Maximum entropy and shear strain of shear zone

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. If x is the distance remote from the shear zone center, which possesses the maximum shear strain, the shear strain γ (x) is given by {Mathematical expression} where γ₀ is the maximum shear strain and x_b 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.