Velocity of ultrasound diffusion in heterogeneous media and its applications

Abstract

This paper investigates the velocity of ultrasonic diffusion in heterogeneous media under the conditions where the diffuse wave approximation is valid ($\lambda \le a$). The diffusion velocity is defined as the moving speed of the peak of the energy evolution curve. The peak arrival time as a function of transport distance is calculated for infinite spaces and bounded domains. The results show that the peak arrival time is independent of the domain’s geometry, i.e. the size, shape, and boundary conditions. This is confirmed by comparing the arrival times in an infinite space and a bounded domain with a geometric feature – a surface-breaking crack of varying depth. Therefore, the velocity of ultrasonic diffusion is an intrinsic property of a medium, and the formula for the infinite three-dimensional space is sufficient to calculate the arrival time–transport distance relationship, given the diffuse properties of the medium. These findings eliminate the needs for the finite element numerical simulations in the applications to determine geometric parameters such as the crack depth using diffuse ultrasound. The diffusion velocity is a function of transport distance in general, while its far-field asymptotic value is constant regardless of the dimensionality and geometry of the domain.