Joseph A. Turner Richard L. Weaver
Dept. of Theor. and Appl. Mech., 104 S. Wright St., Univ. of Illinois, Urbana, IL 61801
A model for the multiply scattered incoherent field in a continuous polycrystalline elastic medium is presented. Unlike a previous development based upon energy and flux conservation considerations [J. A. Turner and R. L. Weaver, J. Acoust. Soc. Am. 93, 2312 (A) (1993)] for a medium containing discrete random scatterers, the present model has been developed from the wave equation and first principles. Appropriate ensemble averaging of the wave equation leads to Dyson and Bethe--Salpeter equations that govern the mean Green's function and the covariance of the Green's function, respectively. These equations are expanded for weak heterogeneity and equations of radiative transfer are obtained. The result is valid for attenuations that are small compared to wave number: (alpha)/k<<1. Polarization effects are included, as before, through five elastodynamic Stokes parameters, one longitudinal and four shear. The theory is applied to a statistically homogeneous cubic polycrystalline half-space immersed in a fluid and illuminated by a plane wave. Results on the angular and temporal dependence of backscattered intensity are presented and compared with the predictions of a single-scattering theory. It is anticipated that this approach may be applicable to microstructural characterization through the study of the time, space, ultrasonic frequency, and angular dependence of multiply scattered ultrasound in elastic media. [Work supported by NSF.]