“Complexity–entropy” diagrams and their application to the study of coal tectonic disturbance

Abstract

It is investigated the possibility of using so–called "complexity–entropy" diagrams for the quantitative description of the degree of coal disturbance using coal images obtained by means of scanning electron microscope (SEM). These diagrams plot structural complexity measure (vertical axis) versus entropy measure (horizontal axis) for distribution of probability given in some way on the image. In this paper, the values of both measures were calculated on the basis of the shearlet transform, and the Jensen divergence was used as the basic divergence for calculating the complexity measure. All calculations were performed for more than 140 images of coal specimens with various degrees of disturbance, obtained from the quiet zone of the seam and the outburst zone. As a result of research, it was found that two-dimensional distributions for measures of complexity and entropy in most cases are informative data sets for differentiating coals by degree of complexity. Moreover, such characteristics of these distributions as mathematical expectation and, to a less degree, mode can be used as simple quantitative descriptors of coals with various degrees of disturbance. These characteristics can be used to show the closeness of the spatial structure for the analyzed coal specimens to strictly periodic or absolutely chaotic ones. On the basis of the obtained results, conclusions about the possibility to separate coals according to the degree of their outburst hazard were done.