## 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

## Coordinate-free characterization of elasticity tensors

We formulated the coordinate-free characterization of symmetries and orientations of elasticity tensors.

Our formulation is based on invariances of tensors, not on their components, since the latter are necessarily coordinate-dependent.

This result removes the need of assuming the orientations of symmetry planes or axes, which are unknown in seismic inverse problems.

Without this work, seismologists had to assume an orientation, and hence bias subsequent interpretations.

Presently, not only the bias has been removed but an independent information is provided.

Vianello, M. (2008) Review MR2333969 . American Mathematical Society

Bóna, A., Bucataru, I., Slawinski, M.A. (2007) Coordinate-free characterization of the symmetry classes of elasticity tensors. Journal of Elasticity 87(2-3), 109–132

Bóna, A., Bucataru, I., Slawinski, M.A. (2007) Material symmetries versus wavefront symmetries. The Quarterly Journal of Mechanics and Applied Mathematics 60(2), 73–84