(FIG-11)
So what I am going to do is to sort of suggest a physical mechanism that controls this kind of behaviour - seismic, aseismic and this kind of anomalous magnitude-frequency relationship and also tsunami earthquake. But I guess not everyone here is interested in great detail of this kind of model. So, I want to divide my talk into 2 parts from here. In the next 2, 3 slides I want to give you essentially the conclusion, without going into detail -just give you the overall idea of how we explain this kind of thing. And then later on, I want to go into some of the more interesting seismological aspects of why this kind of thing can happen.
Well, just to begin with, we need to worry about how an earthquake can happen; it's essentially an energy-release process in the Earth's interior. It's very simple. This is a block of crust and this is a focus; the stress builds up, and eventually failure occurs on this plane. And then during slippage, seismic waves are generated. That's an earthquake.
(FIG-12)
And then you can look at this simple picture. This is the sort of fault plane before an earthquake. When an earthquake happens, there is slip D over this entire plane, and this is after. And during this process the potential energy W decreases from W to W-DW. So DW is the total potential energy available for producing an earthquake. Again it's very simple. Then in terms of a simple energy budget, it can be written this way. The total change in the potential energy is essentially the sum of three things; nothing else. One is the radiated energy, ER, this is the wave energy carried by seismic waves, and this is what we observe. The second one is frictional energy, EF, that is, energy loss due to friction. Any fault plane has some friction, and big debate is whether the friction on the San Andreas fault is more like 100 bar or kilobar, or whether stress is nearly as high as kilobar in other fault zones. These are all outstanding problems. EG is what we call fracture energy. This is the energy required to produce new fault surfaces.
I divided this into 3 parts, but actually there are only two. [I keep having problems with this.] ER is the radiated energy, and EF + EG is non-radiated energy. So the potential energy DW is converted into radiated energy and non-radiated energy. And non-radiated energy, the bulk of it, will be eventually transformed into heat, and that's kind of rather interesting concept. I want to discuss this in detail, but now I just tell you the main consequence of this.
(FIG-13)
Suppose if this faulting happens on a fault plane with some finite friction, and as we know from High School physics, if we have some surface with finite friction, and if something slips on it, it produces heat. So the question is how much heat is generated during seismic faulting. We can't have a definitive answer, because we don't know the level of frictional stress on a fault plane but you can argue this way.
Suppose this is a fault plane S and we have slip D and then how much heat, Q, is generated ? Of course Q is equal to the product of frictional stress, displacement and area. If this heat is distributed over some volume with w as a width, the temperature of this fault zone will be elevated, and this DT which is the increase in temperature of this zone is actually proportional to frictional stress and more importantly the magnitude of the earthquake. This is intuitively very obvious. If for given friction, if the size of the earthquake gets bigger, you have more heat and higher temperature.
(FIG-14)
I want to show you some detail later, but to the first order, what will happen here is that there is a big difference between small and big earthquakes. So for small earthquakes, smaller than say 4 or 5, this DT is not going to be very large -maybe 100 degrees or 200 degrees or something. However, for magnitude 6 or larger, there is a large amount of heat generated, and as a result DT can be very easily higher than 1000 degrees. If the temperature in the fault zone gets up to 1000 degrees, everything changes. In particular, melting may occur, friction drops and the dynamics is going to change.
