Geology Reference
In-Depth Information
Offset
Offset
V
s1
, V
s1
,
ρ
1
V
p2
, V
s2
,
ρ
2
100ms
timing lines
A
I
=
Figure 2.16
Snell
'
s Law.
Figure 2.17.
An example of critical angle energy on an NMO
corrected gather.
2nd term
B
Slope
Gradient
RI
M
contrasts across the boundary. It is generally safe to
assume that the two-term approximation holds to an
angle of incidence up to 30°; for the case in
Fig. 2.19
the second and third order curves start to diverge at
around 40°. If intercept and gradient are to be derived
from seismic then the interpreter needs to ensure
that only traces which show a linear change of ampli-
tude with sin
2
Critical angle
+
1st term
A
R0
NI
Intercept
L
are used (
Chapters 5
and
6
).
The modern day importance of the Shuey equation
is not as a predictor of seismic amplitudes at particular
angles but as a tool for analysing AVO data for fluid
and lithology effects (described in
Chapters 5
and
7
).
Shuey
θ
Rc
0
Sin
2
s equation played a key role in the development
of seismic AVO analysis techniques in the 1980s and
1990s. The simplicity of the equation meant that the
regression coefficients A and B (intercept and gradient)
could be fairly easily derived and a range of AVO
attributes defined by various parameter combinations.
Another, rock property oriented, approximation
to the Zoeppritz equations has been put forward by
'
3rd term
Curvature component
-
Figure 2.18
The three components of the Aki
-
approximation to the Zoeppritz equations.
A+B sin
2
R
ðθÞ¼
θ:
ð
2
:
16
Þ
Shuey
s equation is a simple linear regression. For the
purpose of describing seismic amplitude variation
this approach to linearising AVO is applicable only
over a limited range of angles. The angle at which
the two-term approximation deviates from the
three-term and Zoeppritz solutions depends on the
'
AI
2
AI
1
AI
2
+AI
1
+
σ
2
σ
1
ð
cos
2
sin
2
R
ðθÞ¼
θ
θ: ð
2
:
17
Þ
2
1
σ
avg
Þ
This approximation is effectively the same as the
two-term Shuey equation but has been rearranged to
16
