Because I'm over-caffinated and can't wrap wire for my maille anymore, I thought I'd respond.
Earthquakes generally occur when one of two things happen: either rocks move along a fault, or a subducted chunk of crust breaks off. The big ones--the 8.0+ ones--generally are this latter type, and can be identified by extreme depth, well below the depth of the crust. Think of it like holding a ruler at the edge of a table and bending the end that's off the table down; if it's the wooden type it'll eventually snap, springing back up and likely cracking you in the face (Note: please do not attempt). The subducted slab is kinda similar, but on a scale best measured in kilometers.
The first type is what California needs to worry about. What happens is that chunks of material (not necessarily at plate boundaries, and not necessarily rock--I've seen a beautiful example of faults in sediment in an ancient delta) stop moving for some reason. If they moved smoothly it'd all be fine, but if they get caught by something (and faults generally aren't smooth or straight) tension builds up. On one side you're compressing rock, and on the other you're stretching it. Eventually the blockage fails or the rock does, and that tension is released in what we know as an earthquake. Alternatively pore fluid pressure can increase, causing the rock to separate and basically acting like a lubricant. It facilitates motion, but doesn't diminish the tension/compression at all, so as soon as the material gets to the point where it can move it does move, and you have an earthquake.
There can be any number of things causing the tension. Fundamentally it's all caused by the fact that the mantle is plastic and the crust isn't; the specifics are tricky, and I won't go into them as they're really not critical to earthquake prediction.
As my description above indicates, there are really three main factors in earthquake prediction: 1) the stresses within the rock, 2) the strength of the rock (both the material under stress and the blockage), and 3) pore fluid pressure. If you know those three things, and specifically how they're changing through time, you can predict when an earthquake will occur.
Unfortunately, we can't really know ANY of that. We can make some rough guesses about the strength--we can make guesses about what kinds of rocks are involved, and can test those rocks to see how strong they are--but the stress and the pore fluid pressure, as well as the nature of the blockage, are more or less impossible to see. So there's really no good way to use geology to predict earthquakes as of yet.
I'd guess that earthquakes follow a chaotic pattern (mostly because most of geology does), meaning that you can probably make some predictions based on mathematical models, but if they are chaotic they're inherently unpredictable, for the same reason weather is. And mathematical models based on time-series rather than geophysics would suffer what I consider a critical flaw: a complete lack of theoretical support. You'd be looking at what amounts to a meaningless wiggle (amplitude through time) and trying to predict what the wiggle will look like in the future, without considering what's CAUSING the wiggle.
To make matters worse, they have exactly TWO datapoints and are drawing a line between them. Congradulations, you've just failed basic statistics.
Particularly with a system as complicated as a fault zone (remember, the big ones aren't just one fault) you need a great deal of data. And they plot those two points on a line, which hardly suggests periodicity; in fact, it suggests constant earthquakes of ever-increasing magnitude. I just looked out my window, and there's no quake (I live fairly close to the San Andreas). Spent last week on the Garlock Fault, and no earthquakes there either. So I feel confident we can simply ignore this analysis.
