## Thursday, August 16, 2007

### My fault: boring story part 2

Earthquakes remain boring to us, who live in a fool's paradise. Those, who have recently been whacked, have other worries.

We saw how the crystal grains are little feet on the bathtub, but how does this work up to Peruvian scale? Think of a giant pile of sand, housed in one of those roadside giant boob-huts (is this just an Ontario inside joke?). You are hanging on the rafters, watching a stream of sand fall on the pile. As you watch, you see a pattern of little slides and shifts, and sometimes a bigger slide. The sand is at its angle of repose.

Now, you lower yourself upside down, using your spidey web, with the sand stream reducing as you get closer. As you focus your spidey-vision on the sand, you still see the same pattern of many little slides, and larger ones. In fact, by just looking at the pattern, you can't tell how far away you are, from the sand.

You get closer and closer to the sand. At this time, you switch on the incredible shrinking ray, so you get tinier. Still, the pattern remains the same. Finally, when the sand grains start to look like giant boulders, the pattern breaks, but each boulder is following some simple laws of physics.

In fact, we like to model little blocks because it's fun! And it has some lessons for us, mainly that a tiny movement in one place can trigger a larger movement quite far away.

But back to the pile of sand. We see that the pattern of sand failures is self-similar on all scales, but with a big BUT! That is, the self-similarity only holds between two size scales: that of the whole sand pile, and the size of the individual sand grain.

The concept of two limiting scales really screws up a lot of earthquake people, but I suppose they'll figure it out one day. :) We aren't too sure what the largest scale is (somewhere around a few thousand km), but we do know it varies for each earthquake mechanism. What I find amazing is how small the scale can get. We find that rock bursts in mines behave almost exactly the same as earthquakes, and that rock in a testing machine also shows classical earthquake behaviour to the grain scale. So, I'm fairly confident to state that power law (self similarity) holds from the micro to the mega earthquakes.

So if the entire side of Peru is one big foot in the bathtub, it is composed of smaller feet, which are in turn compose of even smaller feet, down to the tiniest grain. At various times, each foot slips on the bathtub. If you are carefully monitoring the feet with seismometers, you see lots of little slips setting up for a bigger foot. In fact, very roughly, you need about 10 little feet to completely slip, for a foot ten times bigger.

After millions of slips, the biggest one decides to go. It is your biggest foot that does most of the damage, and uplifts the mountains. Those little guys are just a necessary side-show. Is the M8 earthquake in Peru the biggest foot? Most likely not, since that area is know for M9's.

In Ontario, what is our biggest foot? It's probably the dimension of the Hamilton Fault zone, which might be around M6.5. When will that foot drop? The next boring story will concentrate on the need for a continuous operating mechanism to keep the feet slipping.