Analytical solution to the scattering of Rayleigh waves by spherical inclusions

The scattering of Rayleigh waves by various types of inclusions is of great significance to analyzing many experimentally measured surface acoustic waves but still lacks any analytical solution so far. Here we succeed in expressing the Rayleigh wave as a linear combination of spherical harmonic functions with all the coefficients being given in closed-form. In the context of multiple reflections during the scattering of Rayleigh waves by spherical inclusions, the primary “first reflection” introduced by the boundary condition of inclusions is decoupled using spherical harmonic series. Using this framework, we present, for the first time, the near-field analytical solution for the scattered Rayleigh waves by spherical inclusions (in the absence of multiple reflections) of two fundamental types, i.e., a rigid inclusion and a void. The significant difference between scattering signals of the two types provides the possibility to characterize inclusions with different mechanical properties via scattering of Rayleigh wave.