Shear wave horizontal

Fig. 6. MR wave image of acoustic refraction. Shear waves generated in the upper part of an agar gel phantom (horizontal motion) propagate vertically in the stiff part of the phantom (/i 50 kPa cT 7.5 cm/s) and are refracted by the oblique lower part of soft gel (fi 15 kPa cT 4 cm/s). Note the marked reduction of wavelength in the softer medium. From Ref. 23, reprinted by permission of Wiley-Liss, Inc., a subsidiary of John Wiley Sons, Inc.

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. 11.4. Velocities of bulk and surface waves in an (001) plane the angle of propagation in the plane is relative to a [100] direction, (a) Zirconia, anisotropy factor Aan = 0.36 (b) gallium arsenide, anisotropy factor Aan = 1.83 material constants taken from Table 11.3. Bulk polarizations L, longitudinal SV, shear vertical, polarized normal to the (001) plane SH, shear horizontal, polarized in the (001) plane. Surface modes R, Rayleigh, slower than any bulk wave in that propagation direction PS, pseudo-surface wave, faster than one polarization of bulk shear wave propagating in...

Figure 2.1 Pictorial representations of elastic waves in solids. Motions of groups of atoms ate depicted in these cross-sectional views of plane elastic waves propagating to the right. Vertical and horizontal displacements are exaggerated for clarity. Typical wave speeds, Vp, are shown below each sketch, (a) Bulk longitudinal (compressional) wave in unbounded solid, (b) Bulk transverse (shear) wave in unbounded solid, (c) Surface acoustic wave (SAW) in semi-infinite solid, where wave motion extends below the surface to a depth of about one wavelength, (d) Waves in thin solid plates.

Although this chapter is concerned with bulk acoustic wave (BAW) devices, some of the concepts apply to shear horizontal surface acoustic wave (SH-SAW) devices in a similar way [33,34]. When modeling SH-SAW devices, one usually decomposes the wave vector into a vertical and a lateral component. The vertical component obeys similar laws as the shear wave in a BAW resonator. This being said, we confine the discussion to BAW devices (also termed thickness-shear resonators) in the following. 

To solve the problem of measuring shear wave velocity in the soil column, a seismic cone penetrometer has been developed. The seismic cone contains a triaxial set of geophones (i.e., detectors) incorporated in a conventional in situ piezocone. It is typically pushed into the soil from the seabed or from the bottom of an advancing borehole. The source is typically a hydraulically driven spring hammer located on the seabed. It is ideally coupled to the sediment surface and preferentially generates horizontally polarized shear waves. It is important to decouple the drill rods and tools from the seismic cone prior to testing because compression wave energy may be transmitted. This allows the full characteristics of the soil in terms of shear modulus to be determined. 

Figure 2. Schemes for using piezoelectric quartz crystals. A. Quartz crystal microbalance configuration, standing shear wave between facing Au electrode contacts B. Surface acoustical mode configuration, surface undulation caused by bias between metal fingers C. Horizontal shear plate mode.

This paper has dealt exclusively with SAW sensors that exploit the mass sensitivity of the device to achieve chemical vapor detection. Schemes to exploit the SAW sensitivity to coating conductance changes (17) or elastic modulus changes should afford new opportunities for imaginative chemical vapor sensor designs. Finally, the field of liquid phase chemical analysis may also yield to surface acoustic wave devices that utilize plate waves and horizontally polarized shear waves to minimize acoustic losses in the liquid (18). 

FIG. 5-14. Stroboscope photograph of a wave of shear strain double refraction in a 1% solution of sodium deoxyribonucleate at 2S°C, frequency 125 Hz. The driving plate is oscillated vertically shear waves propagated horizontally to the right produce patterns of strain double refraction. Each boundary between black and white provides the same information the inclination of the base lines is specified by the angle between the axes of the Babinet compensator and the analyzing Polaroid (from reference 117). ... 

If both walls are spaced far apart, the pressures on one wall are not influenced by the presence of the other. For low-frequency input motions with frequency less than half the fundamental frequency of the unrestrained backfill, VJAW (Fj is the soil shear wave velocity), the pseudo static conditions are governed (i.e., the dynamic amplification is negligible). For this range of frequencies, wall pressures with plane strain assumption can be obtained from elastic solution for the case of a uniform, constant horizontal acceleration applied throughout the soil. The dynamic earth pressures obtained from this method must be... 

None of these problems affect horizontally polarized shear waves in spherically symmetric media, and in practice useful SH polarities can usually be determined reliably on transverse-component seismograms obtained by numerical rotation. 

In a free-fall deployment, no method is known to assure that the OBS seismometers north axis is aligned with geographic north. For active-source experiments, the orientation of the horizontal components is not always important, but it is essential for many passive seismological methods (e.g., receiver functions, shear wave splitting). There are two main approaches to identify the OBS orientation direct determination by an additional sensor or indirect estimation by analyzing the seismological data. 

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