Monte Carlo Simulations of Ultrasound Scattering and Absorption in Finite-Size Heterogeneous Materials

Abstract

Determination of ultrasound scattering and intrinsic attenuations in heterogeneous media is of importance from material characterization to geophysical applications. Here, we present an efficient inverse method within a finite-size scattering medium, where boundary reflection plays a crucial role. To fit the energy profile of scattered coda waves, we solve the acoustic radiative-transfer equation by Monte Carlo simulations for cylinder and slab geometries, under the isotropic scattering approximation. We show that the fit with the simplistic radiative-transfer solution in an infinite medium may result in underestimated values of the scattering mean free path, ${l}_{s}$, and absorption, ${Q}_{i}^{\ensuremath{-}1}$, by up to 40%. Our main finding is anomalous transport behavior in thin slab samples, where the ballistic peak and the diffusionlike one are merged into one single peak. This anomalous behavior, related to a wave-focusing effect in the forward direction, can mislead the inverse process and lead to an overestimation of ${l}_{s}$ by more than 200%. We compare simulated energy profiles with ultrasound envelopes obtained in a polycrystal-like granite slab from the ballistic to the diffusive regime. The ${l}_{s}$ deduced from off-axis detections agrees with that estimated from the correlation length of the shear-wave velocity by structural imaging analysis.