## 2 Materials and Methods
### GPR Data Acquisition and Processing  
The field data acquisition adopted the SIR-3000 GPR with a ground coupling system, shielded antenna with a central frequency of 400 MHz and 100 MHz, center control unit, and host computer (for data acquisition). The main testing equipment are shown in Figure 4, and the parameter settings for field data collection are shown in Table 1.  
The testing line was arranged in a series of U-shapes along the U-shaped sheet-pile wall, as shown in Figure 5, with the testing line indicated by the red line. The starting point of the measurement was at the southern endpoint of pile #1, and the ending point was at the northern endpoint of pile #6. The length of the test line was about 11.7 m, of which the length of the measuring line of pile #1 was 1.7 m, while that of the other piles was 2 m each. The starting point of the measuring line is displayed in Figure 5. A 400 MHz antenna and 100 MHz antenna were used for the non-destructive testing. Due to the limitation of site conditions, the measuring wheel could not be used, and the GPR data was collected by point detection. Figure 4: SIR-3000 GPR system field detection: (**a**) 400 MHz, (**b**) 100 MHz. Figure 3: U-shaped sheet-pile engineering field profile. The GPR data storage format is binary or hexadecimal in domestic and international systems. Additionally, each GPR data file has a file header. In this study, we adopted [PERSON]'s method to process the GPR data because of the flexibility [18]. In the meanwhile, the converted data can be reconverted to the original data format, and the build-in processing software can be used for display and processing. During propagation in an electric medium, radar signals rapidly attenuate and the amplitude decreases, especially for deep information. In the radar detection of U-shaped sheet piles, deep information is often weak, which is not conducive to the recognition of deep abnormal signals. Therefore, it is very important to develop new GPR data processing methods. Based on the conventional processing (zero correction, bad trace elimination, and background filtering), two kinds of data processing methods to improve deep reflection \begin{table}
\begin{tabular}{c c c} \hline \hline
**Antenna Type** & **400 MHz** & **100 MHz** \\ \hline Collection mode & Point collection & Point collection \\ Distance of points (m) & 0.2 & 0.5 \\ Time window (ns) & 240 & 380 \\ Sampling points & 1024 & 1024 \\ Gain points & 5 & 5 \\ Band-pass filtering (MHz) & 100–800 & 25–300 \\ Transmit ratio (KHz) & 100 & 50 \\ Data bits & 16 & 16 \\ Stack & 64 & 64 \\ Scan number/meter & 64 & 64 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameter settings for field data collection. Figure 5: GPR survey line arrangement diagram. information recognition are studied, namely, time-varying automatic gain and wavelet transform processing. Through the gain processing of the radar signal, the amplitude of deep information can be improved, which is helpful for radar signal comparison and waveform tracking. The commonly used gain processing methods in build-in software are mainly linear gain and exponential gain. In this study, the time-varying automatic gain was studied, and the gain weight was automatically adjusted according to the strength of signals at different moments, to achieve the purpose of automatic gain. The calculation equation is as follows:  
\[x^{\prime}(t)=x(t)w(t) \tag{1}\]  
where \(w(t)\) is the gain weight at \(t\) time, \(x(t)\) is the original signal, and \(x^{\prime}(t)\) is the signal after time-varying automatic gain. By multiplying the stronger signal by a smaller weight and the weaker signal by a larger weight, the purpose of energy balance is achieved and the gain weight changes slowly with time. The calculation process is as follows:  
1. The signal is divided into \(M\) time-windows, with half of each time-window overlapping, to reduce the drastic fluctuation of gain weight. 2. The average amplitude of each time-window \(A(i)\) is calculated.