Abstract
The heterogeneous characteristic of crystal structures in a rock is well known that their size distribution can be expressed by the power law. In this paper we study the inherent stochastic feature hidden in the wave propagating through a granite rock specimen in order to make clear the power law defining the size distribution characteristics of crystal structure and the uncertainty of fissure size distribution in the rock. We develop a system to measure the ultrasonic wave propagation in a rock specimen and a method to analyze the phase characteristic of the wave propagating through the rock specimen. Decomposing the phase into the linear delay part and the fluctuation part from it, we investigate the stochastic characteristics of the phase difference in the fluctuation part. The probability density function of the approximated group delay time is expressed by a unique Levy-flight distribution for any arbitrary small circular frequency intervals. For obtaining the further unique distribution characteristics of phase we investigate the probability distribution characteristics of the second derivative of phase with respect to the circular frequency. Through this study the fractal feature of phase becomes very clear.
