I happened to notice that the recent close pass of the moon (supermoon) coincided with the earth quake in Japan. Has any study been undertaken of the effects of the gravitational field of the moon on the tectonic plates on earth? Is there a correlation between earth quake activity and the proximity of the moon to earth?
The particular 'super Moon' phenomenon is a coincidence of the Moon being at perigee (the closest point on its orbit) and a new or full moon. The Moon completes an orbit and passes through perigee once a month so this close approach of the Moon is not an unusual phenomenon. The eccentricity of the Moon's orbit (how elliptical it is) is quite small so the difference in the tidal influence of the Moon between apogee (the furthest point in its orbit) and perigee is also quite small. The influence of the Sun is larger and is responsible for the 'spring' (slightly higher) and 'neap' (slightly lower) tides that occur on a two week cycle with spring tides occuring around new moon and full moon and neap tides occuring around first quarter and last quarter. By far the largest variation in the tidal effect of the Moon however, and what sets the primary rythm of the tides, is the daily rotation of the Earth.
There have been a number of studies over the years of the effect of the tidal influence of the Moon on earthquakes. Since the largest variation in the tidal influence of the Moon is the roughly twice daily pattern of high and low tides any effect of the Moon on earthquakes should also show this pattern. There is some evidence that it is statistically more likely for earthquakes to occur at a time near high tide, when the Moon is overhead or on the opposite side of the Earth, but the link is not very strong. There is no evidence linking the rather lower level modulations of the tides from the Sun, the eccentricity of the Moon's orbit and the eccentricity of the Earth's orbit to the occurence of earthquakes. The Earth is a seismically active planet and there are thousands of small earthquakes occuring all the time, which would tend to blot out any signal from the gravitational effects of the Moon. The Moon on the other hand is a rather seismically inactive body and there is definite evidence from seismometers left on the Moon by the Apollo astronauts that the Moon experiences weak 'moonquakes' as a result of the Earth's tidal influence. The gravitational influence of the Earth on the Moon is around 100 times larger than that of the Moon on the Earth as well which makes it easier to observe.
To give you a sense of scale the variation in gravity at the Earth's surface due to the main tidal rythm compared to the Earth's gravity is about 1 part in 10 million, in comparison the variation in gravity on the surface of the Moon due to the tidal influence of the Earth is about 1 part in 100,000.