## 3 Simulation Analysis Using SSA for GREATEM Signal De-Noising
### Comparison of SSA and Other De-Noising Methods  
Many scholars use the wavelet threshold method (WT), empirical mode decomposition (EMD), and variational mode decomposition (VMD) to de-noise the GREATEM signal. We compare these four algorithms' de-noising results to verify the superiority of SSA in de-noising GREATEM signals. We use calculated GREATEM signals of the quasi-two-dimensional earth model in Figure 9. We adopt the sym5 wavelet basis, five-layer decomposition, and the principle of fixed threshold (sqtwolog) for WT. The analysis results are shown in Figure 10.  
Figure 9: The apparent resistivity profiles of the quasi-two-dimensional earth model. (**a**) Theoretical model; (**b**) simulation data inversion result; (**c**) inversion result before de-noising; (**d**) inversion result after de-noising.  
Figure 10 shows the calculated GREATEM signal with the higher harmonic noise and the attenuation curve obtained after different de-noising methods. The Xn curve represents the synthetic GREATEM signal with noise; the Sn curve represents the calculated GREATEM signal; the WT, EMD, VMD, and SSA curves represent the de-noising results using WT, EMD, VMD, and SSA, respectively. From Figure 10, we know that all these four de-noising methods can effectively eliminate noise. Among them, the GREATEM signal separated by SSA is closer to the calculated GREATEM signal, proving SSA's superiority in de-noising GREATEM signals.  
Among these four methods, the WT method needs to choose the wavelet base and threshold according to the signal and noise characteristics in the actual de-noising process. The EMD algorithm needs to determine the IMF component structure rules' weight and has end effects. SSA has fewer parameters, easy calculation, and high efficiency. Table 1 shows the comparison of the SNR and RMSE of different methods.  
To further analyze the de-noising effect of the SSA algorithm on the measured GREATEM data, we added the measured noise to the synthetic GREATEM signal and compared four de-noising results in Figure 11. The measured noise contains white noise, spike noise, and power frequency noise. From Figure 11, we see that the signal after de-noising by the SSA is the closest to the original signal, proving that the SSA algorithm can de-noise the measured GREATEM data. Table 2 shows the comparison of the SNR and RMSE of different methods. The effect of the SSA algorithm is more evident when the virtual environment contains considerable higher harmonic noise.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Signal** & **SNR (dB)** & **RMSE** \\ \hline Synthetic GREATEM signal & 26.0822 & 0.0011 \\ Signal de-noised by WT & 39.6726 & 2.2990 \(\times\) 10\({}^{-4}\) \\ Signal de-noised by EMD & 26.9985 & 9.8755 \(\times\) 10\({}^{-4}\) \\ Signal de-noised by VMD & 30.1032 & 6.8469 \(\times\) 10\({}^{-4}\) \\ Signal de-noised by SSA & 54.2960 & 4.2744 \(\times\) 10\({}^{-5}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparison of indexes for different algorithms to eliminate the higher harmonic noise.  
Figure 10: Comparison of de-noising results by different methods. (**a**) Overall view; (**b**) partial enlarged view.