Geoscience Reference
In-Depth Information
is expressed on the seismic section. Although some information can be obtained by
relating reflectors to outcrop geology, by far the best source of stratigraphic informa-
tion, wherever it is available, is well control. Often wells will have sonic (i.e. formation
velocity) and formation density logs, at least over the intervals of commercial interest;
from these it is possible to construct a
synthetic seismogram
showing the expected
seismic response for comparison with the real seismic data. In addition, some wells
will have
Vertical Seismic Profile (VSP)
data, obtained by shooting a surface seismic
source into a downhole geophone, which has the potential to give a more precise tie
between well and seismic data. In this section we shall discuss the use of both these
types of data.
3.1.1
The synthetic seismogram
The basic idea is very simple. To a first approximation we can calculate the expected
seismic response of the rock sequence encountered in the well by treating it as a
one-dimensional problem. That is, we calculate the effect as though the interfaces in
the subsurface are horizontal and the ray-paths are vertical, so that rays are normally
incident on the interfaces. This is usually a reasonable first approximation, but means
that we are ignoring the way that seismic response varies with angle of incidence, which
rather than the full stack, for comparison with the calculated well response, to make sure
that the approximation is valid. If we think of the subsurface as a number of layers, each
with its own acoustic impedance
A
, then the reflection coefficient at the
n
th interface
for P-waves at zero-offset is given by the formula
R
n
=
(
A
n
+
1
−
A
n
)
/
(
A
n
+
1
+
A
n
)
,
where
A
n
and
A
n
+
1
are the acoustic impedance above and below the interface; acoustic
impedance is the product of density and seismic P-wave (sonic) velocity. The derivation
of this formula can be found in Sheriff & Geldart
(1995)
, for example; it is a simple
particular case, valid for normal incidence, of the Zoeppritz relations, which describe
how the reflection coefficient varies as a function of incidence angle.
Both density and sonic values are routinely logged as a function of depth in bore-
holes. Density is inferred from the intensity of back-scattered radiation from a downhole
gamma-ray source; the amount of back-scatter is proportional to the electron density
in the rock which is in turn proportional to the bulk density. Sonic velocity is deter-
mined from the travel-time of a pulse of high-frequency (e.g. 20 kHz) sound between a
downhole source and downhole receivers; the sound travels as a refracted arrival in the
borehole wall. Because of the methods employed, the values obtained for velocity and
density are those in the formation close to the borehole wall, i.e. within a few tens of
centimetres of the borehole. This may or may not be representative of the formation as
a whole. It is possible that the well has drilled an anomalous feature, e.g. a calcareous
