Variance of elastic wave scattering from randomly rough surfaces. (October 2021) - Shi, F.
Abstract: Elastic waves scattered by randomly rough surfaces in solid media play an important role across research topics including ultrasonic wave detection and imaging, seismic wave exploration and phonon boundary interaction. Previous attention has focused upon the mean/expected scattering intensity for both compressional (P) and shear (S) waves. In this article, the variance or the standard deviation (sd) of elastic wave scattering from randomly rough surfaces is studied, which so far has been neglected despite their practical importance in elastic wave applications, via an analytical approach. Theoretical formulae are derived with the aid of the elastodynamic Kirchhoff approximation (KA), to rapidly predict the variance of the scattering amplitude and the intensity, once the statistical parameters of the roughness are known. Theoretical formulae are then successfully validated against high-fidelity Monte Carlo finite element (FE) simulations at different scattering angles across a range of roughness. With the analytical approach the effects of rms roughness, the correlation length and the surface length on the standard deviation of the scattering amplitude are analysed. The significance for applications is illustrated in one important example taken from the field of ultrasonic wave detection of planar rough defects. The theoretical formulae accurately predict the lower bound of the scattering amplitude, which helps set an amplitude threshold confidently, for detecting any possible rough crack in a single inspection while minimising the risk of false alarm. The significantly improved accuracy and confidence of detection enable reliable decisions to be made about whether it is safe to continue using an engineering component.