Effects of microstructure on the speed and attenuation of elastic waves: formal theory and simple approximations

This paper attempts to develop a more unified theory of the attenuation of an elastic wave and its relation to microstructural statistics by following a first principle approach, using developments from other multiple scattering problems and adapting them to the elastic wave case. Several expressions are derived which establish a hierarchy for the statistical information required to evaluate the series. Several simple approximations are presented. The validity of the commonly made assumption that alpha = n-sigma is clarified, and the effective speed is computed. Three basic conclusions are reached: the attenuation exhibits a nearly universal behavior when appropriately scaled; the phase velocity is less sensitive than the attenuation to variations of k /SUB a/ o and c (as specified), and both v and alpha are insensitive to modest variations in pore radius