25 1. Wave propagation If the semi-infinite medium is overlain by a low-velocity surface layer, as occurs in the field where a weathered layer is present, the elastic constants change with depth, and long wavelengths travel faster than short wavelengths, depending on the elastic properties at greater depths. Such conditions alter some of the wave characteristics and the surface wave is referred to as a pseudo-Rayleigh wave. In this case, the harmonic components of longer wavelengths (lower frequencies) travel faster, and different wavelengths sample different depths in the earth and the propagation velocity can be strongly frequency-dependent (dispersion). The degree of dispersion is a measure of seismic wave velocity as a function of depth and can be used to calculate the thickness of surface layers. b) Love waves, (L-waves) – develop only if a horizontal low-velocity layer lies over a solid elastic semi-infinite medium. These waves consist of multiples reflections of SH-waves while trapped in the horizontal layer. Particle motion is transverse and horizontally polarized (Figure 1.3-b). Since the vertical component does not exist, Love waves are not detected by the vertical geophones. Velocity is close to S-wave velocity in the subsurface medium for very long wavelengths; and close to that of the surface layer for short wavelengths. Therefore, these waves always exhibit dispersion and the propagation velocity increases with the period of the harmonic component. (c) Figure 1.3 A depiction of the displacement induced by plane surface waves. Wavelength ( λ): (a) Rayleigh waves; and (b) Love waves (adapted from Alsadi, 2017); (c) geometrical dispersion of Rayleigh waves associated with short ( λ1) and long ( λ2) wavelengths. (Adapted from Socco and Strobia, 2004).
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