Analysis of attenuation and dispersion of Rayleigh waves in viscoelastic media by finite-difference modeling

Viscoelasticity of Earth media has an important influence on Rayleigh-wave propagation. Therefore, it is necessary to study the attenuation and dispersion of Rayleigh-wave by numerical modeling to better understand Rayleigh-wave behaviors in Earth media. Modeling adopts a staggered finite-difference (FD) scheme, which calculates the spatial derivatives by a 12th-order operator and the time derivatives by the fourth-order Runge-Kutta method. In time-space domain, the accuracy of FD method is demonstrated through comparing the modeling results with the analytical solution in an elastic half-space. In frequency-velocity domain, the correctness of modeling results is verified via comparing the dispersive images with the theoretical dispersion curves of Rayleigh-wave. The attenuation and dispersion of Rayleigh-wave are analyzed by comparisons between elastic and viscoelastic modeling results in the homogeneous half-space models in terms of the wave field snapshots, the synthetic seismograms, and the dispersive images, respectively. The two-layer models are also simulated to further investigate the attenuation and dispersion of Rayleigh-wave in viscoelastic layered media. Results show that the viscoelastic Rayleigh-wave presents substantial differences in amplitude and phase velocity compared with the elastic case. Viscoelasticity of media arouses amplitude attenuation of Rayleigh-wave. The high-frequency waves are attenuated more severely than the lower-frequency waves, and the attenuation degree is severe increasingly with offset increasing. Viscoelasticity of media also causes the phase velocity dispersion of Rayleigh-wave. The phase velocity ratio of viscoelastic Rayleigh-wave respecting to the corresponding elastic one increases with frequency, and the resolution of dispersion energy is lower than the elastic one. The attenuation and dispersion of Rayleigh-wave are prominent increasingly with Q decreasing.