Geoscience Reference
In-Depth Information
Location (
X
)
Early time
Frequency (Hz)
Source
10
0
10
1
10
2
10
3
10
4
10
5
10
6
10
7
Middle C
Incident
wavefront
Diffractor
Infra-sound
Human hearing
Ultra-sound
Tomographic
Seismic
surveys
Shallow
Petroleum
Whole crust
Velocity measurements
in the laboratory
Sonic logging
T
=
T
Source
V
= 6000 m/s
1500
150
15
1.5
1.5×10
-1
1.5×10
-2
1.5×10
-3
1.5×10
-4
V
= 4000 m/s
1000
100
10
1
10
-1
10
-2
10
-3
10
-4
V
= 2000 m/s
500
50
5
5×10
-1
5×10
-2
5×10
-3
5×10
-4
5×10
-5
Quarter wavelength (m)
T
= 2
T
Figure 6.7
The range of frequencies used for different types of
seismic survey and for in situ and laboratory velocity measurements.
The quarter wavelength is a measure of the resolution of a seismic
dataset (see
Section 6.7.1
)
. For comparison, the human ear responds
to sound over a frequency range extending from about 20 to
20,000 Hz.
Source
diffraction, reflection and refraction. Note that it is cus-
tomary to refer to seismic wave arrivals that have been
diffracted as simply
T
= 2.5
T
'
diffractions
'
,re ected arrivals as
Source
'
, etc., even though they are all the results of
the processes rather than the processes themselves.
For refraction to occur, only a change in seismic velocity
is required. For diffraction and re
ection to occur there
must be a change in a physical property called acoustic
impedance (
'reflections',
'
Diffracted
wavefront
) which depends on the P-wave velocity (V
P
)
and density (
ζ
T
= 3
T
ρ
):
Source
ζ ¼ ρ
V
P
ð
6
:
7
Þ
Clearly, a difference in acoustic impedance can be caused
by changes in either or both of velocity and density. Of
course, it is also possible for an increase in velocity and a
decrease in density, or vice versa, to combine so that
acoustic impedance remains the same, but usually these
two properties vary sympathetically (see
Section 6.6
).
We illustrate diffraction, reflection and refraction in the
subsurface with a series of consecutive
T
= 3.5
T
Late time
images of
the P-wave wavefronts as time increases after activation of
the figures represents the deformation caused by the wave-
let, with areas of compression and dilation represented by
lighter and darker shades of grey, respectively. In the final
'
snapshot
'
Figure 6.8
Time (T)
images showing the progression of a
source-generated incident wavefront encountering a diffractor in
the subsurface. Summary raypaths are superimposed on the image
at T
'
snapshot
'
¼
3.5
Δ
T.
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