## 3 Synthetic Data Test  
We used synthetic VSP records of a horizontal layered model to test the separation effect of this new method. The parameters of model are listed in Table 1. The separation results were compared with the theoretical results and the results of the high-resolution Radon transform [13; 30]. We set the wavelet as a Ricker wavelet with the peak frequency of 30 Hz, the initial phase was 0 degrees and it acts as an omni-directional point source. As shown in Figure 4, the geophones were located at the depth of 700-900 m with the interval of 5 m. The reflection coefficients were calculated through solving the Zoeppritz equations [31] at all the ray-paths derived using the ray-tracing method proposed by [PERSON] [32]. Then, we synthesized the VSP record (Figure 5) through the convolution of the wavelet and calculated reflection coefficients. Figure 5 shows that the upgoing and downgoing P-waves and S-waves are mixed together. Because of the short array (the array length of the geophones was 200 m, which was 10% of the last layer depth), the events were approximately a straight line. In order to compare the degree of energy spectrum focusing based on the conventional Radon transform and the modified Radon transform, we used Equations (5) and (7) to calculate the results of the two kinds of Radon transform, as shown in Figure 6. Figure 6a presents the results of the traditional linear Radon transform, and the local maximum and minimum points are given; notably, the energy spectrum was dispersive and similar to a \"bow-tie\" shape. Figure 6b shows the results of the modified Radon transform, and some local maximum points were in a vertical arrangement. Through a comparison of Figure 6a,b, we found that the energy spectrum of the modified Radon transform was more focused in the slowness direction, and the resolution was obviously improved, which allowed us to obtain a more accurate slowness. The transform results in Figure 6b show that there were obvious differences in the slowness of the P-wave and S-wave events, and the energy spectra were distributed in different slowness regions. The yellow box in Figure 6b shows the region of the downgoing P-wave energy spectrum. By the linear fitting of the extremum points of this region, we can get \(a=51\), \(b=0\). According to Equations (11) and (12), the downgoing P-wave can be obtained by aligning and median filtering, as shown in Figure 7a. Similarly, by the linear fitting of the extremum points in the region of the S-wave in the red box, we get \(a=89\), \(b=0\). The downgoing S-wave can be obtained through Equation (10), as shown in Figure 7d. The downgoing P-wave and S-wave had only one event, which led to \(b=0\) after linear fitting of the slowness, which means that the dynamic time shift became static. At the same time, the high-resolution Radon transform was used to separate the downgoing P-wave and S-wave from the original VSP data, as shown in Figure 7b,e. To verify the separation results, we synthesized the downgoing P-wave and S-wave, as shown in Figure 7c,f. The travel time, phase, and amplitude of the downgoing P-wave and S-wave were consistent with the theoretical results as determined through  
Figure 6: The results for the (**a**) traditional and (**b**) modified linear Radon transform based on the synthetic VSP records. the comparison of the theoretical results with those from our method and the high-resolution Radon transform method. After separating the downgoing P-wave and S-wave, we used Equation (5) to perform the linear Radon transform for the remaining wavefield, and we used Equation (7) to carry out the modified Radon transform. The results are shown in Figure 8. Similar to Figure 6, Figure 8 shows the energy spectrum divergence in a bow-tie shape, and the energy spectrum of the modified Radon transform was more focused in the slowness direction; the resolution was obviously improved, and so a more accurate slowness could be obtained.