Determination of the reference symmetry axis of a generally anisotropic medium which is approximately transversely isotropic

Ludek Klimes


For a given stiffness tensor (tensor of elastic moduli) of a generally anisotropic medium, we estimate to which extent is the medium transversely isotropic and determine the direction of its reference symmetry axis in terms of the reference symmetry vector. If the medium is exactly transversely isotropic, we obtain its symmetry axis. We can also calculate the first-order and second-order spatial derivatives of the reference symmetry vector. The proposed method is illustrated in various transversely isotropic and approximately transversely isotropic velocity models.


Elastic anisotropy, stiffness tensor, elastic moduli, transverse isotropy, approximate transverse isotropy, reference symmetry axis.

Whole paper

The paper is available in PDF (93 kB).

Seismic Waves in Complex 3-D Structures, 25 (2015), 177-185 (ISSN 2336-3827, online at