Geology Reference
In-Depth Information
a) Zero phase wavelet and selected
frequency components
zero-crossing (brown wave). The turning wheel idea is
useful for describing the angular differences in phase.
Seismic wavelets can sometimes be approximated
as constant phase across the dominant bandwidth. In
such a case (
Fig. 3.3
), the phase of each frequency
component is the same.
Figure 3.3
shows a wavelet in
which the phase is 90°. Thus, a zero phase wavelet is a
special case of a constant phase wavelet. Another case
often seen is linear phase, where phase is related
linearly to frequency (
Fig. 3.4
). In effect, a wavelet
with linear phase is equivalent to a time-shifted con-
stant phase wavelet.
As will be discussed in detail below, the bandwidth
and phase of the seismic signal emitted by the source
is modified in its passage through the subsurface by
the
0 3 6 12 24 40 72Hz
b) Phase spectrum
(
Fig. 3.5
). Shallow targets will gener-
ally have higher bandwidth than deeper targets.
Higher bandwidth essentially means greater resolving
power.
'
earth filter
'
180
0
3.3 Zero phase and minimum phase
From the interpreter
s point of view the ideal wavelet
is zero phase, i.e. symmetrical and with the amplitude
centred on time zero. Real sound sources such as
explosives and airguns typically have minimum phase
signatures. Generally, a minimum phase wavelet is
one that has no energy before time zero and has a
rapid build-up of energy. Each amplitude spectrum
can be characterised by a unique minimum phase
wavelet (i.e. the wavelet that has most rapid build-up
of energy for that given spectrum). It is possible to
find the minimum phase wavelet for a given spectrum
using methods based on the z transform (see e.g.
way to determine whether a given wavelet is min-
imum phase or not. Conversely, to say that a dataset
is minimum phase does not guarantee a particular
shape.
Figure 3.6
shows an example of two minimum
phase wavelets with similar bandwidth but slightly
different rates of change of frequency in the low-
frequency range. Thus, if an interpreter is told that
the seismic data is minimum phase then it is not clear
exactly what response should be expected from a
given interface. What is important is that the inter-
preter is able to assess and describe wavelet shape in
seismic data. Determining wavelet shape from seismic
is described in
Chapter 4
.
A useful semi-quantitative description of wavelet
shape is in terms of a constant phase rotation of an
'
-180
60
20
Frequency Hz
c) Amplitude spectrum
1
Bandwidth (7-55Hz)
Half peak
amplitude point
0
20
60
Frequency Hz
Figure 3.1
Elements of seismic wavelets; (a) sinusoidal frequency
components, (b) phase spectrum, (c) amplitude spectrum (after
Simm and White,
2002
).
Phase can be thought of as a relative measure of
the position of a sinusoidal wave relative to a refer-
ence point, and is measured in terms of the phase
angle (
Fig. 3.2
). The sine waves in
Fig 3.2
all have
the same frequency but are out of phase. At the time
zero reference point, they vary from peak (red wave)
to zero-crossing (blue wave) to trough (green wave) to
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