Geology Reference
In-Depth Information
together as the
ground roll
, but are now finding applications in investigations
of the shallow subsurface (see Chapter 14).
11.1.2 Seismic velocities
The 'seismic velocities' of rocks are the velocities at which sound waves
travel through them. They are quite distinct from the continually varying
velocities of the individual rock particles that are forced into oscillation by
the transmitted energy.
Any elastic-wave velocity (
V
) can be expressed as the square-root of an
elastic modulus divided by the square root of density (
ρ
). For P-waves the
elongational elasticity,
j
, is appropriate, for S-waves it is the shear modulus,
µ
. The equations:
V
p
=
√
(
j
/ρ
)
V
s
=
√
(
µ/ρ
)
suggest that high-density rocks should have low seismic velocities, but
because elastic constants normally increase rapidly with density, the reverse
is usually true. Salt is the only common rock with a high velocity but a low
density.
If the density and P- and S-wave velocities of a rock mass are known, all
its elastic constants can be calculated, since they are related by the equations:
(
V
p
/
V
s
)
2
=
j
/µ
=
2(1
−
σ
)
/
(1
−
2
σ
)
.
e
.
σ
=
[2
−
(
V
p
/
V
s
)
2
]
/
2[1
−
(
V
p
/
V
s
)
2
]
and
=
q
(1
−
σ
/
+
σ
−
σ
µ
=
q
/
+
σ
j
)
(1
)(1
2
)
2(1
)
K
=
q
/
3(1
−
2
σ
)
j
=
K
+
4
µ/
3
where
q
is Young's modulus and
K
is the bulk modulus. The Poisson ratio,
σ
, is the ratio between the amount of shortening experienced by a cube of
material in the direction of an applied compression and the expansion that
then takes place at right angles to it. This ratio has a maximum value of
0.5 (for a completely incompressible material), at which point the
V
p
/
V
s
ratio becomes infinite. Solids can usually be compressed to some extent,
but water and most other liquids are incompressible and S-waves do not
propagate through them. The Poisson ratio in rocks seldom exceeds 0.35,
and P-waves, always the fastest, travel rather less than twice as fast as
S-waves in all but the most consolidated rocks (Figure 11.1).
Most seismic surveys use, and provide velocity estimates for, P-waves
only, and these are rather rough guides to rock quality. Figure 11.2 shows the
velocity ranges for common rocks and also
rippabilities
,definedbywhether
