On the Backus average of layers with randomly oriented elasticity tensors

TL;DR

This paper investigates the Backus average of randomly oriented anisotropic layers, revealing that the resulting medium is transversely isotropic rather than isotropic, contrasting with the isotropic outcome for isotropic layers.

Contribution

It demonstrates that the Backus average of randomly oriented anisotropic layers yields a transversely isotropic medium, not an isotropic one, and establishes a relationship between Backus and Gazis averages.

Findings

Backus average of random anisotropic layers is transversely isotropic.

The average is not generally isotropic, contrary to intuition.

A relationship between Backus and Gazis averages is formulated.

Abstract

As shown by Backus (1962), the average of a stack of isotropic layers results in a transversely isotropic medium. Herein, we consider a stack of layers consisting of a randomly oriented anisotropic elasticity tensor, which-one might 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, a relationship between the Backus and Gazis et al. (1963) averages.