Numerical study of ultrasonic Rayleigh wave fields scattered by vertical cracks buried in half-space

In this study, the properties of Rayleigh wave fields scattered at a surface from open vertical cracks with different shapes are investigated. The scattered Rayleigh wave is determined by both the incident Rayleigh wave and its interaction with the crack, and the wave fields are modeled using the Green's function method based on the reciprocity theorem. The reflection coefficient of the Rayleigh wave in two-dimensional coordinates is employed to simplify the area integration over the crack surface for the scattered Rayleigh wave to a line integration over the length of the crack. Numerical simulations are carried out, and the effects of the crack length and depth on the scattered Rayleigh wave fields are discussed. The results indicate that the distribution of a scattered Rayleigh wave field is mainly determined by the crack length, while the amplitude is closely related to the crack depth. Since the reflection coefficient becomes almost stable when the ratio of the crack depth to the Rayleigh wavelength is larger than 1, the variation in the scattered Rayleigh wave field is insignificant for cracks with the same length but varying depths. This work will be helpful for solving the inverse problem of evaluating crack geometry using ultrasonic Rayleigh waves and for further work on Rayleigh waves scattered by cracks with different directions of extension and angles with the surface.