Spatial behaviour of Rayleigh waves in layered half-spaces under active surface sources

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In the free state, Rayleigh waves are assumed to travel in the form of planar wavefronts. Under such an assumption, the propagation behaviour of the modes of Rayleigh waves in layered half-spaces is only frequency dependent. The frequency behaviour, which is often termed as dispersion, is determined by the shear wave velocity profile of layered soils within the depth related to wavelength (or frequency). According to this characteristic, the shear wave velocity profile can be back-analysed from the dispersion. The technique is widely used in the surface wave testing. However, the wavefronts of Rayleigh waves activated by the surface sources are non-planar. The geometric discrepancy could result in Rayleigh waves manifesting distance-dependent behaviour, which is referred to as spatial behaviour in this paper. Conventional analysis ignoring this spatial behaviour could introduce unexpected errors. In order to take the effects of sources on the propagation behaviour into account, a new mathematical model is established for Rayleigh waves in layered elastic media under vertical disc-like surface sources using the thin-layer method. The spatial behaviour of the activated modes and the apparent phase velocity, which is the propagation velocity of Rayleigh waves superposed by the multiple modes, are then analysed. Aspects of the spatial behaviour investigated in this paper include the equilibrium path, the particle orbit, and the geometric attenuation of the activated Rayleigh waves. The results presented in this paper can provide some guidelines for developing new inverse mathematical models and algorithms.

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