Geology Reference
In-Depth Information
b)
a)
Top Sand
Top Sand
OWC
OWC
θ
=10º
θ
=30º
Zoeppritz
Zoeppritz
c)
d)
Top Sand
Top Sand
OWC
OWC
Shuey
χ
=22º
θ
=39º
χ
=-57º
Modified Shuey
Figure 5.59
Simple 2D models of a Class I oil sand; (a) reflectivity section calculated using Zoeppritz θ ¼ 10°, (b) reflectivity section calculated
using Zoeppritz θ ¼ 30°, (c) section calculated at θ ¼ 39°, χ ¼ 22° using Shuey's equation and showing optimum fluid response, (d) modified
Shuey projection χ ¼57
0
or
χ
¼313
0
highlighting the top reservoir as a continuous reflection.
Implementing AVO projections with partial stack
data is fairly straightforward if it is assumed that the
two-term approximation applies. So, for example,
intercept and gradient might be derived from near
and far stack data using the equations:
One potential advantage in AVO analysis of partial
stacks over intercept and gradient is that residual
move-out effects (see
Chapter 6
) can be taken into
account. So, for example, in the presence of residual
moveout, nears and fars can be picked separately,
adjusting the interpretation for differences in timing,
and the AVO projections can be applied to the amp-
litude maps.
An alternative projection approach with partial
stacks might be to generate the projection directly
from near and far data with an angle of projection
determined from the near vs far crossplot
(
Fig. 5.60
). The angle in near/far space is not the
same as the
A
f
A
n
G
¼
ð
5
:
14
Þ
sin
2
θ
f
sin
2
θ
n
G sin
2
R
0
¼
A
n
θ
n
,
ð
5
:
15
Þ
¼
θ ¼
¼
where A
amplitude,
incidence angle, f
far,
n
near.
Alternatively, AVO crossplot projection angles
can be directly applied to near and far angle stack
data (D. Whitcombe, personal communication):
¼
angle discussed previously so it has
been given the symbol
χ
ψ
. The projection equation
then becomes:
Projection
ðÞ¼
ð
Near
c
Þ
+ Far
ð
k
Þ
,
ð
5
:
16
Þ
∗
∗
where
Projection
ðÞ¼
ð
Near
cos
ψ
Þ
ð
Far
sin
ψ
Þ:
∗
∗
ð
5
:
19
Þ
k
¼ð
tan
χ
tan
χ
near
Þ=Δ
tan
χ
,
ð
5
:
17
Þ
¼
c
1
k,
With this formulation fluid projections tend to have
quite large
and
angles whereas lithology projections
tend to have smaller
ψ
Δ
tan
χ ¼ð
tan
χ
far
tan
χ
near
Þ:
ð
5
:
18
Þ
ψ
angles.
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