Time dependence of multiply scattered diffuse ultrasound in polycrystalline media

Time domain results are presented for the multiply scattered longitudinal intensity backscattered from a polycrystalline medium. The results are solutions to the ultrasonic radiative transfer equation (URTE), the derivation of which is based upon radiative transfer theory. Unlike steady-state solutions obtained previously, time domain solutions will more closely correspond to experiments that use tone burst sources. This paper is concerned with the time dependence of the backscattered longitudinal intensity from a polycrystalline medium excited by a normally incident longitudinal wave idealized as an impulsive deposition of energy. It is shown that multiple scattering effects become significant at times on the order of a mean free time or less. It is anticipated that this work may be applicable to microstructural characterization of polycrystalline, geophysical arid other random media in which multiple scattering effects are important.