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Rock physical and mechanical properties 41
the measurements, Eberhart-Phillips et al. (1989) derived the following
equations (Zoback, 2007):
p ffiffiffiffi
V p ¼ 5:77 6:94f 1:73 C þ 0:446ðs m e 16:7s m Þ
0
0
p ffiffiffiffi (2.18)
V s ¼ 3:70 4:94f 1:57 C þ 0:361ðs m e 16:7s m Þ
0
0
0
where V p and V s are both in units of km/s; s m is the mean effective stress,
in units of kbar (1 kbar ¼ 100 MPa); C is the clay content, and 0 C 1.
If shales have similar relations as shown in Eq. (2.18), then they can be used
for pore pressure estimate when V p or V s and other logging data are
available.
2.3 Sonic or seismic velocities and transit time
2.3.1 Compressional and shear velocities
When a seismic or sonic wave propagates in rock formations, the
compressional and shear waves are two major wave types. The wave
propagation velocities are determined by the appropriate elastic moduli
and densities of the materials that the waves pass through. Therefore, rock
properties and pore pressure can be estimated from seismic interval ve-
locities and the travel time in sonic log. Compressional body waves
(primary or P-waves) propagate by alternating compression and dilation
in the direction of the waves (Barton, 2007). The compressional velocity
(V p ) and dynamic elastic moduli have the following relations:
s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
K d þð4=3ÞG d
V p ¼ (2.19)
r b
s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
E d ð1 n d Þ
V p ¼ (2.20)
r ð1 þ n d Þð1 2n d Þ
b
where K d is the dynamic bulk modulus; G d is the dynamic shear modulus
(or expressed by symbol m d ); E d is the dynamic Young’s modulus; n d is
the dynamic Poisson’s ratio. It can be seen that the dynamic elastic
moduli can be obtained from the compressional velocity and Poisson’s
ratio.
Shear body waves (termed secondary, transverse or S-waves) propagate
by a sinusoidal pure shear strain in a direction perpendicular to the direction
