Analytical solution to Scholte’s secular equation for isotropic elastic media

Abstract

In terms of a method based on Cauchy integrals, we have obtained a robust analytic expression to predict a unique physical solution for the Scholte slowness in all range of possible elastic and isotropic media. Proper analysis of the discontinuities of the secular Scholte equation allows the identification of the velocity of the evanescent wave in one of three possible regimes. When the liquid phase tends to vanish, it was observed: a) the Rayleigh wave solution or the free surface limit, and b) the rarefied fluid medium limit, where there exists a gradual extinction of the Scholte wave as both the density and velocity of the fluid decrease. In general terms, the results show that the propagation speed of a Scholte wave is less than or equal to that of a Rayleigh wave.