LIMITATIONS ON GYRATION CONSTANTS FOR MAIN SYMMETRY SYSTEMS OF ROCKS

Abstract

In the case of propagation of plane elastic waves in anisotropic gyrotropic media, Christoffel tensor is complex; its real part contains stiffnesses and an imaginary part includes components of the fifth-rank gyration tensor. Inequalities relating stiffnesses and gyration constants are derived from the conditions for potential energy to be positive. The necessary and sufficient conditions for the positive definiteness of the complex matrix of stiffnesses and gyration constants are used. Sets of inequalities are obtained for two types of rocks belonging to acentric limit groups ∞∞ and ∞. These inequalities provide a possibility to carry out modelling of elastic wave propagation in the media considered, setting the values of gyration constants not arbitrarily but in accordance with physical laws.