Numerical examination of commutativity between Backus and Gazis et al. averages

TL;DR

This paper numerically investigates how the noncommutativity between Backus and Gazis averages depends on anisotropy strength, showing near-commutativity in weak anisotropy cases.

Contribution

It provides a numerical analysis quantifying the extent of noncommutativity between two important seismic averaging methods based on anisotropy strength.

Findings

Noncommutativity increases with anisotropy strength.

Averages nearly commute under weak anisotropy.

Quantitative relationship between anisotropy and noncommutativity.

Abstract

Dalton and Slawinski (2016) show that, in general, the Backus (1962) average and the Gazis et al. (1963) average do not commute. Herein, we examine the extent of this noncommutativity. We illustrate numerically that the extent of noncommutativity is a function of the strength of anisotropy. The averages nearly commute in the case of weak anisotropy.