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.