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, whichone might reasonably expectwould result in an isotropic medium. However, we showby means of a fundamental symmetry of the Backus averagethat 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.
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