First, what is the probability distribution of fault throw displacement. Uniform distribution seems unlikely, since then small changes would add up to huge huge elevation differences that require a large amount of by erosion to reduce. But the same holds for a Gaussian. Are there any other mechanisms that limits these large differences, like gravity pull-back and pressure from the magma? How can these be described in terms of free-fall, damping etc?
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4$\begingroup$ Fault offsets typically follow a power-law distribution. I don't have time for a complete answer, but as a start, have a look at any of Walsh's papers on fault scaling relationships (e.g. nature.com/nature/journal/v351/n6325/abs/351391a0.html sciencedirect.com/science/article/pii/019181419290127I ) I'm confused by the second half of your question, though. Why would magma, damping, and free-fall have any effect whatsoever on crustal faulting in general? $\endgroup$– Joe KingtonCommented Jun 19, 2014 at 20:29
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$\begingroup$ @JoeKington Why would magma, damping, and free-fall have any effect whatsoever on crustal faulting in general? Because otherwise the earth would either implode or explode depending on very sensitive force balance. $\endgroup$– user877329Commented Jun 20, 2014 at 7:52
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This is a very interesting question, and one that many people have explored. It's also a very complex question, as geology is inherently complex. A complete answer would probably require you attending a semester or mores worth of structural geology lectures, so below is only a very brief introduction.
To answer the first part of your question, there is a general consensus that fault-throw is proportional to fault length, which can be modelled by a power-law relationship. The paper presented by Joe Kington is very useful. Another paper which may be of interest is Kolyukhin, D., and A. Torabi (2012), Statistical analysis of the relationships between faults attributes, J. Geophys. Res., 117, B05406, doi:10.1029/2011JB008880. They show that fault throw is proportional to fault length, fault type (e.g. normal, reverse/thrust) and rheology of the rock and fault zone. So to get an understanding of the probability distribution of fault-throw, you would have to explore the effects that these variables have. I couldn't find papers that explicitly deal with fault-throw probability distribution (they mainly look at predictive models and reasons), so unfortunately cannot help in giving a precise answer.
The second part of your question seems to deal with ways that stress (pressure caused by whatever: tectonic plates moving around, magma moving around, things moving downslope under force of gravity, etc) is accommodated by some Earth response, generally either faulting or magma emplacement. Take a look at the Andersonian theory of faulting to get an understanding of how different stress regimes (in what direction is the prinicipal stress oriented) effect creation/reactivation of faults. This theory will give you some insight into how the Earth accommodates stresses by extending/shortening. The direction and magnitude of faults is explained by the interplay of different stress components. When you were talking about free-fall, I assume that you mean gravity, which is generally reformed as overburden stress, which is an important stress component.
Magma can accommodate stress (as well as induce it!). Take a look at examples from the East African rift system around Afar. Here the fault-throw versus length relationships mentioned above do not hold, because introduction of magma into the area reduces the need for the rock to extend/stretch in the horizontal and shorten in the vertical directions. I don't have any papers on hand, but the examples are very interesting.
