Compressional wave velocity

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).

Compressional wave velocity (i.e., sound velocity) is usually determined by pulse-time delay systems measuring time difference over a fixed path length of the sediment in the laboratory (e.g., Schreiber, 1968 Kermabon et al., 1969 Silver and Moore, 1972 Boyce, 1976 Baldwin et al., 1981 Theilin and Pecher, 1991), in situ (e.g., Hamilton, 1963 Bachman and Hamilton, 1982 Barbagelata et al., 1991), and remotely from boats and deep-tow devices (e.g., Stoll et al., 1991). 

These dynamic moduli correspond to the initial tangent moduli of the stress-strain curve for an instantaneously applied load and are usually higher than those obtained in static tests. The frequency and nature of discontinuities within a rock mass affect its deformability. In other words, a highly discontinuous rock mass exhibits a iower compressional wave velocity than a massive rock mass of the same type. The influence of discontinuities on the deformability of a rock mass can be estimated from a comparison of its in situ compressional velocity, /pf, and the laboratory sonic velocity, /p, determined from an intact specimen taken from the rock mass. The velocity ratio, /pf/t/pi, reflects the deformability and so can be used as a quality index. A comparison of the velocity ratio with other rock quality indices is given in Table 2.7. 

Compressional wave velocities versus bulk density for the series of acid-catalyzed TEOS xerogels investigated by Murtagh el al. [31], The solid lines correspond to the relationship predicted from a fused silica-porosity composite assuming either spherical- or needle-shaped pores. Gel values fall beneath the predicted values, indicating that the skeletal phase is not as stiff as conventional fused silica [31]. 

Poisson s ratio values for MSW have been derived from field measurements of shear and compressional wave velocity at the Oil Landfill (Matasovic and Kavazanjian 1998) and from laboratory measurements of axial and radial strain (Zekkos 2005). Poisson s ratio can also be... 

Achauer U, Evans JR, Stauber DA (1988) High-resolution seismic tomography of compressional wave velocity structure at Newberry Volcano, Oregon Cascade Range. J Geophys Res Solid Earth (1978-2012) 93(B9) 10135-10147... 

For compressional wave velocities is Fp,minerals > kp, water, oil > Fp, gas and for the corresponding compressional modulus is minerals > water, oil > gas-... 

Compressional wave velocity is controlled also by the type of pore fluid (gas, liquid). 

The compressional wave velocity for some fluids is presented in Table 6.3. A detailed compUation of seismic properties of fluids and relevant empirical equations to describe the effects of pressure and temperature have been published by Batzle and Wang (1992) and Wang (2001). In the following sections, only some selected results are presented for details, the direct use of the paper of Batzle and Wang (1992) is recommended. 

TABLE 6.3 Compressional Wave Velocity for Some Fluids... 

Derived from the Relationships (Plots) by Batzle and Wang (1992), and Calculated Compressional Wave Velocities (for Density Values See Also Fig. 4.1). 

The differences in the elastic behaviour of these two groups are based on different physical conditions at the contacts of the rock particles. For the first group, conditions are controlled by friction effects, whereas for the second group, physiochemical phenomena are dominant. Similar to consolidated sedimentary rocks, there exists a significant correlation between velocity and porosity for unconsolidated sediments. Velocity in unconsolidated sediments is distinctly lower than in consolidated sediments. The compressional wave velocity shows a clear difference for the dry sediment (about 200-500 m s ) and water-saturated sediment (about 1600-2000 m s ). 

Figure 6.12 gives examples of the velocity versus porosity correlation for dry sediments (a) and for water-saturated marine sediments (b). It is remarkable that the compressional wave velocity in water-saturated sediments is comparable to that of water velocity or higher. 

FIGURE 6.12 Compressional wave velocity versus porosity for unconsolidated sediments (a) dry unconsolidated sediments (Schim, 1964, 1969, 1983) and (b) water-saturated marine sediments (Hamilton, 1971). 

V [ is the compressional wave velocity of the pore fluid (mostly assumed water). 

Porosity is related to density. Gardner et al. (1974) derived an empirical relation between compressional wave velocity and bulk density that represents an average over many rock types (Mavko et al., 1998) ... 

Compressional wave velocity increases from air to kerosene to water thus, it corresponds to the (compressional wave) velocities of these pore fluids. 

Changing pore fluid has no influence on the elastic properties of the rock skeleton. King (1966) measured compressional wave velocity at water saturation lower than at kerosene saturation (and the shear wave velocity for water-saturated sandstone was extremely) at the Bandera sandstmie. This is an effect of softening of the matrix by water-clay interactions (for example swelling). 

The ratio of compressional wave velocities of water saturated to dry rock increases with porosity, as shown in Fig. 6.15b. This ratio is strrMigly controlled by the contribution of the high compressional modulus of water compared with that of air therefore, the effect increases with porosity. 

The region where the velocity increase starts depends on the pore-size distribution. The Ottawa sand in Fig. 6.16 is well sorted. If the rock has a broad spectrum of pore sizes, then also for low water saturation (approximately 40% or 50%), small pores are totally water saturated and increase the compressional wave velocity. Thus, the shape of the velocity-saturation function is controlled by pore-size distribution and capillary pressure. 

FIGURE 6.17 Compressional wave velocity as a function of confining pressure under different conditions of pore pressure, water-saturated sample of a low porous conglomerate. Data from He and Schmitt (2006). 

The equation demonstrates that a high pore pressure plays the same role as a low external stress, causing the compressional wave velocity to be reduced. This is used in the estimation of abnormal pore pressures from logs or seismic velocities (e.g. Japsen et al., 2006). Since the expected trend in a homogeneous formation would be a monotonous increase of velocity with depth (because the effective stress increases with depth), an overpressure zmie shows up as a low-velocity zone breaking the expected trend. 

Compressional wave velocity perpendicular to the fracture plane is smaller than the compressional wave velocity parallel to this plane... 

Figure 6.27 shows a comparison of calculated compressional wave velocities and measured data for sandstone (same as in Fig. 6.10) and chalk (same as Fig. 6.15, water saturated). The curve for Wyllie s Eq. (6.56) is also plotted. 

The compressional wave velocity of the cubic packing is (White, 1983) ... 

Figure 6.31 shows a comparison with experimental data from Lebedev et al. (1974a,b). Measured compressional wave velocities are normalized with a velocity for the compact solid material of 6150 m s . ... 

Figure 6.32 compares forward-calculated compressional wave velocities with experimental data from chalk samples (Rogen et al., 2005). Measured data points cover a range of aspect ratios between 0.08 and 0.14. 

FIGURE 6.34 Compressional wave velocity versus crack praosity. Curves are calculated for penny-shaped inclusions with different aspect ratios a (0.005. 04) input parameteis are i s=44GPa, Ps=37GPa, and Ps=2.65 g cm (Fig. 6.8). Points are experimental data for... 

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