Rayleigh wave components

Fig. 6.2. Rayleigh wave displacement velocity components as a function of depth from the surface, measured in Rayleigh wavelengths (a) longitudinal and shear components (eqns (6.44), (6.45), (6.51), and (6.52)) (b) components parallel and perpendicular to the surface (eqns (6.59) and (6.60)). The curves have been normalized to give the shear component at the surface a value of unity. The Poisson ratio o = 0.17, corresponding to fused silica, was used to calculate the curve.

Figure 6.2(a), which was calculated using the results to be derived here, shows the amplitudes of the longitudinal and shear components of a Rayleigh wave in fused silica, and their exponential decay below the surface. 

In the surface of a half space that is isotropic, the Rayleigh wave velocity is the same in all directions. If the surface is imagined to be in a horizontal plane, then the Rayleigh wave is composed of a shear wave component polarized in a vertical plane (SV) and a longitudinal wave component. Shear waves polarized horizontally (SH) can also exist, but they do not couple to the Rayleigh wave at all (nor, in the case of fluid loading, would they couple into waves in the fluid). 

Fig. 11.5. Profile of the particle displacement velocities in a Rayleigh wave in a GaAs(OOl) surface, propagating at an angle = 15° to a [100] direction. This figure is analogous to Fig. 6.2(b) for a Rayleigh wave in an isotropic medium, but in this case there are components of displacement in both horizontal axes, because of the anisotropy, and so three curves are needed they are normalized by setting the larger horizontal component to unity at the surface.

This is the generalized three-dimensional scattering relationship for the response just above the surface at x to an oscillatory pressure just above the surface at x, due to Rayleigh wave excitation, in the case where the y component of the wavevector is constant. The three-dimensional scattering function can now be calculated. 

A particular conclusion from this theoretical analysis is that, if a crack has faces that are separated by a thin layer of fluid, so that normal components of traction and displacement are transmitted across the crack but the faces are free with regard to shear components of traction and displacement, then there will be a scattered wave however thin the fluid layer is. This is perhaps not surprising. A Rayleigh wave can exist only because solids can support both longitudinal and shear waves, and the greater part of the displacement in a Rayleigh wave is shear in character ( 6.3). Of course, liquids can support shear stress over a short distance. In a liquid of viscosity r/, and density po, at a frequency o) the amplitude of a shear wave decays by a factor e over a distance... 

For propagation in an isotropic medium or along a pure-mode direction of a crystal (e.g., a plane of symmetry). Equation 3.38 reduces to a Rayleigh wave, characterized by having no transverse component Ux = 0. Since Uy and Uz are 90° out of phase, the particles move in an elliptical orbit in the sagittal plane die surface motion resembles that of the ocean under the influence of a passing wave. 

Finally, Kirkwood Crampin (1981) showed that particle-motion anomalies are diagnostic of anisotropy and that the variations with period can be used to estimate the approximate depth of the anisotropic layer. This is best done using fundamental quasi-Love waves visible on the radial and vertical components, as they will not be contaminated by the later arriving Rayleigh waves (Yu Park 1994). 

Fig. 6. Three-component waveform fits at three distance ranges for synthetic seismograms (dotted line) computed from the southern African velocity model of Priestley (1999) and the observed seismograms (continuous lines). The Love and Rayleigh wave seismograms are fitted with the same velocity model, implying that at least the upper-mantle lid is isotropic. Event 860718 is event 2, Figure 1 910724 is event 7, Figure 1 and 940818 is event 8, Figure 1.

Classical SAW devices utilize a Rayleigh wave, which has a normal component. Therefore SAWs face significant insertion loss when operating in liquids due to radiation of acoustic waves into the liquid. 

Three-component data from all stations are extracted for each event, and the responses are equalized by deconvolution of the instrument response and convolution with standard bandpass filters that depend on the data type. Rotated horizontal components (longitudinal and transverse) are constructed and considered in the analysis. Three types of data are used (1) body waves, which are the signals that arrive in the time window before the arrival of the minor-arc surface waves (2) mantle waves, which consist of up to 4.5 h of data, including several very long-period Love and Rayleigh wave arrivals (e.g., G1-G4 and R1-R4) and (3) intermediate-period surface waves, which consist of a time window centered on the minor-arc arrival times for surface waves. 

Rayleigh waves, and torsion in the presence of SH- or Love waves. The torsion of symmetrical buildings observed in earthquakes is a consequence of obliquely incident seismic waves. Further, the modihcation of the seismic motion depends on the frequency content of the seismic motion with high-frequency components being filtered out by the slab when the respective apparent wavelength is shorter than an effective length of the foundation slab (the diameter for circular foundations). 

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