Geology Reference
In-Depth Information
of only about 10
-10
m.The detection of seismic waves in-
volves measuring these very small particle velocities.
Density-Velocity Cross-plot
6500
Sandstone
Limestone
6000
3.4 Seismic wave velocities of rocks
By virtue of their various compositions, textures (e.g.
grain shape and degree of sorting), porosities and con-
tained pore fluids, rocks differ in their elastic moduli and
densities and, hence, in their seismic velocities. Informa-
tion on the compressional and shear wave velocities,
v
p
and
v
s
, of rock layers encountered by seismic surveys is
important for two main reasons: firstly, it is necessary for
the conversion of seismic wave travel times into depths;
secondly, it provides an indication of the lithology of
a rock or, in some cases, the nature of the pore fluids
contained within it.
To relate rock velocities to lithology, the assumption
that rocks are uniform and isotropic in structure must
be reviewed. A typical rock texture can be regarded as
having mineral grains making up most of the rock (the
matrix
), with the remaining volume being occupied
by void space (the
pores
). The fractional volume of pore
space is the
porosity
(
f
) of the rock. For simplicity it
may be assumed that all the matrix grains have the same
physical properties. This is a surprisingly good approxi-
mation since the major rock-forming minerals, quartz,
feldspar and calcite, have quite similar physical proper-
ties. In this case, the properties of the bulk rock will be an
average of the properties of the matrix minerals and the
pore fluid, weighted according to the porosity.The sim-
plest case is for the density of a rock, where the bulk
density
r
b
can be related to the matrix and pore fluid
densities (
r
m
,
r
f
):
5500
0%
5000
4500
4000
3500
3000
50%
2500
2000
1500
100%
1000
1000
1500
2000
2500
3000
Density in kg m
-
3
Fig. 3.6
The relationship of seismic velocity and density to
porosity, calculated for mono-mineralic granular solids: open
circles - sandstone, calculated for a quartz matrix; solid circles -
limestone, calculated for a calcite matrix. Points annotated with
the corresponding porosity value 0-100%. Such relationships are
useful in borehole log interpretation (see Chapter 11).
For S-wave velocity, the derivation of bulk velocity is
more complex since S-waves will not travel through
pore spaces at all. This is an interesting point, since it
suggests that the S-wave velocity depends only on the
matrix grain properties and their texture, while the
P-wave velocity is also influenced by the pore fluids.
In principle it is then possible, if both the P-wave and
S-wave velocity of a formation are known, to detect
variations in pore fluid. This technique is used in the
hydrocarbon industry to detect gas-filled pore spaces in
underground hydrocarbon reservoirs.
Rock velocities may be measured
in situ
by field meas-
urement, or in the laboratory using suitably prepared
rock samples. In the field, seismic surveys yield estimates
of velocity for rock layers delineated by reflecting or re-
fracting interfaces, as discussed in detail in Chapters 4
=+-
1
)
rrf
(
fr
b
f
m
For P-wave velocity a similar relationship exists, but
the velocity weighting is proportional to the percentage
of travel-time spent in each component of the system,
which is inversely proportional to velocity, giving the
relationship:
1
=+
-
1
)
f
(
f
v
v
v
b
f
m
From the above equations it is possible to produce
cross-plot graphs (Fig. 3.6) which allow the estimation
of the matrix grain type and the porosity of a rock,
purely from the seismic P-wave velocity and density.
