Geoscience Reference
In-Depth Information
be obtained from the seismic data, but have to be added from elsewhere, usually from
a model based on well data and geological knowledge.
6.2
Procedures
6.2.1
SAIL logs
Seismic Approximate Impedance Log (SAIL), which is derived as follows. Instead
of the discrete reflection coefficients of
section 6.1
, we define a piecewise continuous
function of reflection time
t
which is called the reflectivity:
δ
t
→
0
δ
R
/
δ
t
=
0
.
5d(ln
A
)
/
d
t
from which we see that
r
(
t
)
=
lim
t
ln
A
(
t
)
A
(0)
=
2
r
(
t
)d
t
t
0
so that
t
2
.
A
(
t
)
=
A
(0) exp
r
(
t
)d
t
t
0
What we actually have is a seismic signal
s
(
t
)
.
If we can assume that the wavelet is
zero-phase and the data are noise-free, then the signal
s
is a band-limited representation
of
r
(
t
), related to it by an unknown scaling factor, so we can write
t
α
,
A
(
t
)
=
A
(0) exp
s
(
t
)d
t
t
0
where
α
takes account of this unknown scaling. Assuming that the exponent is small,
as is likely in practice, the exponential term can be expanded as a series and truncated,
to give the approximate relation:
t
A
(
t
)
=
A
(0)
1
+
α
s
(
t
)d
t
t
0
or
t
(
A
(
t
)
−
A
(0))
/
A
(0)
=
α
s
(
t
)d
t
,
t
0
