## 2 Materials and Methods
### Algorithms for the Primary Processing of GPR Data  
As part of this research project, experimental studies were conducted using the OKO-2 series GPR (GEOTECH company, Moscow, Russia). A 400 MHz central frequency antenna was used for probing, providing an optimal balance between penetration depth and resolution. Measurements were performed with a sampling frequency of 1 GHz, an antenna separation of 0.3 m, and a scanning step of 0.15 m along the survey line. The algorithm for primary data processing was implemented using the specialized CartScan software [31] (GEOTECH company, Moscow, Russia) supplied with the GPR equipment. The main objectives of the processing were to suppress low-frequency noise, eliminate external interference, and enhance reflected signals corresponding to the boundaries of the road pavement layers. Figure 1 presents the raw profile of a 500-meter-long radar image acquired without signal amplification. Figure 1: Subsurface structure acquired using the OKO-2 series GPR system. Figure 1 shows the subsurface structure, where the vertical axis (\(Oz\)) indicates the depth within the pavement structure (with a maximum signal penetration depth of 3 m), and the horizontal axis (\(Ox\)) represents the length of the surveyed road segment (with a maximum length of 500 m). The image also displays black, white, and gray shades. Black areas correspond to local signal maxima, white to minima, and gray to intermediate values. Drawing a vertical line from any point \(x_{0}\) of the radar profile (Figure 1) along the \(Ox\)-axis yields a 2D graph, as shown in Figure 2.  
The 2D graph depicted in Figure 2 is referred to as a trace. The trace represents a time-dependent function (the medium's response), illustrating the behavior of an electromagnetic pulse as it propagates through the subsurface medium. Here, the absolute value of the function corresponds to the signal amplitude. The distance between adjacent traces along the \(Ox\)-axis is 15 cm. The collection of all traces forms the radar profile (Figure 1). Given that the length of the road in the radar profile is 500 m, the number of traces in the profile is approximately 3333. Since the signal has a central frequency of 400 MHz, it exhibits minimal sensitivity to noise and interference. Therefore, bandpass filtering, intended to remove noise and interference, is unnecessary. The next step involves applying mean subtraction (Figure 3), which entails calculating the average trace across all traces in the profile and subtracting it from each trace. The subsequent step involves applying automatic gain control (AGC) (Figure 4) to enhance the visibility of the signal at greater depths, accounting for the attenuation of the signal amplitude with depth. AGC represents an algorithm utilized in data processing systems, including mobile applications for road diagnostics, such as the CartScan software package [31]. The primary purpose of AGC is to maintain a stable input signal level through dynamic gain adjustment. This is particularly critical when analyzing vehicle vibrations, as it enables compensation for variations in driving conditions, vehicle types, and smartphone mounting configurations. The algorithm evaluates the power or amplitude of the accelerometer signal, compares it with a reference level, and adjusts the gain to maintain the signal within the optimal range. This enhances the system's sensitivity to minor road surface defects and improves the quality of subsequent analysis, including the identification of potholes and surface irregularities. Figure 2: Trace representing the subsurface medium at a specific location \(x_{0}\) along the \(Ox\)-axis. AGC is also widely employed in other fields, such as global satellite navigation systems (GNSS), where its performance may be compromised by intentional interference, including high-power interference signals (jamming) or signal spoofing [32]. In such cases, signal characteristics may be altered, leading AGC to produce inaccurate estimations, thereby impacting the overall system performance.