A new concept, seismic gyrotropy, is presented in the context of both
phenomenological and microlevel theory; comparison with the advanced t
heory of optical gyrotropy is given. Seismic gyrotropy is introduced a
s manifestation of spatial dispersion of elastic properties in a first
approximation. Hooke's law (a material equation connecting stresses w
ith strains) is used with additional terms proportional to strain deri
vatives; the factors of proportionality are components of the gyration
tensor b, the tensor of fifth rank, invariant with respect to a group
of rotations. The tensor b is given for following acenrtic groups of
symmetry: infinity,infinity, infinity, infinity 2, infinity m, 222, 2m
m, 2, m; geological media with gyrotropic properties may belong to the
se groups. Using a medium of group symmetry infinity infinity, it is s
hown that enantiomorphous media are <<rotating>>. For <<rotating>> med
ia, the nature of structure dissymetry on microlevel is found: microob
jects of such media are situated in 3D-space accordingly to the princi
ple translation plus azimuthal turn. Three types of micromodels for ge
ological media are put forward which are constructed on this principle
; these are models for sandy rocks, rocks with scattering inclusions a
nd thin-layered media. As for the model of sandy rocks, numerical esti
mates of specific rotation are given, obtained by numerical simulation
.