Page 52 - Applied Petroleum Geomechanics

Rock physical and mechanical properties 43

reach values of 20e40 for near surface formations, for which Poisson’s ratio
is commonly greater than 0.45. Therefore, V p /V s can be used for the rock
quality interpretation; for example, the mean value of V p /V s ¼ 1.89 in the
more heavily jointed rocks (perhaps a rock quality Q z 1e10) and the
mean value of V p /V s ¼ 1.80 in sparsely jointed rocks (perhaps a rock
quality Q z 10e100) (Barton, 2007).
The ratio V p /V s may also be used for porosity and rock failure analysis
(Zhang et al., 2009). When elastic waves travel in a rock, the wave velocities
are dependent on rock lithology and rock strength. For instance, rocks with
greater strengths have higher velocity values, whereas the velocities in loose,
unconsolidated sediments correspond to lower velocity values. Laboratory-
measured compressional and shear velocities for intermediate to high
velocity rocks on limestones, dolomites, and sandstones show a distinct
difference in velocity ratios (V p /V s ) exhibited by different rocks (Pickett,
1963). The limestones have the highest V p /V s ratio (1.9e2.0), and the clean
sandstones have the lowest V p /V s (1.6e1.75). Experimental data compiled
by Castagna et al. (1985) show that the clay minerals and calcite without
porosity have the highest velocity ratio of V p /V s ¼ 2.0. The quartz without
porosity has the lowest velocity ratio of V p /V s ¼ 1.5.
Zhang et al. (2009) examined the in situ velocity ratios of deepwater Green
Canyon wells where the sonic compressional and shear velocities were ac-
quired from stable and unstable borehole sections; caliper logs were utilized
to determine the borehole stability while gamma ray logs were used to
determine lithology. Fig. 2.6 presents the V p /V s ratios in the stable wellbore for
shales, shaly sandstones, and sandstones calculated from downhole-measured
compressional and shear velocities. For shales the ratio of V p /V s ranges
from 1.9 to 2.1; shaly sandstones from 1.85 to 2.0; and sandstones from 1.7 to
1.9, very close to the laboratory results presented by Pickett (1963).
Based on in situ sonic and field seismic measurements in mudrocks,
Castagna et al. (1985) proposed the following relationship of V p and V s (the
velocities are in km/s):

V s ¼ 0:8621V p 1:1724 (2.25)

For sandstones, compressional and shear velocities have an easy-to-
remember relationship (Han, 1986):

V s ¼ 0:79V p 0:79 (2.26)
where the velocities are in km/s. The above equation was shown by Mavko
et al. (2009) to give a very good fit to a wide variety of water-saturated