Geology Reference
In-Depth Information
a)
b)
c)
d)
θ =0º
θ =20º
θ =30º
θ =0º
θ =20º
θ =30º
sin 2
θ = tan χ
+
G
G
G
χ
+
Shale/wet sand
-
+
OWC
χ
sin 2
R(0)
R(0)
R(0)
θ
Rc
0
Shale/oil sand
-
-
χ =0º
χ =7º
χ =14º
Figure 5.55 The principle of AVO projections; (a) AVO data plotted on the AVO plot, (b)-(d) AVO crossplots showing data projections for
various angle rotations.
projection of the points along the y axis onto the
intercept axis of the AVO crossplot ( Figs. 5.55a , b ).
Increasing the angle of the projection involves rotating
the axes in an anticlockwise direction ( Figs. 5.55c , d ),
with the degree of rotation determined by the function
that relates the angle of incidence (
channels within the field. Note that beyond this angle
the maps do not change significantly. It is character-
istic that there is usually a high degree of sensitivity to
angle in the region of the fluid angle.
Notionally, it should be possible to generate pro-
jections at any AVO crossplot (
θ
) to the AVO
χ
) angle, but Shuey
'
s
crossplot angle (
χ
):
equation has an angle limit of
θ ¼
90° (i.e.
χ ¼
45°). It
might be thought that sin 2
θ
could simply be replaced
sin 2
θ ¼
tan
χ ð
Whitcombe et al
:
2002
Þ:
ð
5
:
10
Þ
with tan
angles (beyond around 70°)
the projections show a rapid rise in calculated values
and the reflection coefficient may exceed unity. Whit-
combe et al.( 2002 ) showed that this problem was
essentially overcome by scaling Shuey
χ
, but at large
χ
For example, angle projections at
30°
are achieved by rotating the AVO crossplot axes anti-
clockwise by 7° and 14° respectively ( Figs. 5.55c , d ).
Note how in the case of the
θ ¼
20° and
θ ¼
14° projection the
amplitude of the shale on water sand is effectively
zero whereas the shale on oil sand is a soft (negative)
response. This is what Hendrickson ( 1999 ) terms the
'
χ ¼
'
s equation in
terms of cos
χ
, which gives:
R
¼
R 0 cos
χ
+G sin
χ:
ð
5
:
11
Þ
'
This
equation allows for reflectivity
calculations across the whole range of
'
modified Shuey
'
, turning a dim spot on a full stack
section into a bright spot on a projected stack.
The idea of AVO projections has a fundamental
impact on the practical approach to AVO analysis.
Hendrickson ( 1999 ) realised that maps can be gener-
ated at any incidence angle and that a comparison of
these maps is useful in appreciating the nature of the
AVO response. Figure 5.56 illustrates an example
from the Auger Field in the Gulf of Mexico. Note that
the optimum angle of
magic of AVO
angles and
gives results that maintain correct relative differences
between AVO responses. As such it can be considered
the generalised two-term AVO equation. To quote
from Whitcombe et al. 2002 , it is important that the
interpreter understands that the aim of this manipu-
lation is not
χ
produce a model that replicates
observed reflectivity beyond 30 0 and up to the critical
angle
to
'
useful model that can be con-
structed for any real linear combination of A (inter-
cept) and B (gradient), effectively extrapolating the
observations along the sin 2
'
but to create a
'
18° gives the most consist-
ent anomaly which fits closely to the structural spill of
the field (i.e. this is the optimum fluid angle). In
contrast,
θ ¼
axis in either direction
beyond the physically observed range
θ
30° shows a different map with the main
amplitude anomaly oriented at an angle and
extending down-dip beyond the closing contour.
The change is interpreted to be due to the dominant
influence of lithology rather than fluid and the amp-
litude is
θ ¼
.
One of the reasons for modifying Shuey
'
s equa-
tion was to accommodate the possibility of projec-
tions which sometimes emphasise lithological
variations. Figure 5.57 shows AVO responses for
'
95
related to the orientation of
turbidite
 
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