### ASA 126th Meeting Denver 1993 October 4-8

## 4aPA9. Radiative transfer and multiple scattering of diffuse ultrasound in
polycrystalline media.

**Joseph A. Turner
Richard L. Weaver
**

**
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*Dept. of Theor. and Appl. Mech., 104 S. Wright St., Univ. of Illinois,
Urbana, IL 61801
*

*
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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.]