When elastic waves propagate through a heterogeneous medium, the material fluctuations in density or elastic modulus create incoherent, or diffuse, energy that scatters in all directions. The spatial statistics of these fluctuations govern the degree of scattering and its angular directivity. This phenomenon is the cause of attenuation of coherent waves and is the mechanism by which diffuse-field methods are based. Several measurement techniques have been developed to exploit the wave behavior to characterize the material or to detect defects within the background medium. Toward this goal, recent researchers have explored the use of digital microstructures from which relevant calculations are made. In this presentation, the fundamentals associated with digital microstructures will be discussed with a focus on the scattering behavior of polycrystals. First, ultrasonic scattering theory is reviewed to clarify the role of the material statistics within the model. Then, digitization specifics are discussed in terms of the frequency constraints that arise including the role of grain morphology and elastic modulus fluctuations. Finally, examples are presented for assorted microstructures, including those with a range of grain-size distribution widths and grain elongation, with a focus on two-point spatial correlations, ultrasonic backscatter, and longitudinal and shear attenuations.
Turner et al. (Wed,) studied this question.