Geoscience Reference
In-Depth Information
(b)
(a)
Time
A
B
C
D
Phase velocity
A
B
C
D
A
B
C
D
Group velocity
A
B
C
D
U
U
2
U
3
A
B
C
D
U
U
3
U
2
1
f
1
−
1
f
3
−
1
f
2
−
1
Period (frequency)
-1
Figure 4.5.
(a) Seismic records of dispersive surface waves obtained at increasing
distances from the source (at the origin). The phases A, B, C and D are each
associated with a different frequency from one record to the next - frequency
decreases with increasing distance in this example. The inverse slope of the dashed
line linking the phases is the phase velocity, which is a function of frequency. The
straight solid lines have inverse slopes
U
1
,
U
2
and
U
3
, the group velocities for
frequency
f
1
,
f
2
and
f
3
. The group velocity is a constant for each frequency and, in
this example, decreases with increasing frequency. (From Officer (1974).) (b) Group-
and phase-velocity dispersion curves for the example shown in (a).
Both Rayleigh waves and Love waves are, in practice,
dispersive
,which means
that their velocities depend on frequency (i.e., different frequencies travel at dif-
ferent velocities). Dispersion means that a wave train changes shape as it travels
(see Fig. 4.18(b) for an example). The first surface-wave energy to arrive at any
seismometer is of those frequencies that have the greatest velocities. The other
frequencies will arrive later, according to their velocities. Therefore, seismome-
ters at increasingly greater distances from an earthquake (measured along the
great-circle arc linking seismometer and earthquake) record wave trains that are
increasingly long. The velocity with which surface-wave energy associated with
a particular frequency travels is called the
group velocity
. The other velocity used
in dealing with the surface waves is the
phase velocity
,which is defined as the
velocity with which any particular phase (i.e., peak or trough) travels. The group
velocity and the phase velocity are both functions of frequency.
Consider Fig. 4.5,which illustrates a record section
3
of surface waves. Notice
that, on each seismogram, the lower-frequency waves arrive before the higher-
frequency waves. The first phase to arrive on each record is peak A. Notice
also that the frequency of peak A is not a constant from one record to the next:
the frequency decreases (period increases) as the distance increases. The dashed
3
A record section is a travel time versus distance display of seismograms.
