Geology Reference
In-Depth Information
amount of reflected energy is proportional to R
2
,
whereas the transmitted energy is proportional to
(AI
2
/AI
1
) T. Thus, less energy is transmitted through
boundaries with high AI contrasts (e.g. such as a hard
sea floor or the top of a basalt layer). In extreme cases,
lateral variations in AI contrasts can result in uneven
amplitude scaling deeper in the section.
Transmission effects are important in understand-
ing the general nature of recorded seismic energy.
O
Lithology
V
p
AI
(V
p
)
Rc
- +
1
3
4
5
amplitudes at depth appear to be higher than can be
accounted for with a simple (normal incidence)
model of reflection and transmission at individual
boundaries. It was concluded that seismic reflection
energy is being reinforced by reflections from thin
layers for which the top and base reflections have
opposite sign (Anstey and O
'
6
cumulative effects of many cyclical layers can be sig-
nificant and this may provide an explanation for the
observation that reflections tend to parallel chrono-
stratigraphic boundaries.
To generate a synthetic seismogram requires
knowledge of the shape of the seismic pulse as well
as a calculated reflection coefficient series. A recorded
seismic pulse typically has three dominant loops, the
relative amplitudes of which can vary according to the
nature of the source, the geology and the processes
applied to the data (
Chapter 3
). Assuming that no
attempt has been made to shape the wavelet or change
its timing, a time series representation of the recorded
wavelet will start at time zero (i.e. the wavelet is
causal).
Figure 2.7
shows the reflection coefficient
series from
Fig. 2.6
convolved with a recorded seismic
pulse, illustrating how the synthetic trace is the add-
ition of the individual reflections.
With regard to the polarity representation of the
wavelet shown in
Fig. 2.7
, reference is made to the
recommendation of a SEG committee on polarity pub-
geophone movement or increase in pressure on a
hydrophone should be recorded as a negative number
and displayed as a trough (
'
Figure 2.6
The reflection coefficient as defined by the
differentiation of the acoustic impedance log (re-drawn and
modified after Anstey,
1982
).
AI
2
AI
1
AI
2
+AI
1
R
¼
,
ð
2
:
1
Þ
where AI
1
is the acoustic impedance on the incident
ray side of the boundary and AI
2
is the acoustic
impedance on the side of the transmitted ray. Reflect-
ivity can be either positive or negative. In the model
of
Fig. 2.6
the top of the limestone (interface 6) is
characterised by a positive reflection whilst the top of
the gas sand (interface 1) is characterised by a negative
reflection.
It should be noted that the equation above is
relevant for a ray which is normally incident on a
boundary. The change in reflectivity with incident
angle (i.e. offset dependent reflectivity) will be dis-
cussed in more detail later in this chapter. A useful
approximation that derives from the reflectivity equa-
tion and which describes the relationship between
reflectivity and impedance is:
Þ
Effectively, the amount of reflected energy determines
how much energy can be transmitted through the
section. Following the normal
R
≈
0
:
5
Δ
ln AI
:
ð
2
:
2
)
(
Fig. 2.8
). This definition is almost universally adhered
to in seismic recording. The implication is that a
reflection from a positive reflection coefficient (a posi-
tive or
'
SEG standard polarity
'
incidence model
described
above,
the
transmission
coefficient
(at normal incidence) is defined by
reflection), will start with a trough. Note
that a positive reflection is the interpreter
'
hard
'
s reference
for describing polarity.
Figure 2.7
conforms, therefore,
to the SEG standard polarity convention with
positive reflections such as the top of the limestone
'
Þ
Given the boundary conditions of pressure continuity
and conservation of energy it can be shown that the
T
¼
2AI
1
=ð
AI
2
+AI
1
Þ:
ð
2
:
3
8
