Scattering of plane harmonic P , SV or Rayleigh waves by a completely embedded corrugated cavity

SUMMARY Scattering of plane harmonic P , SV or Rayleigh waves by a 2‐D corrugated cavity completely embedded in an isotropic half‐space or full‐space is investigated by using a direct boundary integral equation method. The corrugated scatterer is generated by superimposing a sinusoidal perturbation of arbitrary amplitude and period to a smooth elliptical shape. Extensive testing of the numerical results is done through comparisons with analytical and numerical solutions for the corresponding smooth surface limits. The displacement field is evaluated along the half‐space surface or the scatterer for a wide range of frequencies and corrugation shapes. The results clearly demonstrate the importance of the cavity roughness on the ensuing motion. The cavity response is found to strongly depend upon the corrugation amplitude and period as well as the frequency of the incident wave. For the half‐space problem with a vertical P or SV incidence, the rough cavity far‐field surface motion may attenuate differently from the free‐field result than the corresponding smooth cavity response. In the near field, the corrugated response is found to be significantly different from the equivalent smooth cavity result. For an oblique P , SV or a Rayleigh incidence, the rough cavity motion at the illuminated portion of the half‐space surface may be greatly different from the corresponding smooth cavity motion. In the shadow portion of the half‐space, the presence of the corrugation may produce an important shielding effect in the surface motion. These key differences between the rough and smooth cavity responses are especially pronounced for shorter corrugation periods and at higher frequencies. In addition, a strong site effect is observed atop the rough cavity.