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 Raylei gh angle, E-s, was theoretically derived by considering the interaction bet ween the energy: bf the penetrated Rayleigh wave, E-0, and the microstructu re in the subsurface within the Schoch displacement. Delta(s), as E-s = 0.2 5 alpha(s)Delta(s)E(0), where alpha(s) is the attenuation coefficient due t o scattering. The backscattered ultrasonic energy, E-Bs, at the Rayleigh an gle was also derived as E-Bs proportional to D(3)f(3) in the Rayleigh scatt ering region and E-Bs proportional to Df in the stochastic scattering regio n, 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 analy sis of the backscattered signals from the interface between the water/stain less 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 th an or equal to 6 pi D and lambda(R) less than or equal to 6 pi D, respectiv ely. 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 distributio n in the region of lambda(R) less than or equal to 6 pi D. This implies tha t 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 backsc attered ultrasonic wave at the Rayleigh angle was built up predominantly by the scattering from the grain boundaries in the subsurface within the Scho ch displacement and the direct scattering from the irregularities on the su rface.