A new identity for the surface-impedance matrix and its application to the determination of surface-wave speeds

It is well known in surface-wave theory that the secular equation for the surface-wave speed v can be written as det M = 0 in terms of the surface-impedance matrix M. It is shown in this paper that M satisfies the simple identity (M - iR)T-1 (M + iR(T)) - Q + rhov(2) I = 0 in the usual notation in the Stroh formalism. This identity provides an efficient method for calculating the wave speed of surface waves in unstressed or pre-stressed elastic half-spaces. The method is explained and illustrated by examples. It is also shown that the buckling/wrinkling pre-stress for a pre-stressed elastic half-space can be calculated using the same procedure but with pre-stress playing the role of v.