## 3 Results and Discussion
### Laboratory Tests  
As shown in Figure 5, from top to bottom, the constructed top-coal structure in laboratory conditions mainly includes a rock layer, a coal layer, a gangue layer and a coal layer; two groups of GPR central frequencies (900 MHz and 1500 MHz) were selected to verify the GPR data fusion effectiveness in the laboratory environment. In the experiments, we separately used two frequencies for the GPR antenna to detect the top-coal structure; subsequently, preprocessing and spatial alignment were carried out to deal with the multi-frequency GPR data. Assume that the time window of each frequency GPR profile was uniformly set to 15 ns, and the number of sampling points was 512 channels. For the sake of simple analysis, we selected 400 trace data of multi-frequency GPR to verify the fusion effectiveness.  
The experimental results are provided in Figure 6. We can see that the detection accuracy and image resolution of the 1500 MHz GPR profile in Figure 6a are more accurate than that of the 900 MHz GPR profile in Figure 6b with a range of 0-7.5 ns, while the 1500 MHz GPR profile penetration distance is limited to about 7.5 ns; when the transmitting time is greater than 7.5 ns, the reflection signal is almost invisible in the GPR profile. Conversely, the 900 MHz GPR profile still has a reflection signal between 7.5 ns and 11 ns. To effectively combine the high detection resolution of the 1500 MHz GPR data and the large penetration depth of the 900 MHz GPR data, we used our proposed method to fuse the 1500 MHz and 900 MHz frequency GPR data; the experimental results are provided in Figure 6c. We can see that the fusion results of the 900 MHz and 1500 MHz GPRs not only possess high-resolution characteristics of high frequency in a range of 0-7.5 ns but also have a large penetration depth of low frequency in a range of 7.5-15 ns.  
To quantitatively evaluate the multi-frequency GPR data fusion effectiveness in a laboratory environment, our proposed method was compared with the genetic [11], time-varying [14] and wavelet transform [16] fusion methods based on the _IE_, _SF_ and _LG_ evaluation criteria. The comparison results are provided in Table 1; it can be seen that the low-frequency GPR profile (900 MHz) has a higher value of _IE_ and _LG_ due to its greater penetration depth, while the high frequency (1500 MHz) possesses a higher value of _SF_ because of its higher resolution. The fusion results for the 900 MHz and 1500 MHz GPR data using our proposed method possess the best performance. Compared with the genetic, time-varying and wavelet transform fusion methods, the fusion results for the _IE_, _SF_ and _LG_ evaluation criteria improved by \"12.74%, 11.46% and 11.97%\", \"13.59%, 11.47% and 11.96%\"; and \"12.77%, 8.51% and 10.64%\", respectively. Furthermore, the above experimental results prove that the multi-frequency GPR data fused by our proposed method possess both the merits of high-frequency GPR data--higher-resolution and low-frequency data and greater detection depth--further proving our presented method to be feasible and effective.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Item**} & \multirow{2}{*}{**900 MH**} & \multirow{2}{*}{**1500 MH**} & \multicolumn{2}{c}{**Our**} & \multirow{2}{*}{**Genetic**} & \multirow{2}{*}{**Time-Varying**} & \multirow{2}{*}{**Wavelet**} \\  & & & **Proposed** & & & & **Method** \\ \hline _IE_ & 6.74 & 5.24 & 7.85 & 6.85 & 6.95 & 6.91 \\ _SF_ & 26.33 & 28.21 & 43.57 & 37.65 & 38.57 & 38.36 \\ _LG_ & 0.37 & 0.31 & 0.47 & 0.41 & 0.43 & 0.42 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The comparison results of our proposed method with the genetic, time-varying and wavelet transform methods using 900 MHz and 1500 MHz GPR data.  
Figure 5: The complex top-coal structure model. It consists of four different layer structures, from top to bottom: a rock layer, a coal layer, a gangue layer and a coal layer; also, every layer has a different dielectric constant and conductivity.