There's plenty of folks who think that the crustal tides caused by the Moon have an effect on earthquakes. It's not an entirely outlandish idea. After all, the daily 'Earth tide' is just as real as the ocean tides. It follows quite logically that all that motion of the crust should have an effect on tectonics and seismicity.

It seems that most people look at the position of the Moon relative to where earthquakes have happened. Specifically, they look at the 'phase angle'. If you were to draw a line from the center of the Moon to the center of the Earth, the point on the surface of the Earth is known as the sub-lunar point. The longitude of this position, and the longitude of where the quake occurs forms an angle. There seems to be consensus amongst predictors that if one analyzes these angles, a correlation will found - that more earthquakes occur at certain angles, and that this information can be used to predict when earthquakes are more likely to occur.
In thinking about this method I wonder if the phase angle is enough. I don't think it is sufficient to simply determine what the Moon's longitude is and look for quakes at other longitudes a certain distance away. Rather, I feel other parameters need to be taken into account.

First of all, the phase angle is not two dimensional. It's three dimensional. We are dealing with spherical bodies. Finding the longitude is not enough. The latitude needs to be taken into account as well. For example, if the Moon were directly over the equator on the prime meridian (0° latitude, 0° longitude), the phase angle relative to the Moon will be different for all locations along that meridian. In other words, the angle is different if you are on the equator versus Greenwich England. It should also be noted that the phase angle at the North Pole would be less than 90°, simply because the pole is half the Earth's diameter above the equatorial plane where the Moon must be if it's sub-lunar point were as stated in this example. Remember, the real world is 3D.

Second, the Moon's orbit is chaotic. It's orbital plane relative to the Earth's equator is not fixed. It tips and tilts. This is why the Moon appears to wander around the sky from phase to phase, from season to season, from year to year.

In order to find the true phase angle, one must compute the actual sub-lunar point based on accurate astronomical ephemerides. Fortunately, these calculations aren't terribly difficult to do, although it does take some programming skills to implement properly.

Another parameter which I think is extremely important, and that is totally lacking in all the predictive efforts and analyses that I am aware of, is the phase angle relative to the fault plane. In other words, it's not sufficient to to know which direction the Moon is relative to any possible epicenters, but also which way the fault is oriented and which way it moves.

Take for example two bricks stacked one on top of the other. If you apply a force straight down on the bricks, not much is going to happen, because the force is applied such that it forces the bricks together. On the other hand, if you apply the same force at a 45 degree angle to the plane where the two bricks touch, odds are much better that the bricks may be forced to slide over each other.

Now, this seems at first glance to be an important realization. After all, in this real 3D planet we live on, faults are oriented in the crust in all directions of the compass and all angles relative to the surface of the Earth above.

So why shouldn't this angle have importance? Two reasons.

First, even if the lunar phase angle relative to the fault plane is important, and shows significant correlation to earthquake occurrences, all we've done is narrow down the times when quakes are more likely to occur to those times when the lunar phase angle relative to a particular fault plane is significant, and this happens at least once nearly every 24 hours for any particular fault, due to the rotation of the Earth. This does not even take into account the fact that faults must build up enough strain to be "trigger ready". So about all that we've shown is that a fault that is ready to pop has popped preferentially at a certain time of day, but not which day it will pop.

Second, the gravitational forces from the Moon that cause Earthly crustal tides are distributed nearly equally on both sides of the fault. Yes, the part of the Earth closer to the Moon experiences slightly stronger gravitational attraction to the Moon than the part further away, perhaps on the other side of a fault. But this difference is very small.

The question is, is this difference enough to influence the fault? Take for instance our example previously with the two bricks. If you push sideways on the top brick with a certain force and not on the bottom one, you may have enough force to cause the top brick to slide on the bottom one. But remember, the Moon's gravity acts on both sides of a fault. So in our example, the force on one brick may be a few percent stronger than the other. What is important is this difference in forces. Since the differential force is so small, there is not enough to overcome the static friction and allow the bricks to slide.

It's fairly easy to determine the maximum gravitational gradient across the Earth by the Moon's gravity. Turns out the gravitational pull on the near side of the Earth is about 15% stronger than on the far side. This may seem like a lot, but the exact amount is about 5.3 Newtons of force, and that is spread across the entire 12,472 km diameter of the Earth.

To put that into perspective, 1 Newton is about the force you feel when you have a 100g gram weight sitting in the palm of your hand. So 5.3 Newtons is about the same force you feel with a half liter bottle of water in your hand.

Now, spread that force out across the diameter of the Earth. That's about 413 nanoNewtons per meter. The force of a grain of sand in your palm is over half a million times stronger.

In conclusion, I think the idea has some overlooked parameters, which can easily be checked. All we need to do is compare the lunar phase angle against a list of focal mechanisms. On the other hand, there much reason to doubt that anything will be found. The weight of an average human has far more impact on the crust than the Moon's gravity. Keep that in mind the next time you visit Parkfield and want to jump across from the Pacific Plate to the North American in one giant leap.

Brian