On the Backus average of a layered medium with elasticity tensors in random orientations

As shown by Backus (J Geophys Res 67(11):4427–4440, 1962 ), the average of a stack of isotropic layers results in a transversely isotropic medium. Herein, we consider a stack of layers consisting of randomly oriented anisotropic elasticity tensors, which—one might reasonably expect—would result in an isotropic medium. However, we show—by means of a fundamental symmetry of the Backus average—that the corresponding Backus average is only transversely isotropic and not , in general, isotropic. In the process, we formulate, and use, an analogy between the Backus and Gazis et al. (Acta Crystallogr 16(9):917–922, 1963 ) averages.