## Mathematical constraints of Backus averaging

## Mathematical constraints of Backus averaging

## Mathematical constraints of Backus averaging

## Mathematical constraints of Backus averaging

## Mathematical constraints of Backus averaging

## Proofs of only eight symmetry classes of a Hookean solid

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.

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