## 3 Results  
### Investigation in Simple Scenarios  
The basic approach for identifying the unstable rock structures is to identify the rock interfaces, which is firstly investigated in this paper. Two simple scenarios, a practical radargram with buried objects and a numerically simulated radargram with predefined cracked rock areas, are under investigation to evaluate the accuracy of the developed signal processing approach in locating object interfaces. Firstly, GPR acquired the subterranean profile with two pre-buried pipelines (32 cm diameters), which are sparsely distributed with around 2.5 m interval. The pipelines are discernible enough and will not interfere each other's signals because of the large burying distance. The central frequency  
Figure 1: (**a**) Representative ground penetrating radar (GPR) signals from two measurement traces with and without buried objects beneath respectively. (**b**) Fast Fourier transform results of these two signal series. of GPR antenna is 700 MHz. Figure 2 illustrates the pre-processed radargram, with the measurement length \(L\) (\(0\leq L\leq 6\) m) and detection depth \(Z\) (\(0\leq Z\leq 2.5\) m). The pre-processing parameters are \(\alpha=0.56\), \(\varphi=0.1\) and \(Z_{0}=0.25\) m. Two red circles are manually supplemented to the illustration corresponding to the locations and sizes of the pipelines. Although hyperbolic signals appear at pipeline locations, their two 'pseudo' tails (marked as dashed boxes in Figure 2) have extended outside the pipeline interfaces, which will result in misidentifying normal areas as our targets. These hyperbolic interference signals are generated by the wide-angle transmission of electromagnetic waves [16]. Intensive signals in the near-surface portions (with depth less than 0.75 m) are polluted by noises and without consideration in this research. Two representative signal traces (seen in Figure 3) on Lines 1 and 2 with and without buried pipelines respectively are compared to analyze the mode difference. Distinct local modes appear around \(Z=1\) m due to the existence of pipelines. Figure 4 shows the decomposition results by EEMD on both traces. IMF1s are noise-polluted mode functions with limited physical meanings because white noises are added to signals in EEMD procedures. IMF2s, IMF5s and IMF6s present little evidence of mode difference between Lines 1 and 2, thereby not suitable for further object identification. This missing characteristic reappears in IMF3s and IMF4s, as visible oscillations exist around Z = 1 m on Line 1 (corresponding positions marked in Figure 4). Therefore, IMF3s and IMF4s on all traces of the pre-processed radargram are chosen to reconstruct the subsurface profile. Figure 3: GPR signals of Line 1 and 2 from pipeline detection with initialized duration. Figure 2: GPR signal amplitude profile of two pre-buried pipelines after pre-processing. Figure 5 illustrates the reconstructed profiles by IMF3s and IMF4s respectively, which are decomposed from all signal traces. It is reasonable to eliminate the IMF signals weaker than the added white noises (amplitudes less than 500) to avoid artificial noise issues, and this would affect little on the actual modes (strength 20-40 times). In the IMF3s profile (Figure 5a), the two hyperbolic 'tails' of each pipeline have been eliminated. Meanwhile, the pipelines have been revealed from the noisy subterranean environment with highlighted locations and sizes. In contrast, these commendable results have not appeared as expected in the IMF4s profile (Figure 5b). Interference signals remain outside the pipeline interfaces, and near-surface signals have extended to deeper areas (from 0.75 m in Figure 2 to 1 m in Figure 5b) thereby polluting the pipeline signals. Although signals inside the pipeline portions are intensive, this reconstructed IMF4s profile is insufficient to identify the objects. Therefore, only IMF3s acquired by the developed approach can reconstruct a promising underground profile.