On commutativity of Backus and Gazis averages
  We show that the Backus (1962) equivalent-medium average, which is an average over a spatial variable, and the Gazis et al. (1963) effective-medium average, which is an average over a symmetry group, do not commute, in general. They commute in special cases, which we exemplify. 
David R. Dalton and Michael A. Slawinski
physics.geo-ph