Feasibility of Detecting Voids with Rayleigh-wave Diffraction

Void detection is challenging due to the complexity of near-surface materials and the limited resolution of geophysical methods. Although multichannel, high-frequency, surfacewave techniques can provide reliable S-wave velocities in different geological settings, they are not suitable for detecting voids directly based on anomalies of the S-wave velocity because of limitations on the resolution of S-wave velocity profiles inverted from surface-wave phase velocities. Therefore, we studied the feasibility of directly detecting voids with surface-wave diffractions. Based on the properties of surface waves, we have derived a Rayleigh-wave diffraction traveltime equation. We also have solved the equation for the depth to the top of a void and an average velocity of Rayleigh waves. Using these equations, the depth to the top of a void can be determined based on traveltime data from a diffraction curve. In practice, only two diffraction times are necessary to define the depth to the top of a void and the average Rayleigh-wave velocity that generates the diffraction curve. We used four two-dimensional square voids to demonstrate the feasibility of detecting a void with Rayleigh-wave diffractions: a 2 m by 2 m with a depth to the top of void of 2 m, 4 m by 4 m with a depth to the top of the void of 7 m, and 6 m by 6 m with depths to the top of the void 12 m and 17 m. Rayleigh-wave diffractions were recognizable for all these models after FK filtering was applied to the synthetic data. The Rayleigh-wave diffraction traveltime equation was verified by the modeled data. A real-world example is presented to show how to utilize the derived equation of surface-wave diffractions.