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Two S-wave eigenvectors of the Christoffel matrix need not exist in anisotropic viscoelastic media

Abstract

The 3×3×3×3 frequency-domain stiffness tensor is complex-valued in viscoelastic media. The 3 × 3 Christoffel matrix is then also complex-valued. Using a simple example, we demonstrate that a complex-valued Christoffel matrix need not have all three eigenvectors at an S-wave singularity, and we thus cannot apply the eigenvectors to calculating the phase-space derivatives of the Hamiltonian function.

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Acknowledgements

The suggestions by three anonymous reviewers made it possible for me to improve the paper. The research has been supported by the Czech science foundation under contract 20-06887S, and by the members of the consortium “Seismic Waves in Complex 3-D Structures” (see “http://sw3d.cz”).

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Klimeš, L. Two S-wave eigenvectors of the Christoffel matrix need not exist in anisotropic viscoelastic media. Stud Geophys Geod 65, 291–295 (2021). https://doi.org/10.1007/s11200-021-0824-z

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  • DOI: https://doi.org/10.1007/s11200-021-0824-z

Keywords

  • attenuation
  • anisotropy
  • wave propagation
  • ray theory
  • ray tracing