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The matrix sign function is shown to provide a simple and direct method toderive some fundamental results in the theory of surface waves in anisotropicmaterials. It is used to establish a shortcut to the basic formulas of theBarnett-Lothe integral formalism and to obtain an explicit solution of thealgebraic matrix Riccati equation for the surface impedance. The matrix signfunction allows the Barnett-Lothe formalism to be readily generalized for theproblem of finding the surface wave speed in a periodically inhomogeneoushalf-space with material properties that are independent of depth. No partialwave solutions need to be found; the surface wave dispersion equation isformulated instead in terms of blocks of the matrix sign function of i timesthe Stroh matrix.

The matrix sign function for solving surface wave problems in homogeneous and laterally periodic elastic half-spaces