The frequency of length of strike-slip faults in continental crust follows a lognormal probability distribution, and a nonlinear positive correlation exists between length and offset. These results appear to be scale-independent. An explanation of the observations is presented in terms of a stochastic model which treats the occurrence of faulting as a Kolmogorov-type process obeying the law of proportionate effect. This model accounts for the length distribution of faults. Tentatively, the correlation between length and offset is ascribed to an allometric law relating the relative growth rates of these two parameters. The possibility of the application of the concepts of continuum damage mechanics to the problem is also briefly explored as a way to introduce time-space averages of tectonic stress and strain-rate into the model.

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Keywords continuum mechanics, stochastic process, structural geology
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Journal Journal of the International Association for Mathematical Geology
Ranalli, G. (1980). A stochastic model for strike-slip faulting. Journal of the International Association for Mathematical Geology, 12(4), 399–412. doi:10.1007/BF01029423