2017/04/18 by Len Bos, Bos, Len, David R. Dalton +4
Earth and Planetary Sciences · Engineering · Physics and Astronomy · #FOS: Physical sciences #Geophysics (physics.geo-ph) #Geophysics and Sensor Technology #High-pressure geophysics and materials #Ionosphere and magnetosphere dynamics #Seismic Imaging and Inversion Techniques #Seismic Waves and Analysis
paper · pdf · doi:10.48550/arxiv.1704.05541
openalex publication_date 2017/04/18 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
We show that, in general, the translational average over a spatial\nvariable---discussed by Backus citebackus, and referred to as the\nequivalent-medium average---and the rotational average over a symmetry group at\na point---discussed by Gazis et al. citegazis, and referred to as the\neffective-medium average---do not commute. However, they do commute in special\ncases of particular symmetry classes, which correspond to special relations\namong the elasticity parameters. We also show that this noncommutativity is a\nfunction of the strength of anisotropy. Surprisingly, a perturbation of the\nelasticity parameters about a point of weak anisotropy results in the\ncommutator of the two types of averaging being of the order of the it\nsquare / of this perturbation. Thus, these averages nearly commute in the case\nof weak anisotropy, which is of interest in such disciplines as quantitative\nseismology, where the weak-anisotropy assumption results in empirically\nadequate models.\n