Geoscience Reference
In-Depth Information
within the reservoir are coloured dark blue. The frequency content is obviously much
consistent with the well and seismic data, but there is no guarantee that it is correct;
we would need to examine a whole suite of realisations to see which of the features are
well constrained. Because of this, the technique tends to be rather time-consuming and
expensive, and is generally regarded as a rather specialised tool.
6.4
AVO effects
So far it has been implicitly assumed that the seismic data can be treated as though
they were acquired at zero-offset. The discussion of AVO in
chapter 5
shows that in
some cases there are significant changes of amplitude with offset. In particular, with
class III AVO responses it may well give better results to invert a far-offset sub-stack.
There is then a problem in that we need somehow to modify the acoustic impedance
log at the wells in order to have values that can be compared with far-stack inverted
amplitudes. It is not clear what we mean by acoustic impedance at non-zero-offset. It
is possible to calculate the reflectivity at each interface and to integrate it to give an
'impedance' variation, but this is not a property of the rock in the same way that true
acoustic impedance is; it is a function of the incidence angle.
of an elastic impedance which is a function of incidence angle
E
(
θ
), such that the
reflection coefficient at an interface is given by
R
n
(
θ
)
=
(
E
n
+
1
−
E
n
)
/
(
E
n
+
1
+
E
n
)
in analogy with the equation connecting acoustic impedance to zero-offset reflectivity
in
section 6.1
. From this, using a simplification of the Zoeppritz equations, he obtains
x
y
z
E
(
θ
)
=
α
β
ρ
where
α, β
and
ρ
are the P- and S-wave velocities and density, respectively, and
x
,
y
,
z
are given by
x
=
(1
+
tan
2
θ
)
8
K
sin
2
y
=−
θ
4
K
sin
2
z
=
(1
−
θ
)
,
where
K
is an average value of (
β/α
)
2
over the entire zone of interest. This equation
can be used to calculate an elastic impedance curve from well log data which can, in
turn, be used to constrain and calibrate inversions of sub-stacks in just the same way
acoustic impedance is used for zero-offset data.
