Radiative transfer of ultrasound

A radiative transfer equation is used to model the diffuse multiple scattering of ultrasound in a medium containing discrete random scatterers. An assumption of uncorrelated phases allows one to write an equation of energy balance for the diffuse intensity. This ultrasonic radiative transfer equation contains single-scattering and propagation parameters that are calculated using the elastic wave equation. Polarization effects are included through the introduction of an elastodynamic Stokes vector which contains a longitudinal Stokes parameter and four shear Stokes parameters similar to the four Stokes parameters used in optical radiative transfer theory. The theory is applied to a statistically homogeneous, isotropic elastic half-space containing randomly distributed spherical voids illuminated by a harmonic plane wave. Results on the angular dependence of backscattered intensity are presented. It is anticipated that this approach may be applicable to materials characterization through the study of the time, space, ultrasonic frequency, and angular dependence of diffusely scattered ultrasound in elastic media with microstructure.