Estimation of the fracture diameter distributions using the maximum entropy principle

Fracture size is often estimated from trace length measurements. It is well recognized to be a typical non-unique inverse problem. This paper presents a distribution-free method for estimating the fracture diameter distributions using moments in conjunction with the maximum entropy principle. In this method, moments are used to characterize the statistical nature of the probability distributions. The method involves the inference of the moments of the true trace lengths from the sampled trace data, the explicit expression of moments of fracture diameters using general stereological relationship, and the estimation of fracture diameter distribution using the maximum entropy principle by a given set of moments of fracture diameters. The proposed method makes it possible to achieve a universal form for the fracture diameter distribution without any particular parametric form, and to match the moments of fracture diameters up to the fourth order. The overall behavior of the method is validated by an example, and the results show that it is capable of estimating the fracture diameter distributions.