*Article* **The Characteristics of Seismic Rotations in VTI Medium**

**Lixia Sun 1, Yun Wang 1,\*, Wei Li <sup>1</sup> and Yongxiang Wei <sup>2</sup>**


**Abstract:** Under the assumptions of linear elasticity and small deformation in traditional elastodynamics, the anisotropy of the medium has a significant effect on rotations observed during earthquakes. Based on the basic theory of the first-order velocity-stress elastic wave equation, this paper simulates the seismic wave propagation of the translational and rotational motions in twodimensional isotropic and VTI (transverse isotropic media with a vertical axis of symmetry) media under different source mechanisms with the staggered-grid finite-difference method with respect to nine different seismological models. Through comparing the similarities and differences between the translational and rotational components of the wave fields, this paper focuses on the influence of anisotropic parameters on the amplitude and phase characteristics of the rotations. We verify that the energy of S waves in the rotational components is significantly stronger than that of P waves, and the response of rotations to the anisotropic parameters is more sensitive. There is more abundant information in the high-frequency band of the rotational components. With the increase of Thomsen anisotropic parameters ε and δ, the energy of the rotations increases gradually, which means that the rotational component observation may be helpful to the study of anisotropic parameters.

**Keywords:** rotation; translation; isotropic medium; VTI

**Citation:** Sun, L.; Wang, Y.; Li, W.; Wei, Y. The Characteristics of Seismic Rotations in VTI Medium. *Appl. Sci.* **2021**, *11*, 10845. https://doi.org/ 10.3390/app112210845

Academic Editor: Jong Wan Hu

Received: 12 October 2021 Accepted: 10 November 2021 Published: 17 November 2021

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