Numerical examination of commutativity between Backus and Gazis et al.   averages
  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. 
David R. Dalton and Michael A. Slawinski
physics.geo-ph