Geoscience Reference
In-Depth Information
Head Wave
amplitude L x
(b)
Diving Wave
amplitude x
(c)
Interference Head Wave
amplitude L x
(a)
3/2
−
1
−
1/2
−
3/2
−
1/2
a
a
a
z
z
z
Figure 4.40.
Amplitude-distance behaviour for head waves, diving waves and
interference head waves. (From Kennett (1977).)
x
is the distance and
x
c
is the critical distance (Fig. 4.38(a)). This relationship
holds for values of
L
greater than five or six times the predominant wavelength
of the seismic signal (i.e., for 8-km s
−
1
10 km).
At distances much greater than the critical distance, the amplitude of the head
wave varies as
x
−
2
.
In the case of continuous refraction in a velocity gradient (Fig. 4.38(b)), the
refracted wave is a body wave, so its amplitude varies as
x
−
1
. This type of arrival
therefore dominates head waves at long distances.
However, if the velocity beneath the interface
material and a 5-Hz signal,
L
>
α
(
z
) continues to increase with
depth
z
as
α
(
z
)
=
α
0
(1
+
bz
)
(4.64)
the resultant head wave has an interference character (Fig. 4.38(c)). The first
arrival is no longer the head wave but a wave continuously refracted below the
interface. This is closely followed by a succession of continuously refracted
waves, which have been reflected from the undersurface of the interface. Those
that arrive within
T
is the duration of the incident
signal, interfere and are termed the
interference head wave
.For
Lb
2
/
3
T
of each other, where
λ
−
1
/
3
>
1, where
is the wavelength just below the interface, the amplitude of this
interference head wave increases with range as
L
3
/
2
x
−
1
/
2
.Atlong ranges, when
the first arrival arrives more than
λ
T
before the interference packet, the ampli-
tude of the first arrival varies as
x
−
1
.Itshould be clear, therefore, that introduc-
tion of velocity gradients can have a considerable effect on amplitude-distance
behaviour.
Synthetic refraction seismograms
The best way to determine a velocity structure from seismic-refraction data is
to compute synthetic (theoretical) seismograms and to compare these with those
recorded in the refraction experiment. The velocity model can then be adjusted,
