On closest isotropic tensors and their norms

2016/04/13 by Danek, Tomasz, Noseworthy, Andrea, Slawinski, Michael A.
#74J05 #FOS: Physical sciences #Geophysics (physics.geo-ph)

paper · doi:10.48550/arxiv.1604.03833

Abstract

An anisotropic elasticity tensor can be approximated by the closest tensor belonging to a higher symmetry class. The closeness of tensors depends on the choice of a criterion. We compare the closest isotropic tensors obtained using four approaches: the Frobenius 36-component norm, the Frobenius 21-component norm, the operator norm and the L2 slowness-curve fit. We find that the isotropic tensors are similar to each other within the range of expected measurement errors.

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