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A stochastic approach to the cricktip propagation model

Czechowski Z.

Acta Geophysica Polonica

2000

Vol. 48, nr 1

57-68

System of faults can be regarded as a stochastic non-linear dynamic system. We investigate a dynamic response of such a system to a stochastic input. As an example of the non-linear stochastic differential equation, the model of the cracktip motion is considered. The influence of fault interactions and the medium structure is perceived as the input stochastic process. We are looking for such input distributions for which the stochastic output is consistent with observations (e.g. Gutenberg-Richter law). This allows us to describe the physical nature of internal stresses and the medium avoiding investigations of complex deterministic models of the fault system. It appears that even purely random input processes are transformed by the model into a power-like distribution. Discussion concerning the causes for the appearance of exponential and inverse-power distributions is included.