## 2 Materials and Methods  
### Ground-Penetrating Radar  
Ground-Penetrating Radar (GPR) is a non-destructive geophysical method that emits high-frequency electromagnetic (EM) waves to generate images of subsurface structures and buried utilities [5]. The effectiveness of GPR is based on variations in the physical and electrical properties of subsurface materials, which influence the propagation and reflection of EM waves [13].  
GPR typically operates within a frequency range of 10 MHz to 1000 MHz. Higher frequencies provide finer resolution but limited penetration depth, while lower frequencies penetrate deeper but offer lower resolution [9]. When EM waves encounter interfaces between materials with different dielectric constants, a portion of the wave is reflected back to the receiver, and the remainder continues to travel deeper into the subsurface [5; 6].  
The strength of these reflections and the velocity of wave propagation are governed by the dielectric contrast between the layers. By analyzing the time delay of the returned signals, it becomes possible to estimate the depth, thickness, and geometry of features such as layers, fractures, and voids [9; 12]. This capability makes GPR a widely applied tool for detecting both metallic and non-metallic objects embedded in materials such as soil, rock, and concrete [12].  
As illustrated in Figure 1, when EM waves encounter boundaries between materials with differing dielectric properties, the reflected signals generate a time delay profile. These profiles can then be processed to produce detailed cross-sectional images of subsurface structures [14].  
The reflection strength and wave velocity are governed by the contrast in dielectric properties, and by measuring the time delay of returned signals, it is possible to estimate the depth, thickness, and spatial distribution of subsurface features such as layers, fractures, and voids. This makes GPR a widely used non-destructive method for locating both metallic and non-metallic objects buried within soil, rock, or other opaque media [15; 16; 17; 18; 19; 20; 21; 22]. As illustrated in Figure 1, when electromagnetic waves encounter interfaces between materials with different dielectric properties, a portion of the signal is reflected back to the receiver while the remainder continues to propagate through the medium. This interaction generates a time delay profile that enables the visualization of subsurface structures, as described by [14].  
Recent developments have focused on improving the detection of buried non-metallic pipelines using advanced signal processing and hybrid sensing methods. For instance, ref. [23] proposed a GPR-based technique specifically tailored for fiber-reinforced polymer (FRP) and non-metallic pipe detection. Ref. [8] offered a comprehensive review of acoustic-based methods, highlighting their integration potential with GPR systems. Refs. [24; 25] introduced wavelet cross-correlation and acoustic attenuation models for localizing polyethylene (PE) pipelines, demonstrating an enhanced accuracy under complex subsurface conditions. Furthermore, ref. [26] applied an elliptical inversion model to estimate pipe direction and curvature from GPR imagery, representing a novel approach to the spatial interpretation of buried infrastructure.