We presented proofs that show that there are only eight symmetry classes of a Hookean solid, and that their hierarchy is only partially ordered.
Our proofs are based on group theory.
Without this work, many seismologists implicitly assumed that there would be a possibility of extending the number of symmetry classes as could be necessary to accommodate modelling needs.
Also, many seismologists assumed a sequential hierarchy proceeding from the general anisotropy to isotropy.
The recognition of these intrinsic properties of a Hookean solid allows for a reliable interpretation of seismic models, which — for the most part — are based on such a solid.
Bóna, A., Diner, Ç., Kochetov, M., Slawinski, M.A. (2010) On symmetries of elasticity tensors and Christoffel matrices . arXiv:1011.4975
Bóna, A., Bucataru, I., Slawinski, M.A. (2004) Characterization of elasticity-tensor symmetries using SU(2). Journal of Elasticity 75(3), 267–289
Bos, L.P., Gibson, P.C., Kochetov, M., Slawinski, M.A. (2004) Classes of anisotropic media: A tutorial. Studia Geophysica and Geodætica 48, 265–287