The elastic moduli that best approximate the acoustical properties of an anisotropic material

Abstract The issue of how to find the best acoustical fit to a set of anisotropic elastic constants is addressed. The optimal moduli are determined which minimize the orientation averaged squared-norm of the difference in the acoustical tensors. The optimal moduli are derived explicitly and turn out to be identical to those obtained by minimizing the Euclidean distance function, or equivalently, by projecting the tensor of elastic stiffness onto the appropriate symmetry. This has implications for how to best select anisotropic constants to acoustically model complex materials.