## 3 Model Test
### Test 3: Vertical Prisms Model Test  
The third model test contains three vertical prisms. This is the same model used to test new ways to improve the confidence of structural interpretation by an improved Euler inversion and phase congruency method for the field data by [PERSON] et al. [27]. The  
Figure 4: Euler solutions. (**a–c**) Original Euler solutions generated by the finite-difference Euler deconvolution, our method, and the DST method. Solutions are saved if the vertical derivative of gravity of the window center is not negative. (**d–f**) Selected Euler solutions. Figure 5: Euler solutions obtained from the noise-corrupted model. (**a–c**) Original Euler solutions generated by finite-difference Euler deconvolution, our method, and the DST method. Solutions are saved if the vertical derivative of gravity of the window center is not negative. (**d–f**) Selected Euler solutions. geometric and physical parameters of this model are listed in Table 2. Figure 6a shows the gravity anomaly resulting from these prisms. The input data grid has 101 \(\times\) 101 points. Solutions are calculated using a window size of 7 \(\times\) 7 grid points and solutions are rejected if the vertical derivative of gravity of the window center is negative. Figure 7a shows the original results obtained from applying the finite-difference Euler deconvolution to the data in Figure 6. Figure 7d shows the results after selection. Figure 7b shows the original results obtained from applying the improved Finite-difference Euler deconvolution method to the data in Figure 6. Figure 7e shows the results after selection. Figure 7c shows the original results obtained from applying the Euler deconvolution based on DST to the data in Figure 6a. Figure 7f shows the results after selection. Comparing Figure 7d and Figure 7e (or Figure 7a and Figure 7b), we can easily find that our algorithm better depicts the boundary of the prisms, and the inversion result is more accurate. Next, we will compare the inversion effects of the improved finite-difference Euler deconvolution method and Euler deconvolution based on DST. Comparing Figure 7e and Figure7f (or Figure 7b and Figure 7c), we can find that the distribution shapes of the solutions generated by the two algorithms are almost the same. In Figure 7e,f, the mean value of all the \(x_{0-\text{estimate}}\) is 39,617 and 39,397, and the mean value of all the \(y_{0-\text{estimate}}\) is 39,161 and 38,898. The difference is less than the grid spacing. For these two methods, the difference of \(z_{0-\text{estimate}}\) is also far less than the grid interval. The difference in the mean value of the estimated \(x_{0}\), \(y_{0}\), and \(z_{0}\) in Figure 7b,c is also far smaller than the grid interval. To further compare the accuracy of the two algorithms, two profiles are selected. Figure 8 shows the solutions. When the sliding window is in or near the projection area of field sources A1 and A2, the solutions generated from our algorithm and the DST Euler deconvolution algorithm are the same. However, when the sliding window is in or near the projection area of source A3, the solutions generated from the two algorithms are slightly different, and they also reflect the source position. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Cuboid No.**} & **Length along \(x\)** & **Length along \(y\)** & **Thickness along \(z\)** & \\  & **(km)** & **(km)** & **(km)** & **Depth to Top (m)** & **Density (g/cm\({}^{3}\))** \\ \hline
**A1** & 20 & 20 & 5 & 1.5 & 0.3 \\
**A2** & 10 & 10 & 4 & 2 & 0.3 \\
**A2** & 80 & 1 & 5 & 1 & 0.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of model 3. Figure 6: True location of synthetic prisms (the black rectangles) and the gravity anomaly produced by them. (**a**) Theoretical gravity anomaly. (**b**) Theoretical gravity anomaly corrupted with 2% Gaussian random noise. Noisy Data  
To further test the stability of our method, we apply it to noise-corrupted data.