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

Olga Malinnikova,Denis Uchaev,Vasiliy Malinnikov,Dmitry Uchaev,Catherine Ulyanova,M Guzev,I Rasskazov,V Makarov

doi:10.1051/e3sconf/201912901016

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.

Highlights

Natural coal is a product of a complex chain of transformations of heteromolecular substances of plant remains under the influence of biological, chemical and tectonic factors at high temperatures and pressures
Coal seams may contain a large amount of gas, mainly methane, most of which is in the absorbed state in the coal substance [1]
It is known that the outburst–hazardous coal seams generally have a more disturbed structure, which is often a superposition of several systems of exogenous and endogenous fracture, and have increased microporosity

Summary

Introduction

Natural coal is a product of a complex chain of transformations of heteromolecular substances of plant remains under the influence of biological, chemical and tectonic factors at high temperatures and pressures. The complex irregular structure of the pore space of fossil coals is largely determined by the distribution of voids (pores, microcracks) filled with gas by their number, size and directions. Chaos occurs in many natural and living systems where nonlinearity exists In this regard, the question arises: does the image of the surface structure of the coal show the result of a chaotic or random process? In the case of studying the disturbance of coals by their SEM– images, methods of forming a measure that take into account the high degree of anisotropy of the surface of the coal samples are interesting. We studied the possibility of using "complexity–entropy" diagrams based on shearlet transform to quantitatively describe the degree of disturbance of coals by their SEM–images

Methodology of research

Entropy and complexity measures based on shearlet transform

Source data

Research results