**4. Effects of Anisotropic Parameters on Rotations**

In order to further explore the effects of anisotropic parameters on rotational motion, we changed the Thomsen parameters *δ* and *ε*, based on the same seismic observation system to simulate the three-component velocity fields. Eight different models are defined as illustrated in Table 2: models 2–5 were mainly used to study the effects of *ε* on rotational components by increasing *ε* from 0 to 0.3 as *δ* is constant, and model 4 and models 6–9 were employed to explore the influence of *δ* by gradually increasing *δ* from −0.2 to 0.2 as ε is constant. We first analyzed the simulation results under the explosion source in detail, shown in Figures 5–12.


**Table 2.** Anisotropic parameters of different models. **Parameter Model 2 Model 3 Model 4 Model 5 Model 6 Model 7 Model 8 Model 9**

**Figure 5.** Components generated from the expansion source in different models.

**Figure 6.** Wave field snapshots of *Ry* generated from the expansion source at 0.05 s.

**Figure 7.** FK spectra of *Ry* generated from the expansion source in different models.

**Figure 8.** *Cont*.

**Figure 8.** Influence of ε on seismic records generated from the expansion source: (**a**) the seismic records of the 30th trace; (**b**) the seismic records of the 90th trace.

**Figure 9.** *Cont*.

**Figure 9.** Influence of δ on seismic records generated from the expansion source: (**a**) the seismic records of the 30th trace; (**b**) the seismic records of the 90th trace.

**Figure 10.** Influence of anisotropy parameters on amplitude spectra of the 90th trace generated from the expansion source: (**a**) when *ε* varies; (**b**) when *δ* varies.

**Figure 11.** Influence of anisotropy parameters on phase spectra of the 90th trace generated from the expansion source: (**a**) when *ε* varies; (**b**) when *δ* varies.

**Figure 12.** Influence of ε and δ on peak values of the 90th trace generated from the expansion source.

The seismic records, wave field snapshots, and FK spectra of different models are shown in Figures 5–7. Figure 5 demonstrates that, contributed by the velocity anisotropy, both *P* and *S* waves existed in the components in the VTI media. The energy of *S* waves became stronger with increasing *ε*, while the effects of *δ* were almost invisible.

The shape of wavefronts in *Ry* components became elliptical in VTI media, as seen in Figure 6. The eccentricities of the ellipse gradually increased with increasing *ε*, while the eccentricity of the ellipse gradually decreased with increasing *δ*.

There are obvious *P*- and *S*-wave energy groups in the rotational components in the FK spectra (Figure 7). With the increase of *ε*, the energy of *P* waves decreased gradually, but became more concentrated at the same time, while the energy of *S* waves gradually increased. However, the FK spectra of rotational components were almost unchanged with increasing *δ*.

We extracted and boosted the 30th and 90th traces' waveforms to study the effects of *ε* and *δ* on the amplitude and phase of seismic waves, which represented the far and near offset traces, respectively, to analyze the dynamic characteristics in detail. With the increase of ε, the amplitude and phase of the seismic waveforms showed obvious variations, as illustrated in Figure 8. In the near offset, with the increase of *ε*, the *X* components changed slightly. The peak values of *Z* components decreased gradually, while those of *Ry* components increased gradually. However, in the far offset, the peak values of *Ry* components increased slightly, while the phase varied widely with the increase of *ε*.

The effects of *δ* on waves' dynamic characteristics are shown in Figure 9. The effects of anisotropy on the *X* components were nearly negligible in the far offset, while the effects on the *Ry* components were obvious. The *Z* components changed substantially with the increase of *δ* in the near offset. The waves on the rotational components changed more obviously than those on translational components with increasing *δ*.

Furthermore, the influence of *ε* and *δ* on different components is shown in the amplitude and phase spectra (Figures 10 and 11). We can conclude that the rotational components had more high-frequency information than the translational components, since the spectra of *X* components were mainly in the frequency range 60–100 Hz, *Z* components are mainly in the frequency range 70–110 Hz, and *Ry* components in the frequency range 80–120 Hz. The amplitude variation of the *Ry* components was much greater than that of the *X* components with the variation of *ε*. On the *Z* components, the bandwidths of the wave fields became smaller, and the central frequencies became lower as *ε* increased. In addition, *δ* had less of an influence on the amplitude spectra of the three components than *ε*. With the increase of *δ*, the amplitudes of the wave fields on the *X* components and the *Ry* components increased slightly, while the amplitudes on the *Z* components showed a greater increase in the high frequencies.

In Figure 11, there are barely visible variations in the phase spectra of the *X* components with variation of *ε*, demonstrating that *ε* had a minor effect on the *X* components. The *Z* components of the four models differed mainly in the frequency range 100–200 Hz, while they were almost the same in the low frequencies. With the increase of *ε*, the phase spectra of *Ry* components varied more greatly than the translational components. The effects of *δ* variation on the phase spectra of three components were less pronounced than the effects of *ε* variation. The phase variation of *X* components was weak except in the frequency range 180–200 Hz, while it was more substantial in the frequency range 90–130 Hz for the *Z* components. With the increase of *δ*, the phase spectra of *Ry* components differed slightly, but they were significantly different from the isotropic condition. It can be deduced that rotation observations may be preferable to the study of anisotropic parameters.

Peak values of the 90th trace in different models can be seen in Figure 12. We found that the peak values of the rotational components increased gradually with the increase of *ε*, while they were almost the same with increasing *δ*.

To demonstrate the influence of the source on rotation, the seismic synthetic data and snapshots of wave fields at 0.05 s generated from different sources for different models are shown in Figures 13 and 14. There are obviously *P* waves and *S* waves in the seismic synthetic data generated from the radial concentrated force source, while there are few *P* waves in the seismograms generated from the other sources. The energy of *P* waves in the *Ry* components generated from the radial concentrated force source was stronger than that generated from the vertical concentrated force source and shear source. With the increase of *ε*, the energy of *P* waves generated from the radial concentrated force source was much more enhanced than that of *S* waves, which is completely opposite to the outcome observed with increasing *δ*. Since *S* waves existed in the *Ry* components generated from the vertical concentrated force and shear source, it can be seen that the energy of *S* waves gradually increased with the increase of *ε* and *δ*.

**Figure 13.** *Cont*.

**Figure 13.** *Cont*.

**Figure 13.** Seismograms. (**a**) Radial concentrated force source. (**b**) Vertical concentrated force source. (**c**) Shear source.

**Figure 14.** *Cont*.

**Figure 14.** Snapshots of wave fields at 0.05 s. (**a**) Radial concentrated force source. (**b**) Vertical concentrated force source. (**c**) Shear source.

The shape of the wavefront was an ellipse in VTI media generated from the shear source and concentrated force source in the *Ry* components, while the wavefront was round in isotropic medium. The energy of *P* waves was much weaker than that of *S* waves, although it could barely be seen in the snapshots of wave fields generated from the shear source and vertical concentrated force source. With the increase of *ε*, the eccentricity of the wavefronts gradually increased. However, with the increase of *δ*, the eccentricity of the ellipse gradually decreased to near-circular. We conclude that the sources have a great influence on the wave fields of the *Ry* component.
