happen then. In fact, earthquakes occur at all times of day. It is easy to notice the earthquakes that fit the pattern and forget the ones that don't.
Many people believe that earthquakes are more common in certain kinds of weather.
In fact, no correlation with weather has been found. Earthquakes begin many kilometers below the region affected by surface weather. People tened to notice earthquakes that fit the pattern and forget the ones that don't. Also, every region of the world has a story about earthquake weather, but the type of weather is whatever they had for their most memorable earthquake. Of course, the ocean is not a great hole into which California can fall, but it is itself land at a somewhat lower elevation with water above it.