Far-field scattering model for wave propagation in random media

Abstract

A simple approximate model is developed for ultrasonic wave propagation in a random elastic medium. The model includes second order multiple scattering and is applicable in all frequency ranges including geometric. It is based on the far field approximation of the reference medium Green's function and simplifications of the mass operator in addition to those of the first smooth approximation. In this approximation, the dispersion equation for the perturbed wave number is obtained; its solution yields the dispersive ultrasonic velocity and attenuation coefficients. The approximate solution is general and is suitable for nonequiaxed grains with arbitrary elastic symmetry. For equiaxed cubic grains, the solution is compared with the existing second order models and with the Born approximation. The comparison shows that the obtained solution has smaller error than the Born approximation and shows reasonably well the onset of multiple scattering and the applicability limit of the Born approximation at high frequency. The perturbed wave number in the developed model does not depend explicitly on the crystallite elastic properties even for arbitrary crystallographic symmetry; it depends on two nondimensional scattering elastic parameters and the macroscopic ultrasonic velocity (those are dependent on the crystallite moduli). This provides an advantage for potential schemes for inversion from attenuation to material microstructure.

Analytical attenuation and scattering models for polycrystals with uniform equiaxed grains

“…Analytical attenuation (scattering induced attenuation) models have been developed for aggregates of arbitrary symmetry grains. 4,5 Although these general models adopted exponential form TPCFs, this study follows their schemes to derive analytical attenuation coefficients for a texture-free aggregate of triclinic grains using the analytical TPCF from Eq. (1).…”

“…There are three key elements in scattering modeling, namely, effective elastic moduli for the reference medium, inner products, and the spatial Fourier transform of a TPCF. 4,5,9 For statistically isotropic polycrystals of triclinic grains, the effective elastic moduli C 0 11 ; C 0 44 , and longitudinal and transverse velocities V 0L ; V 0T are given in Refs. 4 and 5.…”

Stress-dependent second-order grain statistics of polycrystals

“…Other scattering configurations where the incident wave is scattered into an arbitrary direction are dependent on other components of N abcd ijkl . [48][49][50] Additionally, other scattering related phenomenon such as ultrasonic attenuation [21][22][23][24][25]51 and radiative transfer of ultrasound 48,[52][53][54] depend on inner products with N. The stress-dependence of each of these models is included by using the definition of N defined in this article.…”

“…This concept motivates the use of perturbation theory to model wave propagation and grain scattering in random elastic media. [20][21][22][23][24][25] In such theories, the second-and higher-order perturbations are able to capture the losses of energy from the mean or average wave field due to scattering at grain boundaries.…”

Ultrasound finite element simulation sensitivity to anisotropic titanium microstructures

“…Even for the simple anisotropic sphere case, near-field wave interactions become quite complex as these multiple vibration modes, angles, and wave fronts interfere. Recent analytical approaches have focused on far field backscattering approximations [5,6,7] but understanding the complex near field influence of anisotropy on wave propagation is largely unexplored and well suited to finite element approaches.…”