GPR hyperbolic fitting in multi-layered structure: A depth-weighted velocity correction approach

Ground Penetrating Radar (GPR) is a popular non-destructive tool for detecting sub-surface utilities such as pipelines and rebar, which typically produce hyperbolic patterns in radargrams. Although hyperbolic fitting is commonly employed to determine burial depth and wave velocity, these techniques traditionally depend on the assumption of homogeneous media—an assumption that neglects Snell's Law and is seldom realized in field conditions, leading to errors in velocity estimation. To address this challenge, this article introduces a depth-weighted velocity correction approach designed to improve velocity estimation accuracy within layered media. Analogous to Dix conversion in seismology, the algorithm assumes that the effective wave velocity obtained from hyperbolic fitting is a depth-weighted average of the velocities corresponding to each layer, with the proportional distance traveled by electromagnetic (EM) waves through each layer aligning with the layer's relative thickness. By incorporating known thicknesses and velocities of the overlying layers, the algorithm recalculates the wave velocity in the layer containing the target object. It is adaptable to two different hyperbolic models based on the availability of target radius and antenna separation information. The efficacy of the proposed method has been validated through extensive numerical and laboratory experiments, including a sensitivity analysis of the algorithm's parameters. Results confirm that the proposed method effectively reduces the impact of non-target layers, enhancing the accuracy of wave velocity estimations by 9% and 11% in single-overlying and double overlayying cases, respectively. This advancement is beneficial for sub-surface utility detection beneath horizontal overlays such as tunnel linings and asphalt pavement, as well as in air-coupled radar applications for extraterrestrial exploration. Most importantly, Snell's law can not and should not be neglected in GPR analysis.