Symmetry Properties of Spatial Distribution of Microfracturing in Rock

Kazuyoshi Nanjo¹, Hiroyuki Nagahama¹ and Eiji Yodogawa²

¹Institute of Geology and Paleontology, Graduate School of Science, Tohoku University, Sendai 980-8578, Japan
E-mail: nanjo@dges.tohoku.ac.jp; nagahama@dges.tohoku.ac.jp
²Department of Computer Science and Communication Engineering, Kogakuin University, Shinjuku, Tokyo 163-8677, Japan
E-mail: yodogawa@ee.kogakuin.ac.jp/ yodogawa@ieee.org

(Received November 19, 1999; Accepted January 29, 2000)

Keywords: Symmetry, Rock Fracture Experiment, Symmetropy, Two-Dimensional Discrete Walsh Transform

Abstract. We measure quantitatively symmetry and entropy regarding symmetry of spatial distributions of acoustic emissions generated by microfracturings during creep before ultimate whole fracture of a rock specimen. In the measurement, symmetry properties of the two-dimensional discrete Walsh functions are utilized, and the two-dimensional discrete Walsh transform is applied to the spatial distributions. We find that the spatial distributions of acoustic emissions are rich in double symmetry. Moreover, it is found that the richness in double symmetry increases and the entropy decreases with the evolution of microfracturing process. This decrease of the entropy comes from the increase of the richness in double symmetry. Thus we conclude that the microfracturing process evolves under constraint of the increase of the richness in double symmetry.