Maximum entropy and shear strain of shear zone

Abstract

The principle of maximum entropy can be used to determine the shear strain in natural shear zones. When the margin of a shear zone is assumed, the principle leads to the truncated exponential distribution of the shear strain. Ifx is the distance remote from the shear zone center, which possesses the maximum shear strain, the shear strain γ (x) is given by $$\gamma (x) = \gamma _0 \frac{{e^{ - \beta x} - e^{ - \beta x_b } }}{{1 - e^{ - \beta x_b } }}$$ where γ0 is the maximum shear strain andxb is the boundary distance. This relationship agrees with the observed data remarkably well. Further given no margin to distance, this relation generates the Becker's relation (γ(x)=γ0m−x) under the condition β>0. This truncated exponential distribution function which fits the observed data remarkably well is expected to be valid for the strain analysis of natural shear zones.