**1. Introduction**

It is well known that the six-component records of ground motion include threecomponent translations and three-component rotations [1]. In the past two decades, with the development of rotational seismometers, the observation of rotations has gradually increased, and rotations caused by earthquakes have attracted increasing attention in the scientific and seismic engineering fields, and great progress has been made in both theoretical research and practical applications [2–6].

In order to study the mechanism of seismological rotations, many meaningful inquiries have been made by means of indirect calculation, direct observation, and numerical simulation. Aiming at the Newport–Inglewood (NI) fault in America, Wang et al. [7] used a finite-difference method to simulate several earthquakes with magnitude 7 in different hypocenters, and found the influence of source and receiving geological conditions on the rotations. They also found that the variations of the source produce a great effect on the rotations. Therefore, rotational observations may contribute to the exploration of the mechanism of NI earthquakes. Ferreira et al. [8] simulated the rotations recorded at the fundamental mode of surface waves with the full ray theory (FRT) for laterally smooth heterogeneous Earth models, and found that the synthetic seismograms showed good agreement with the real ones. With the joint observations of rotation rates and accelerations, the one-dimensional S-wave velocity at the observing locations can be obtained. Pham et al. [9] calculated the amplitudes of rotational rates based on the Kelvin–Christoffel equations and found that the rotational rates caused by anisotropies were large enough in strong earthquakes to predict the underground structures and constrain anisotropic parameters. Tang et al. [10] developed a new method, the generalized reflection and transmission coefficient method, which could obtain the translational and rotational synthetic seismograms in VTI media.

Barak et al. [11] performed a synthetic seismic experiment on a simple two-layer model of a water-covered seabed, where there were isolated high-velocity spheres different from the background medium. They found that the energy of the Scholte waves on rotational components was stronger than that on translational components, which would be helpful to identify different modes of waves and separate the surface waves from the body waves. More importantly, with seven-component seismic data, including the pressure components recorded by hydrophones, displacements recorded by three-component geophones, and rotations recorded by three-component rotational seismometers, their analyses presented the possibility to recover the vector characteristics of wave fields. Additionally, we previously discuss the differences between body waves and surface waves projected on the rotational components in 2D isotropic media [12], and Zhang et al. [13] found that the responses of the anomalies with a lower velocity were more obvious on the rotational components than on the translational components, and the energy of the shear waves on rotational components was stronger than that of P waves.

Although there is much research about rotations at present, the characteristics of rotations in transverse isotropic media with a vertical axis of symmetry (VTI) have not yet been clarified, and the influence of the anisotropic parameters on rotations is still unclear. In order to study the characteristics of the rotations generated from different sources in VTI media and explore the significance of rotations to the research of anisotropic parameters, we simulate the seismic rotations and translations based on the first-order velocity-stress equations using the staggered-grid finite-difference method in 2D VTI medium, analyze the similarities and differences between translations and rotations, and focus on the influence of the Thomsen parameters [14] on rotations so as to promote the relationship of the rotations and the anisotropies of the media, which can be helpful for the wave–field separation, inversion of the anisotropic parameters and the study of the earthquake source mechanism.
