PROPAGATION IN AN ANISOTROPIC PERIODICALLY MULTILAYERED MEDIUM

An anisotropic multilayered medium is studied using the method of tran sfer matrices, developed by Thomson [J. Appl. Phys. 21, 89 (1950)] and Haskell [Bull. Seismol. Soc. Am. 43, 17 (1953)]. The propagation equa tions in each layer of the multilayered medium use the form developed by Rokhlin et al. [J. Acoust. Soc. Am. 79, 906-918 (1986); J. Appl. Ph ys. 59 (11), 3672-3677 (1986)]. Physical explanations are given, notab ly when a layer is made up of a monoclinic crystal system medium. The displacement amplitudes of the waves in one layer may be expressed as a function of those in another layer using a propagation matrix form, which is equivalent to relating the displacement stresses of a layer t o those in another layer. An anisotropic periodically multilayered med ium is then studied by using a propagation matrix that has particular properties: a determinant equal to one and eigenvalues corresponding t o the propagation of the Floquet waves. An example of such a medium wi th the axis of symmetry of each layer perpendicular to the interfaces is then presented together with the associated reflection coefficients as a function of the frequency or of the incident angle.