Effect of near-surface topography on high-frequency Rayleigh-wave propagation

Abstract

Rayleigh waves, which are formed due to interference of P- and Sv-waves near the free surface, propagate along the free surface and vanish exponentially in the vertical direction. Their propagation is strongly influenced by surface topography. Due to the high resolution and precision requirements of near-surface investigations, the high-frequency Rayleigh waves are usually used for near-surface structural detecting. Although there are some numerical studies on high-frequency Rayleigh-wave propagation on topographic free surface, detailed analysis of characters of high-frequency Rayleigh-wave propagation on topographic free surface remains untouched. Hence, research of propagation of Rayleigh waves on complex topographic surface becomes critical for Rayleigh-wave methods in near-surface applications. To study the propagation of high-frequency Rayleigh waves on topographic free surface, two main topographic models are designed in this study. One of the models contains a depressed topographic surface, and another contains an uplifted topographic surface. We numerically simulate the propagation of high-frequency Rayleigh waves on these two topographic surfaces by finite-difference method. Soon afterwards, we analyze the propagation character of high-frequency Rayleigh waves on such topographic models, and compare the variations on its energy and frequency before and after passing the topographic region. At last, we discuss the relationship between the variations and topographical steepness of each model. Our numerical results indicate that influence of depressed topography for high-frequency Rayleigh waves is more distinct than influence of uplifted topography. Rayleigh waves produce new scattering body waves during passing the depressed topography with reduction of amplitude and loss of high-frequency components. Moreover, the steeper the depressed topography is, the more energy of Rayleigh waves is lost. The uplifted topography with gentle slope produces similar influence as the depressed topography on propagation of high-frequency Rayleigh waves. When slopes are getting steep, however, the obstacle influence of the uplifted topography becomes weak. In addition, in the uplifted-topography case, part of Rayleigh-wave energy is absorbed by the uplifted terrain, which includes the trapped energy between the uplifted boundaries and the generation of scattering waves. Meanwhile, local topography strongly affects the character of Rayleigh-wave dispersion. Egregious error may be introduced, when pick Rayleigh-wave phase velocities on dispersion energy images for an MASW survey, if the local free-surface topography is ignored.