Numerical Simulation of Stoneley Surface Wave Propagating Along Elastic-Elastic Interface
Abstract:There are seven waves in dynamic theory of elasticity that are named after their discoverers. In 1885, Lord Rayleigh had published a paper where he described a wave capable to propagate along a free surface of an elastic half-space. In 1911, Love had considered a pure shear motion for a model of an elastic layer, bounded by an elastic halfspace. In 1917, Lamb had discovered symmetric and asymmetric waves propagating in an isolated elastic plate. Stoneley (1924) had found that a surface wave can propagate along an interface between two elastic halfspaces for some parameter combinations, and then Scholte had shown in 1942, that in a model where one of the halfspaces is fluid, the surface wave can exist for any parameters. The sixth wave is named after Biot (1956), and it describes a slow diffusive wave in a fluid-saturated poroelastic media. Finally, in 1962 Krauklis had found a dispersive fluid wave in a system of a fluid layer bounded by two elastic halfspaces.
Remarkably, all but one of the named waves were found and predicted theoretically as the results of mathematical and physical approaches in Nature exploration to be later confirmed in experiments and used in various scientific and practical applications. The only wave, which was not observed neither numerically nor experimentally until now is Stoneley wave. A likely reason for that is in rather restricted combinations of material parameters for this wave to exist. Indeed, the ratio R of shear velocities a model must be inside of the interval (0.8742 – 1). The ratio of the Stoneley wave velocity to the largest share wave velocity must be in the interval (0.8742 – R).
To fill the gap, we performed 2D finite-difference simulation for a model consisting of polysterene (with velocities Vp1=2.350 m/s, Vs1=1190. m/s, and density Rho1= 1.06 g/m3) and gold (with velocities Vp2=3.240 m/s, Vs2=1200. m/s, and density Rho2= 19.7 g/m3). A corresponded root of a dispersion equation was found with a help of original analytical solution developed by WaveLab. A point force source oriented along the meadia interfaces was used. A clear localized energy following the both direct shear waves is the Stoneley wave (Figure 1).