Numerical investigation of Rayleigh-wave propagation on canyon topography using finite-difference method

Abstract

High-frequency Rayleigh-wave method plays an important role in the near-surface seismic investigation. Rayleigh wave propagates along the free surface, and its propagation is seriously affected by the topographic surface. Rayleigh-wave propagation is more affected by canyon topography than by hill topography. Hence, it is critical to analyze effects of complex canyon topography on high-frequency Rayleigh waves. To further study effects of topography on Rayleigh-wave dispersion images and Rayleigh-wave conversion, we synthesized near-surface seismograms on 2D Gaussian shape canyon topography model through finite-difference modeling scheme. We compared the seismograms and their dispersion images of Rayleigh waves by using the horizontal offset along the horizontal direction and the real offset along the topographic free surface. These dispersion images were compared with the corresponding theoretical dispersion curves that were obtained by models with a flat free surface. Our numerical results indicated that using the real offset can obtain a better quality of Rayleigh-wave dispersion imaging and then obtain a higher precision of dispersion curves than those using the horizontal offset. Our numerical results also showed that errors of the picked Rayleigh-wave phase velocities can be constrained within 8% if the ratio of canyon depth to the predominant wavelength (λm) of Rayleigh waves is <0.5 with canyon width being greater than the λm. Modeling results of horizontal and slope free surface half-space models demonstrated that wavefield separation technique can be used to model Rayleigh-wave propagation on topography with high accuracy. Wavefield separation results indicated that the energy of S waves converted from Rayleigh waves is greater than that of P waves converted from Rayleigh waves in the left corner of the canyon. The analysis suggested that using this technique can distinguish complex waveforms and study the converted energy of Rayleigh waves on arbitrary topography.