Investigation of Surface Roughness–Induced Attenuation of Reflected Waves Using a Quasi-Monte Carlo Method

Abstract An understanding of the influence of surface roughness on wave scattering and accurate predictions of wave amplitudes are crucial for quantitative ultrasonic nondestructive testing and evaluation. In this work, the effects of surface roughness on the reflection coefficient are investigated using a quasi-Monte Carlo (QMC) method. The wave fields reflected from smooth and rough interfaces with an immersion transducer are modeled using the Rayleigh integral method, and the solutions are efficiently calculated using the QMC method for interfaces constructed using pseudo-random samples. The reflected wave fields are simulated and presented, and the properties of coherent and incoherent waves affected by interface roughness are discussed. The surface roughness–induced attenuation of reflected waves is calculated using the ratio of received pressures for waves reflected from rough and smooth interfaces, and the predicted results are compared with those obtained using other recognized methods. It is shown that at low levels of roughness, excellent agreement is obtained between the results from the QMC method and the well-known Kirchhoff approximation, while for high levels of roughness, where the Kirchhoff theory gives pessimistic results, the predicted values agree well with those simulated using a finite element modeling approach, thus verifying the effectiveness of the proposed method.