## 3 GPR Image Characteristics Analysis
### Characteristics of Loose Defect  
In the instantaneous amplitude image (see Figure 6a), at 2 ns, 6 ns, and 12 ns, the electromagnetic waves consistently generated strong reflective signals. The uniform distribution of the reflective signals at 2 ns and 6 ns indicated a subgrade structural interface. However, at 12 ns, divergent reflective signals indicated a significant disparity in the relative permittivity of the filling medium, suggesting the upper boundary of a loose defect region. At 15 ns, the reflective signals continued to display divergence, accompanied by minor fluctuations, which implied the persistence of the loose defects within the area. As shown in Figure 6b, the normalized instantaneous amplitude of the loose defect revealed strong reflections at 2 ns, 6 ns, and 12 ns, with the strongest signal observed at 2 ns, followed by a secondary peak at 6 ns and a weaker signal at 12 ns. These peaks corresponded to the locations of changes in the electrical parameters between the subgrade structural layers and the target anomaly. By analyzing the instantaneous amplitude and the fluctuation amplitude of the reflected wave in the GPR image, information about the subgrade structural layers and the upper interface of the defect could be inferred.  
In the instantaneous phase image (see Figure 6a), when the electromagnetic wave traveled at 10 ns, discontinuities in the phase and emission-like patterns were observed at both ends. Between 10 ns and 30 ns, the instantaneous phase image exhibited a downward-diverging wave, characterized by disrupted, intersecting, and discontinuous in-phase axes. This pattern allowed for the estimation of the size and boundary information of the loose defect in the subgrade. As shown in Figure 7b, which presents the normalized single-trace instantaneous phase image, the presence of electrical differences within the subgrade structure could be inferred based on the reversal of the in-phase axis at 2 ns and 6 ns. The areas marked by green circles in the figure indicate where the electromagnetic waves propagated within the pavement surface and the base layer, showing continuous in-phase axes without phase reversal due to the absence of anomalies. Between 10 ns and 30 ns, multiple phase reversals occurred, indicating multiple reflections and refractions within the anomalous region between 10 ns and 30 ns.  
In the instantaneous frequency image (see Figure 8a), during the propagation of the electromagnetic waves within the loose defect area, high-frequency reflection waves exhibited random and irregular distributions. The boundary between the subgrade structural layers and the target anomaly, due to electrical differences, led to higher instantaneous frequencies of the reflection waves at travel times of approximately 2 ns, 6 ns, 10 ns, 14 ns, and 18 ns. Outside these intervals, when the electromagnetic waves propagated within the pavement and base layers, no anomalies were present, resulting in the absence of abnormal high-frequency reflections. Based on the characteristics of the instantaneous frequency image, the boundaries of the subgrade structural layers and anomalies could be inferred.  
Figure 6: Loose defect instantaneous amplitude features.