# Data Interpretation Technology of GPR Survey Based on Variational Mode Decomposition
## 4 Time Frequency Analysis of GPR Simulation Signal
### Time Frequency of VMD Comparison with Other Methods  
For further verifying the advantage of the proposed method, VMD comparison with other methods were studied for signal interpretation of GPR and they used a detection of three-layer concrete  
Figure 8: Time-frequency section of GPR.  
Figure 9: Space frequency section of GPR.  
pavement as an example. See Figure 10a for the GPR forward sketch. The model measured 2.5 m \(\times\) 0.45 m; the uppermost layer was air, the middle layer was concrete, and the bottom layer was dry sand. There was one incline facet between the concrete and dry sand. The depth of the concrete was between 0.15 m and 0.25 m. The permittivity and conductivity of the concrete were 6 and 0.005 S/m, respectively, while the permittivity and conductivity of the dry sand were 3 and 0.0001 S/m respectively. During the simulation of GPR with FDTD, the computational grid size was 0.0025 m, the length of the time window was 12 ns, and the absorbing boundary was an unsplit field perfectly matched layer (UPML). The central frequency of the transceiver antenna was set to 900 MHz, the transceiver antenna distance was 0.025 m, and the work mode was self-excitation and self-receiving. From the left 0.1 m position to the right 2.3 m at 0.02 m intervals, a total of 115 trace data was obtained. Figure 10b shows the scanner result of the simulation.  
In Figure 10b, each IMF can be decomposed using VMD and the frequency division section can be obtained while using the Hilbert transform. Figure 11 shows the frequency division section of the simulation signal of GPR at 1.0 and 1.2 GHz frequencies.  
According to Figure 11, the frequency division section at 1.0 GHz clearly shows the ground-coupled direct wave (Figure 11a), and the slice of the time-frequency spectrum at 1.2 GHz clearly shows the reflected wave between the concrete and the dry sand interface (Figure 11b). It can be seen that the time-frequency spectrum separates the different GPR components that are based on VMD.  
EMD and EEMD were used to calculate the time-frequency spectrum of the GPR signal simulation in order to further study the effects of VMD on GPR signals, respectively. Figure 12 shows the time-frequency spectrum at 1.0 GHz and 1.2 GHz based on EMD, and Figure 13 shows the time-frequency spectrum at 1.0 GHz and 1.2 GHz based on EEMD.  
Figure 11: Frequency division section based on VMD: (**a**) frequency division section at 1.0 GHz; and, (**b**) frequency division section at 1.2 GHz.  
Figure 10: Simulation model of GPR: (**a**) forward geometry model; and, (**b**) simulation signal of GPR.  
In Figure 12, the frequency division section at 1.0 GHz has a weak performance on the direct wave (Figure 12a). However, the frequency division section at 1.2 GHz does not show a reflected wave on the interface between the concrete and sand (Figure 12b), but there is still direct wave information present. The time-frequency spectrum that was obtained using EMD is not clear on the separation between the different components of the radar signal.  
Figure 13a shows the frequency division sections at 1.0 GHz based on EEMD. The frequency division section at 1.0 GHz shows direct waves. However, the time-frequency spectrum at 1.2 GHz displays reflection at the interface of concrete and sand (Figure 13b), but the effect is not obvious. There are direct waves and other information in Figure 13b. EEMD cannot decompose each of the frequency components of the simulation GPR signal. VMD is better than the other two methods in separating the different components of the GPR signal among the three methods for solving the time-frequency spectrum analysis.