Shear wave velocity

Thus, by using two VISARs, and by monitoring two beams at 6, both the longitudinal velocity and the shear-wave velocity can be determined simultaneously by solving the above two equations. With a lens delay leg VISAR (Amery, 1976), a precision in determining F(t) to 2% can be achieved. The longitudinal and transverse particle velocity profiles obtained in a study of aluminum are indicated in Fig. 3.12. 

The parameters for the model were originally evaluated for oil shale, a material for which substantial fracture stress and fragment size data depending on strain rate were available (see Fig. 8.11). In the case of a less well-characterized brittle material, the parameters may be inferred from the shear-wave velocity and a dynamic fracture or spall stress at a known strain rate. In particular, is approximately one-third the shear-wave velocity, m has been shown to be about 6 for various brittle materials (Grady and Lipkin, 1980), and k can then be determined from a known dynamic fracture stress using an analytic solution of (8.65), (8.66) and (8.68) in one dimension for constant strain rate. 

The static Poisson ratio is determined in a triaxial cell. The dynamic Poisson ratio is calculated with the sonic compressional and shear wave velocities. They usually are different. 

The value of the Rayleigh velocity depends primarily on the shear wave velocity of the material, and rather less strongly on the ratio of the shear velocity to the longitudinal velocity. The ratio of the Rayleigh velocity to the shear velocity may be considered as a function of the Poisson ratio cr. From Table 6.1, the Poisson ratio may be expressed as... 

In an isotropic medium, cracks do not move faster than half the shear wave velocity Vu so the implications of the 0.8V curve in Figure 4 were not explored. In the two-phase ABS system, however, one can imagine cracks or crazes propagating rapidly in the matrix (V /2 <—B20 meters/sec), and thence into the rubber particle [at 23°C, polybutadiene (V /2 /—29 meters/sec)] where violent branching would occur. 

Fig. 4.8 Dissipation of shear wave velocity with distance (adapted from Kanazawa and Gordon, 1985)...

Example 2.4 Calculate the compressional and shear wave velocities in aluminum and polyethylene. 

Ritsema J., van Heijst H. J., and Woodhouse J. H. (1999) Complex shear wave velocity structure imaged beneath Africa and Iceland. Science 286, 1925-1928. 

Fig. 2. Large-scale velocity structure beneath the Canadian Shield as determined by Grand et al. (1997). The scale indicates the shear-wave velocity anomaly as a percentage relative to IASP91 (Kennett Engdahl 1991). O, locations of the TWiST seismic stations A, from south to north, the permanent seismic stations ULM (CNSN), FFC ffRIS) and FCC (CNSN).

Fig. 4. Inversion for shear-wave velocity model (continuous line) which best fits the Rayleigh-wave interstation phase velocities. The grey area shows range of acceptable solutions. Three other velocity models are shown for comparison dashed line, Brune Dorman (1963) dot-dashed line, Grand Helmberger (1984) dotted line, PREM (Dziewonski Anderson 1981). It should be noted that the TWiST model shows no indication of a low-velocity zone below a continental root.

Perhaps the most important change that has occurred since Qiu et al. s study is in our understanding of seismic velocities at high temperature and seismic periods, (studied by Gribb Cooper (1998, 2000) and Jackson (2000). Before those studies, laboratory measurements of seismic velocities were made at ultrasonic frequencies and the ultrasonic results extrapolated to seismic frequencies. New laboratory experiments made at seismic frequencies strongly suggest that the decrease in shear-wave velocity beneath the seismic lithosphere of the shields results from elevated temperature and is not an indication of the presence of melt (Gribb Cooper 2000). This question is discussed in more detail below. 

McWilliams 1977). Qiu et al. (1996) used earthquakes in southern Africa recorded at stations in Zimbabwe and South Africa (Fig. 1) to obtain an average velocity model for southern Africa. The main features of their model are a high shear-wave velocity lid in the upper mantle shown by both seismic and petrological data, below which there is a decrease in the shear-wave velocity shown by the seismic data. Priestley (1999) reexamined the seismograms studied by Qiu et al. (1996) and included additional data to determine... 

Fig. 2. Comparison of the density, shear-wave velocity and compressional-wave velocity profiles beneath southern Africa from Priestley (1999) (bold continuous lines), and the density and velocity profiles for PREM (fine continuous lines). The shaded area denote estimates of the uncertainties in the density and velocity model of Priestley (1999) derived from the waveform fitting tests, the earthquake location errors as described by Qiu et al. (1996), and c. 2% anisotropy as proposed by Vinnik et al. (1995).

The comparison at 2106 km distance (Fig. 3c) shows an acceptable match of the synthetic and observed waveforms with the base of the lid at 160 km depth. Thicker lids advance the arrival time of the wavepacket, but the waveform shape is not altered. At this distance range, the higher modes are equivalent to an S wave turning in the mantle transition zone. Increasing the lid thickness reduces the delay time caused by the lower shear-wave velocities beneath the lid, resulting in an advance in the arrival time but no change in the amplitude at this epicentral distance. 

James Pouch (2002) showed intermediate period fundamental mode Rayleigh wave phase and group velocity data measured across the Kalahari Craton and a shear-wave velocity model from inversion of these data. They find evidence for a weak low-velocity zone below 120-130 km depth. The phase velocity data of James Pouch (2002) are not significantly different from the Rayleigh wave phase velocity measured by Priestley (1999). However, such intermediate period fundamental mode dispersion data do not provide stringent constraints on mantle velocities below c. 200 km depth. 

Recent global tomographic models (Ritsema van Heijst 2000) include intermediate-frequency surface-wave data. These models show the high shear-wave velocities extending to no more than 200 km depth beneath the Kalahari Craton with PREM-like velocities below 200 km depth, consistent with the model shown in Figure 2. 

Manghnani, M. H. Ramananantoandro, R. 1974. Compressional and shear wave velocities in granulite facies rocks and eclogites to 10 Kb. Journal of Geophysical Research, 79, 5427-5446. 

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