Feasibility of Detecting Voids with Rayleigh‐Wave Diffraction

Abstract

Void detection is challenging due to the complexity of near‐surface materials and the limited resolution of geophysical methods. Although multichannel, high‐frequency, surface‐wave 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.