Influence of the microstructure on the ultrasonic backscattered energy from a liquid/solid interface at the Rayleigh angle

The scattered ultrasonic energy from a liquid/solid interface at the Rayleigh angle, E-s, was theoretically derived by considering the interaction between the energy: bf the penetrated Rayleigh wave, E-0, and the microstructure in the subsurface within the Schoch displacement. Delta(s), as E-s = 0.25 alpha(s)Delta(s)E(0), where alpha(s) is the attenuation coefficient due to scattering. The backscattered ultrasonic energy, E-Bs, at the Rayleigh angle was also derived as E-Bs proportional to D(3)f(3) in the Rayleigh scattering region and E-Bs proportional to Df in the stochastic scattering region, where D is the average grain size and f is the frequency. The grain size and the frequency dependence of the backscattered ultrasonic energy at the Rayleigh angle were obtained by both, integration and power spectrum analysis of the backscattered signals from the interface between the water/stainless steel plates with the average grain size varying between 5.6 and 40.5 mu m. The exponents of the grain size and the frequency dependence obtained by both methods were about 3.5 and 2 in the region of lambda(R) greater than or equal to 6 pi D and lambda(R) less than or equal to 6 pi D, respectively. The deviation of the exponents is attributed to the direct scattering from the surface irregularities in the region of lambda(R) greater than or equal to 6 pi D and the stochastic scattering due to grain size distribution in the region of lambda(R) less than or equal to 6 pi D. This implies that the exponents depend on the ratio of the average size of the scatterer to the wavelength of the Rayleigh wave. The results suggested that the backscattered ultrasonic wave at the Rayleigh angle was built up predominantly by the scattering from the grain boundaries in the subsurface within the Schoch displacement and the direct scattering from the irregularities on the surface.