A hybrid analytical and numerical approach for backscattering of leaky Rayleigh waves from inclusions at an inviscid...

A hybrid analytical and numerical approach is developed to describe the backscattering of leaky Rayleigh waves (LRWs) from surface and subsurface elastic inclusions at an inviscid fluid/solid interface. The method combines analytical expressions for leaky attenuation with the Born approximation for weak scattering, thus separating the scattering contribution from small inclusions and the leakage. Model predictions agree well with finite element simulations across a range of inclusion shapes, sizes, and depths. The analysis reveals that the validity of the analytical model is governed by the effects of the normalized frequency, the acoustic impedance mismatch, and the inclusion depth. While the model remains accurate for inclusions situated within a sub-wavelength depth and with characteristic dimensions up to approximately one wavelength under weak impedance contrasts, this upper size limit decreases progressively as the impedance mismatch increases. It also confirms that leaky attenuation is independent of inclusion-induced scattering. Meanwhile, comparisons with vacuum-solid and fluid-solid boundaries indicate that fluid loading modifies the backscattered amplitude by influencing the LRW wavenumber. The results provide physical explanations for Rayleigh-type wave behavior at fluid-loaded interfaces and establish a general framework for modeling LRW-inclusion interactions in elastic media.