# The Characteristics of Seismic Rotations in VTI Medium
## 3 Synthetic Examples  
In order to study the influence of the source mechanism on rotations, we defined model 1 as a 2D isotropic full-space homogeneous elastic medium, as illustrated in Table 1. Since \(P\) waves theoretically do not generate rotational motion in isotropic media [9], we compared the translational and rotational components generated from the concentrated force and the shear source. With a size of 200 m \(\times\) 200 m, the shot in the center of the model, and the receivers arrayed at a depth of 100 m with 1 m intervals, the translational and rotational components \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Model** & \(\mathbf{v}_{p}\) **(m/s)** & \(\mathbf{v}_{s}\) **(m/s)** & \(\rho\) **(kg/m3)** & \(\varepsilon\) & \(\delta\) \\ \hline Model 1 & 2000 & 1200 & 2000 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of model 1.  
generated from different sources are shown in Figures 2-4, where the sample interval is 0.1 s and the total recording time is 0.1 s.  
Figure 2: The seismograms. (**a**) The radial concentrated force source. (**b**) The vertical concentrated force source. (**c**) The shear source. Figure 4: _Cont_. Figure 3: Seismograms of the 30 th trace. In Figure 2, it is obvious that there are only \(S\) waves in the three components because the model is isotropic and only \(S\) waves are produced by the shear source, while it can be clearly seen that there are the first arrivals of \(P\) and \(S\) waves generated from the radial and vertical concentrated force sources. The energy of the \(R_{y}\) component generated from the concentrated force source is so weak that it needed to be magnified 10 times to be visible at the same energy level with the other two components on the records. It can be found that \(P\) waves are much stronger than \(S\) waves in the \(X\) component generated from the radial concentrated force source, while \(S\) waves cause a stronger rotational motion, and \(P\) waves are hardly visible in \(R_{y}\) components. We extracted the 30 th trace of the seismic records to make a further comparison of translations and rotations, as shown in Figure 3. The influence of sources in the \(X\) component and \(R_{y}\) component is much stronger than that in the \(Z\) component in the far offset. The amplitude of \(P\) waves in the \(X\) component generated from the radial concentrated force source is much stronger than that from the other two sources. However, the amplitude of the \(S\) waves generated from the radial concentrated force source is weak in all three components. All these anomalies can be enhanced in the snapshots of different components generated from different sources (Figure 4), where there are only \(S\) waves in the \(R_{y}\) components. In all snapshots, the shapes of the wavefronts in the \(X\) and \(Z\) components are round, which is consistent with [PERSON]'s research [17]. It can be seen that the wavefront propagates with reverse phase along the horizontal axis in the \(R_{y}\) component generated from the radial concentrated force source, while it propagates with reverse phase along the vertical axis in the \(R_{y}\) component generated from the vertical concentrated force source. However, it propagates with the same phase around the circumference in the \(R_{y}\) component generated from the shear force. The wavefronts in the \(X\) components and \(Z\) components are complex and different from the \(R_{y}\) components. Obviously, the energy of \(S\) waves is significantly stronger than that of \(P\) waves on the \(R_{y}\) component, which means the \(R_{y}\) component may be helpful to identify different body waves. Figure 4: Snapshots of wave fields at 0.05 s. (**a**) Radial concentrated force source. (**b**) Vertical concentrated force source. (**c**) Shear source. Figure 6: Wave field snapshots of \(R_{y}\) generated from the expansion source at 0.05 s.  
Figure 7: FK spectra of \(R_{y}\) generated from the expansion source in different models. Figure 8: _Cont_.