In anisotropic gyrotropic media, Christoffel tensor is complex; whereas a real part contains stiffnesses, an imaginary part<br>includes gyration constants. In this work, inequalities relating stiffnesses and gyration constants are presented. They have<br>been derived from the condition for potential energy be positive. The criterion for the positive definiteness of the<br>complex matrix of stiffnesses and gyration constants is used. Sets of inequalities are presented for the two types of rocks<br>belonging to acentric limit groups ∞∞ and ∞ (isotropic and transversely isotropic media with gyrootropic properties).<br>These inequalities enable to carry out modelling of elastic wave propagation in the media considered setting values of<br>gyration constants in the definite limits and with accounting for the inequlities relating stiffnesses and gyration constants.


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