Some theoretical and numerical observations on scattering of Rayleigh waves in media containing shallow rectangular cavities

Based on the Betti–Rayleigh reciprocity theorem and the thin layer method (TLM), the discrete analytical displacement expression of Rayleigh waves scattered from heterogeneities in layered half spaces are presented. A parametric study on the scattering of Rayleigh waves is conducted for homogeneous half spaces with rectangular cavities present in the far field. For cavities that are long in the direction of wave propagation, the theory of Lamb waves in free plates is used to explain the propagation behavior of the waves above cavities. Some numerical simulations are used to verify the analyses. In order to establish the relationship between the depth of cavity and the wavelength, the spectra in the frequency domain are converted into ones in the wavelength domain. Effects of wave scattering on the spectral pattern in the offset-wavelength domain are investigated. The results show that the scattering of Rayleigh waves is not only related to the dimensionless location parameters ht/λR and h/λR but also ω2, where ht, h, λR and ω denote the depth and the height of the cavity, the wavelength of Rayleigh waves and the angular frequency, respectively. For long cavities, the near and the far faces of cavity can be roughly located from the “ripples” of the spectra and changes in the energy in the offset-wavelength domain and the depth of the cavity can be estimated from the critical wavelength associated with the onset of disturbance in the spectra above the cavity. ► The discrete displacement expression of the scattered waves is derived. ► The scattering of R-waves and the body waves can be separately studied. ► The propagation behavior of the scattered waves is analyzed. ► Effects of the cavity sizes and the frequency on R-wave scattering are discussed. ► The method to estimate the locations of the cavity is suggested.