So if you subtract nothing from something, you are left with something, and that something is still sitting there, and there is no other choice except to go to heat. So this simply means that a large amount of potential energy was actually converted into heat during the Bolivian earthquake; the heat must be there in the fault zone.
(FIG-17)
You might wonder what this much of heat means, 1018 joule; this is almost the same as the total thermal energy released during the 1980 Mount Saint Helens eruption. This is the Mount Saint Helms eruption; so what happened during the Bolivian earthquake is that this much of thermal energy was released in a matter of 10 to 50 seconds in a very small volume surrounding the source of the Bolivian earthquake. Then you can understand that earthquake is not really a mechanical process. It's essentially a thermal process which converts potential energy into heat. Only a very small fraction, almost negligible fraction, of that is released as seismic waves, and seismologists study that small amount of energy to make some sense. But anyway, the important thing is： thermal energy or thermal process is a very important part of a seismic event.
This is for deep earthquakes. The next question is how we can scale this problem to shallow earthquakes. For shallow earthquakes you have to modify the calculation, one way or another. And to do that, we go back to this original figure (FIG-13), the same thing basically - we know the amount of slip, we know the area, and you assume some frictional stress, and ask how much temperature rise could happen if a magnitude, say, 6 or 8 earthquake happens. This can be done very easily. You can do a fairly complicated analysis, and you end up with this kind of diagram (FIG-14). It's simple： if w is 1 millimeter, even for a modest sf of about 100 bars, if the magnitude exceeds 4, the temperature gets up to 1000 degrees. If w is 1 centimeter, in order to get up to 1000 degrees, you need a magnitude of 6, but just this order of magnitude calculation shows that, if the magnitude exceeds 6, almost certainly the thermal process takes over in the fault zone, so the friction will drop significantly, and the faulting process goes into some sort of runaway kind of situation, and slippage is promoted to produce a big earthquake.
(FIG-18)
Well, do we have evidence for melting? And of course again drilling program would play a very important role. There have been several papers in which evidence for melting in a fault zone has been presented. This is the most recent one which I found very exciting. This is from the Nojima fault which produced the Kobe earthquake, and this is taken from the paper by Otsuki. He found pseudotachylites in rocks from the Nojima fault. Pseudotachylite is a glassy material probably produced by melting. He estimated that the temperature was about 1100 degrees, and melting occurred in a narrow layer. The second one is from Obata and Karato. This sample is from the Alps with w, the thickness, about a centimeter. They argued that it must have been formed under a differential stress of 3 kilobars, and the whole process took place in a matter of a hundred seconds or so. So, it must have been produced by seismic faulting. Thus, we do have evidence of melting - at least in some places, if not everywhere.
So what this means is that melting is a very important process during seismic faulting. I'm not saying that there is a completely fiat molten layer in a fault zone; this may not happen everywhere because a fault zone could be extremely heterogeneous.
(FIG-19)
How about permeability ? Until recently we didn't have this kind of data, and the figure on the left is again from the Nojima fault reported by Ito and others. This is the distance from the shear zone and as you go very close to the fault, the permeability is less than 10-18 m2. This is the data from the Cajon Pass on the San Andreas reported by Morrow and Byerlee. Again all the values are in the range of 10-16 to 10-22 m2, so this means there are places in a fault zone where the permeability is very small - small enough to trap fluid when it is heated. Thus, fluid can lubricate fault plane, and can cause very rapid brittle failure, which can grow to, say, magnitude 8.
