Geoscience Reference
In-Depth Information
Sw
EI for c =
−
90
−
70
−
50
−
30
−
10
10
30
50
70
90
°
Fig. A3.9
On the left, a water saturation curve showing several gas-bearing zones (deflection to the
left). On the right, calculated elastic impedance for
χ
angles from
−
90
◦
to
+
90
◦
. Visually, the best
match is at around
χ
=
30
◦
(arrowed).
where
R
0
is the AVO intercept and
G
is the AVO gradient. We can rewrite this equation using
χ
as
R
(
χ
)
=
R
0
+
G
tan
χ,
or a scaled version as
R
c
(
χ
)
=
R
0
cos
χ
+
G
sin
χ.
As
χ
varies between 0
◦
and 90
◦
we generate sections that correspond to normal incidence (
χ
=
0
◦
)or
AVO gradient (
χ
=
90
◦
) or weighted mixtures of both. Thus we can construct a stack for any required
χ
value from AVO intercept and gradient volumes. In practice it is not necessary to calculate the
intercept and gradient explicitly; instead, traces at different offsets can be added or subtracted with
the correct weights to construct the required
angle stack, which can then be inverted to give the
required elastic impedance volume. It is also possible to invert pre-stack data and combine the results
to create the desired elastic impedance volume. One approach is to create a number of stacks over
limited ranges of incidence angles (e.g. 0-10
◦
,10-20
◦
and 20-30
◦
) and invert them; another approach
is to invert the pre-stack gathers directly.
Whatever approach is adopted, pre-stack inversion makes severe demands on the quality of the
input data. Conventional stacking simply adds together the traces of a CMP gather, and is a very
robust process. The weighted combination of traces involved in creating elastic impedance volumes,
however, may involve negative weights and thus the subtraction of traces; small errors will tend to be
magnified in effect. Another way of thinking of this is that extrapolation beyond the range of observed
θ
values becomes more error-prone the further we need to extrapolate. There are three main issues.
χ
