The Extended Concept Of Symmetropy And Its Application To Earthquakes And Acoustic Emissions

There is the notion of symmetropy that can be considered as a powerful tool to measure quantitatively entropic heterogeneity regarding symmetry of a pattern. It can be regarded as a quantitative measure to extract the feature of asymmetry of a pattern (Yodogawa, 1982; Nanjo et al., 2000, 2001, 2002 in press). In previous studies, symmetropy was estimated for the spatial distributions of acoustic emissions generated before the ultimate whole fracture of a rock specimen in the laboratory experiment and for the spatial distributions of earthquakes in the seismic source model with self-organized criticality (SOC). In each of these estimations, the outline of the region in which symmetropy is estimated for a pattern is determined to be equal to that of the rock specimen in which acoustic emissions are generated or that of the SOC seismic source model from which earthquakes emerge. When local seismicities like aftershocks, foreshocks and earthquake swarms in the Earth's crust are considered, it is difficult to determine objectively the outline of the region characterizing these local seismicities without the need of subjectiveness. So, the original concept of symmetropy is not appropriate to be directly applied to such local seismicities and the proper modification of the original one is needed. Here, we introduce the notion of symmetropy for the nonlinear geosciences and extend it for the purpose of the application to local seismicities such as aftershocks, foreshocks and earthquake swarms. We employ the extended concept to the spatial distributions of acoustic emissions generated in a previous laboratory experiment where the failure process in a brittle granite sample can be stabilized by controlling axial stress to maintain a constant rate of acoustic emissions and, as a result, detailed view of fracture nucleation and growth was observed. Moreover, it is applied to the temporal variations of spatial distributions of aftershocks and foreshocks of the main shocks, using natural observable data of earthquakes in and around Japan. Our results show the successful applicability of the extended concept of symmetropy to earthquakes and acoustic emissions. Furthermore, it is pointed out that the concept of symmetropy or the extended one of it might be adapted to any pattern recognition in many fields of science, particularly in the nonlinear geosciences and the sciences of complexity. References: Yodogawa, 1982, Percept. Psychophys., v. 32, p. 230-240; Nanjo et al., 2000, Forma, v. 15, p. 95-101; Nanjo et al., 2001, Forma, v. 16, p. 213-224; Nanjo et al., 2002 in press, Symmetry: Art and Science, v. 2.