تاثیر توپوگرافی نزدیک به سطح روی انتشار موج ریلی با فرکانس بالا Effect of near-surface topography on high-frequency Rayleigh-wave propagation

Underneath shear (S)-wave velocity has gained popularity in engineering and environmental studies. Since it is directly proportional to shear modulus of underneath materials, it becomes a fundamental indicator of stiffness of earth material (Imai and Tonouchi, 1982). Evaluation of S-wave velocity profile has been one of the critical tasks in geotechnical engineering (e.g., Craig, 1992; Xia et al., 1999, 2002). At present, an S-wave velocity profile is often obtained by surface-wave method. For example, the Multichannel Analysis of Surface Wave (MASW) method (e.g., Xia et al., 1999, 2002) is one of the successful surface-wave methods. It is based on the dispersive nature of Rayleigh waves in vertically heterogeneous media and the horizontal layer assumption of earth model. The earth, however, is not composed of perfectly flat-layered medium. Clarifying propagation properties of Rayleigh wave in complex structure plays a critical role in understanding Earth structures (e.g., Zhao, 1991). To our knowledge, surface-wave transmission is substantially affected by the irregular surface. The earliest reports of surface-wave propagation on topographic surface began in 1958. The studies include the transmission and reflection of Rayleigh waves at corners (deBremaecker, 1958), characters of reflection and transmission coefficient of angle topography by experiment studies (Knopoff and Gangi, 1960), and the theoretical formula of reflection and transmission at a corner (e.g., Hudson and Knopoff, 1964; Mal and Knopoff, 1965, 1966; Fujii et al., 1984). Snieder (1986) studied the effects of topography on three dimensional surfacewave scattering and conversions by the Born approximation method. In his study, the scattering of surface wave by topography was compared with the scattering of surface wave by a mountain root model. He also analyzed the interference effects between surface waves scattered by different parts of heterogeneity. These previous theoretical results lead us to a considerable improvement in the explanation of real-world data and experiments. Analyzing the dispersion characters of Rayleigh waves on topographical surface, however, is too complicated. These studies are less general in either analytical method or numerical simulation. With the development of propagation theory of seismic waves and the progress of numerical simulation techniques, further studies of topographic influence on Rayleigh-wave propagation have been done. Numerical simulation techniques are important tools to remedy the weakness of analytical methods. They have been widely used in studying the problem of surface-wave propagation on complex geological structures. Fuyuki and Matsumoto (1980) simulated the scattering of Rayleigh waves on topographic free surface by the finite-difference method. Wong (1982) studied the frequency response of a canyon to Rayleigh waves. Kawase (1988) studied the time domain response of Rayleigh waves by the boundary element method. Afterwards, Sánchez-Sesma and Campillo (1991) discussed such response of more general topography. Based on the boundary element method, Hévin et al. (1998) numerically simulated the propagation of Rayleigh waves across various surface cracks. From the simulation signals, the variations of spectral ratios between the transmitted and incident waves are studied as a function of the crack depth. Their study can be used to design an effi- cient procedure for the determination of crack depths. Zhang and Liu (2000) studied the problem of elastic wave diffraction on a semicylindrical pit-case topographical surface. They proved that Rayleighwave diffraction was stronger than P waves, when the wavelength of Rayleigh waves was shorter than the P waves. Cao et al. (2007) numerically simulated the propagation of Rayleigh waves across surface crack by the finite element method. At the same year, Nasseri-Moghaddam et al. (2007) numerically investigated the propagation of Rayleigh waves on solid space with cavity. Their numerical tests showed that the buried depth and the size of the cavity detected by the surface wave method were a function of Rayleigh-wave frequency spectrum. Zhou and Chen (2007) studied the effect of depressed topography on low-frequency (b2 Hz) Rayleigh waves stimulated by a near-surface explosive source. They pointed out that Rayleigh-wave energy and frequency response were changed when Rayleigh waves passed through the depressed topography. In numerical modeling of high-frequency Rayleigh-wave propagation on topographic free surface, Zeng et al. (2012a) proposed an improved vacuum formulation to incorporate surface topography and internal discontinuity for finite-difference (FD) modeling of Rayleigh waves in the near surface. By their scheme, they numerically investigated the propagation of Rayleigh waves on topographic free surface (Zeng et al., 2012a), and the application of the MASW method in the presence of free-surface topography (Zeng et al., 2012b). Wang et al. (2012) developed an effective FD scheme to simulate Rayleigh-wave propagation in the topographical model, which incorporated Robertsson’s ‘staircase’ method (Robertsson, 1996) and the acoustic/elastic interface approach (AEA approach) (Xu et al., 2007). Strong influence of topographic free surface on Rayleigh-wave propagation was demonstrated by numerical examples of three simple topographic models. The previous numerical studies are all done either under the assumption of independent Rayleigh-wave source (Fuyuki and Matsumoto, 1980; Wong, 1982; Kawase, 1988; Sánchez-Sesma and Campillo, 1991), or under the assumption of low-frequency Rayleigh waves stimulated by explosive source (Zhou and Chen, 2007). However, due to the high resolution and precision requirements of near-surface investigations, the high-frequency Rayleigh waves are usually chosen for near-surface structural detecting. They are typically generated by a surface impact source, such as a sledgehammer hitting a steel plate. Research of propagation of high-frequency Rayleigh waves on topographic surface plays a critical role for surface-wave methods in near-surface applications. Though there are some numerical studies on highfrequency Rayleigh-wave propagation on topographic free surface (e.g., Nasseri-Moghaddam et al., 2007; Zeng et al., 2012a,b; Wang et al., 2012), detailed analysis of characters of high-frequency Rayleigh-wave propagation on topographic free surface remains untouched. We configure a depressed and an uplifted topographic model to further study the propagation of high-frequency Rayleigh waves on topographic free surface. Propagation of high-frequency Rayleigh waves on these two topographic surfaces is numerically simulated by Wang’s FD scheme (Wang et al, 2012). Based on the numerical simulations, we analyze the propagation character of high-frequency Rayleigh waves in such two typical topographic free surfaces, and discuss the variations of high-frequency Rayleigh waves in energy, frequency spectrum and amplitude response. Afterwards, we discuss the relationships between the variations and the topographical steepness of each model. Lastly, we analyze the influence of local topography on Rayleigh-wave dispersion characters.