A new scale of hierarchically structured representations as a characteristic for ranking entities in a geomedium

Abstract

1. Based on studies previously conducted at the Mining Institute, Siberian Division of the Russian Academy of Sciences in the field of nonlinear geomechanics and the results of analysis presented in a paper on the hierarchically structured makeup of metamorphic granite masses, therefore, it is possible to conclude that in processing experimental physical or geomechanical information, a semi-log or log-log scale on a base of ten A ∨ log A ↔ x ∨ log x and A = f(x), where A and x are functionally related quantities normalized in a special manner) is the most convenient and natural theoretical description of nonlinear processes in structured media. 2. Recommendations are given for sampling the dimensions of the averaging base and discretization interval of a data file for graphic representation or computer analysis of experimental information, and also in smoothing operations performed in accordance with the sliding-window method. 3. The canonical scale that we developed for hierarchically structured representations of physical information can be used as a ranking characteristic for entities in geomedia. This provides for the possibility of a spectroscopic approach to the identification of the atoms of the elements in Mendeleev's table or their mechanical compounds, which has come into widespread use in physics and chemical analysis; this would even be applicable, however, to analysis of nonlinear physical or geomechanical processes (quasi-resonance approach), including confirmation of the hypothesis of the existence of an acoustic-electromagnetic rainbow [7].