Analytic relations between the elastic constants and the group velocity in an arbitrary direction of symmetry planes of media with orthorhombic or higher symmetry

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Abstract
This paper presents various closed-form analytic formulas that relate the group velocity of elastic pulses propagating in an arbitrary direction of the symmetry planes of elastic media with orthorhombic or higher symmetry to their elastic constants. Simple equations relating the direction of a group velocity to that of the corresponding wave normal are derived for both quasilongitudinal and quasitransverse modes. A forward solution to obtaining the elastic constants from the group-velocity data on the symmetry planes by using these relations is illustrated with examples of transversely isotropic zinc and cubic silicon crystals. Both numerically simulated and experimental data are used to check the derived relations and to demonstrate their usefulness.