## Saturday, April 2, 2011

### Fault Rupture Boring Story

A mixture of original research, hard facts, humour, and general stubbornness against the 'established' pay wall.

This was on my blog as one of my many 'boring stories', which I have pieced together for prosperity.  I thought up these when I had numerous cousins at the cottage, and I wanted to put them to sleep.

It's fun on the dock, fishing. All my intellectual energy is totally drained from me, especially if I'm cut off from civilization for a long time. I'm back for a couple of days, and thought it's time for another boring story. This one is about fault mechanics, which I think is the most misunderstood subject of all time (it helps to have a rock mechanics background!).

The whole reason we have earthquakes is because of a simple little physical phenomenon that we observe when we have a shower in a cheap hotel, while forgetting to put in the rubber bathmat.

One minute our feet are firmly on the tub, stuck like glue. The next second, we do one little thing, and swoosh! If we are lucky, the clingy plastic shower curtain has saved us.

This is the most dramatic demonstration that I know, showing the difference between static and dynamic friction. I've done some more details in Fault Friction.

Wet, fractured rock behaves almost the same throughout the world, and this is the stuff of earthquakes! Without a difference, in wet rock, between static and dynamic friction, we would be without most earthquakes (those extremely deep earthquakes are a bizarre exception, but who cares about them?)

So all earthquakes start with a single crystal (grain) of rock (mineral), rubbing against another. There is shear stress, which is a force trying to slide the grains past each other, and there is the normal stress, which is the force jamming them together. At the very tiny point of contact, the minerals (quartz, most likely), are cold-welded, making a very strong adhesion bond.

The shear stress attempts to break these bonds, by inducing tiny molecular earthquakes. Studies show that if we bake these things so that there is no water, then new bonds are formed as quickly as old ones are broken. Thus, the resistance to slipping remains a constant value.

Thus, good old water is need for some action! If we sprinkle in some water, then two very interesting things happen. Firstly, we do not have stability at the near-failure point, because the water acts to eat away at the adhesion points. This little thing, called stress corrosion, is one of the best, totally unappreciated discoveries from the giant money-sucking pit, called the AECL Underground Research Laboratory (URL) (RIP). (Thanktheloard for massive gov't pork!)

Secondly, once the adhesion bonds start to break, they are covered in little water molecules, just like the other potential contact points. When a new adhesion contact wants to form, there's that nasty water gunking things up!

So now it takes some time to form some new bonds, time that the slippery feet (or mineral grains) don't have if there is a big following force (like gravity, or the San Andreas!). The sliding surface starts to zoom, and we have dynamic friction.

As you fall asleep, you may wonder what bathtub feet, and mineral grains have to do with a big old fault. The answer lies in self-similarity and Power Law. Much like a ratty old US bridge, everything can be represented as tiny little feet slipping, over and over again, combining into larger and larger feet, until the whole shebang blows!

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, and about 30 time more energy when it slips.

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?

If you recall, I left you asleep at the point of wonder why we have earthquakes at all in Eastern North America (ENA). Really, if the continent is one big massive piece of tombstone granite, then any stress-relieving earthquake should just carve a 'stress-hole' like drilling a mine.

Once this giant Tim Hortons donut gets formed, the remaining rock arches around it, and leaves a perfectly stable structure, with an extinct fault in the middle. This doesn't happen on the plate margins, with all those plates sliding past each other, like those sliding number puzzles we had as kids. For the equivalent, we would need mountain ranges or visible fault sliding to keep the similar ENA earthquake hotspots going for a few million years.

Take a typical fault zone trying to grow up in ENA. It starts with a fractured weak spot, perhaps reactivated by the modern stress field. Eventually (perhaps), the shear stress builds up along a fracture, and the bath-tub feet let go! The fractured rock behaves exactly the same as in California or Peru.

But that's it! Our poor little earthquake has shot its load. The feet have lost their stress, and the surrounding rock has clamped up on our poor little fellow. He can't grow up...

That is, if our earthquake follows conventional thinking for ENA earthquakes. But no, our earthquake fault zone is smarter than that, it is following Harold's original thinking, which doesn't get into the university cartel, because they all got tenure!

Once our earthquake has caused its bump (like a Utah coalmine!), it looks around and sees what it has done, which is to freshly fracture a lot more rock. Its seismic effort hasn't gone into mountain building, or plate sliding, it's gone into fracture surface energy! The academics never thought of that!

But this isn't enough for Quakey (like that name?), in its battle against the implacable rock. Luckily, he's (she's?) under a big hunk of water, and water slowly flows into the new fractures. Now things are cooking! The water does all sorts of wonderful things. First, the water pressure reduces the normal stress on the faults and makes them more likely to slide again. Second, the water hydrofractures and extends existing tension cracks. Finally, the fresh water is corrosive and starts chewing at the adhesion points.

Quakey has become a growing entity, like the Blob that ate New York. So, under Hamilton, New Madrid, countless other ENA locations, we have growing things, which although not actually alive, can give a darn good account of themselves!

As Quakey grows, he can tap into more stress from the surrounding rock, just like we were excavating a new Utah coal mine (or an underground nuclear waste thingie!). He gives many signs of his growth, lots of little earthquakes, just like his bigger plate margin brothers. All the bathtub feet are working, and eventually there is a large, scale-limited earthquake. The process begins again for a bigger earthquake!

Quakey may start as a simple thrust fault along a pre-existing fracture, but soon suffers growing pains. The old fracture provides the water, but a simple thrust fault isn't enough to suck out all the stress from the surround rock. In order to avoid another stress lockup, he must start developing shear wings, which produce strike-slip earthquakes. When he eventually grows into a monster, he resembles the New Madrid fault system.

All the time, these zones are sending the signals to prove Harold is right, and the others are wrong, but the scientists and politicians are too cheap to provide the detailed seismic monitoring that is required. Only the Southern Ontario Seismic Network probably has sufficient horsepower and density, but the Hamilton zone is just a baby!

Everyday, these zones try to show themselves. They send typical 'fluid injection' earthquakes, they mix thrust and strike-slip mechanisms, and they only show up under bodies of water. But without monitoring, the world goes on arguing with Harold. :)