Simulation characteristics of seismic translation and rotation under the assumption of nonlinear small deformation

Abstract. The conventional theory of elastic-wave propagation is based on classical elastodynamics, assuming linear small deformations of particles. However, recent observations of seismic rotation have revealed significant disparities between actual rotational motions induced by earthquakes in focal areas and near fields compared to theoretical calculations and simulations. Considering the nonlinearity may be the main cause of the discrepancies and based on classical elastodynamic principle, we derive seismic elastic-wave equations with Green strain tensor without the linear small deformation assumption, a different way from using complex nonlinear constitutive relation and try to interpret the mechanism of seismic rotation. By simulating and analyzing translational and rotational components subjected to the three basic and typical vibrating sources, namely, isotropic (ISO), double couple (DC), and compensated linear vector dipole (CLVD), represented by moment tensors, we investigate the wavefield differences between elastic-wave equations based on linear and nonlinear geometric relations and quantify the differences in homogeneous elastic full-space model. Subsequently, we simulate two observed six-component Taiwan earthquakes and compare their differences caused by nonlinear simulations. The results indicate that linear approximation errors are more pronounced in seismic ISO and CLVD sources. And the nonlinearity of small deformation has a more pronounced effect on rotational motions deduced by strong earthquakes. Also, the nonlinear mechanics of seismic rotation can attribute to the complex propagation paths and source mechanisms simultaneously.