Geology Reference
In-Depth Information
Z
0
¼ ρ
V
p0
(vertical P impedance),
G
0
¼ ρ
V
p
ðÞ
≈
V
p0
1+
½
δ
sin
2
θ
cos
2
θ
+
ε
sin
4
θ
V
p
90
≈
V
s0
V
p0
1+
½
ε
(vertical shear modulus),
2
4
0
@
1
A
3
5
2
δ
are the Thomsen parameters, equal to zero
for the isotropic case.
and
ɛ
V
p0
V
s0
sin
2
cos
2
V
s
⊥
ðÞ
≈
V
s0
1+
ð
ε δ
Þ
θ
θ
It is evident from
Eq. (5.5)
that in order to model
the effect of polar anisotropy on P wave AVO it is
not necessary to know
sin
2
V
s
k
ðÞ
≈
V
s0
1+
½
γ
θ
90
≈
V
s
k
V
s0
1+
½
γ
:
(gamma). This is due to
the fact that horizontally polarised shear waves are
not excited by P waves or vertically polarised V
s
waves. The main problem with using the Rüger
approximation for practical purposes is obtaining
relevant measurements for the input parameters.
Available data are sparse and often ambiguous.
There are no real rules of thumb for the interpreter
to draw on or indeed convincing and accessible
case studies that illustratetheissueofanisotropy
as a problem for amplitude interpretation.
Unless there is a specific need for such informa-
tion, the relevant data are not acquired in most
exploration wells. Published measurements of
polar anisotropy or VTI have been derived in the
laboratory and from the analysis of walkaway and
multi-component VSPs (e.g. Thomsen,
1986
;
Vernik and Liu,
1997
;Ryan-Grigor,
1997
;Macbeth,
2002
).
Figures 5.40
γ
ð
:
Þ
5
2
Additionally, common descriptions of P wave and
S wave anisotropies are:
V
p90
V
p0
ε
≈
P wave anisotropy,
ð
5
:
3
Þ
V
p0
V
s
k
90
V
s0
γ ¼
S wave anisotropy
:
ð
5
:
4
Þ
V
s0
Polar anisotropy can have a large effect on seismic
velocities rendering simple assumptions in seismic
processing inadequate. Ignoring the problem causes
mis-positioning and degraded focusing of reflections
(e.g. Leaney,
2008
). In particular, accounting for polar
anisotropy can be a key issue in the flattening of
seismic gathers (see
Chapter 6
). Incomplete correc-
tion for anisotropic effects has the effect of stretching
and squeezing the relative values of the AVO gradient
with respect to the intercept (Thomsen,
2002
). This
may not necessarily have a detrimental impact on
qualitative definition of AVO anomalies but it is
likely to cause problems for AVO calibration at far
angles.
In terms of modelling the effect of polar anisot-
ropy on seismic amplitude an approximation pub-
lished by Rüger (
1997
) gives useful insight. This is
an anisotropic
-
5.43
show a compilation of
measurements.
Some general observations can be made:
δ
may not be zero (as is often assumed) in sands;
δ
values are generally positive for sands but can be
negative as well as positive for shales;
ε
is usually positive for sands and shales:
ε
values in shales are generally higher than in
sands, and may be higher than
δ
by a factor of
2 or more.
equivalent of
the Aki
-
Richards
approximation:
In an attempt to derive a useful rule of thumb in the
absence of accurate data, Ryan-Grigor (
1997
) sug-
gested that the relationship between
"
#
+
1
2
2
Δ
Δ
V
p0
V
p0
Δ
1
2
Z
0
Z
0
2V
s0
V
p0
G
0
G
0
+
and V
p
/V
s
can
be simplified by assuming a relationship
between C
13
/C
44
and V
v
/V
s
(
Fig. 5.44
). Using pub-
lished laboratory data the following relationship can
be derived:
δ
R
p
ðÞ¼
Δδ
sin
2
+
1
2
Δ
V
p0
V
p0
+
sin
2
tan
2
θ
Δε
θ
θ
,
ð
:
Þ
5
5
C
13
C
44
¼
61
V
p
where
θ ¼
3
:
V
s
5
:
06
:
ð
5
:
6
Þ
angle of incidence,
V
p0
¼
average P wave (vertical) velocity,
V
s0
¼
average S wave (vertical) velocity,
This allows the calculation of
δ
from
85
