Geoscience Reference
In-Depth Information
velocities are greater than Rayleigh-wave group velocities (Fig. 4.5(a)), which
means that Love waves usually arrive before Rayleigh waves on seismograms
(see Fig. 4.17(b)).
Dispersion curves contain much information about the velocity structure of the
crust and upper mantle, but it is no simple matter to extract it. A
linearized inver-
sion technique
(an iterative scheme that obtains a best fit between actual dispersion
curves and the model curves which would be generated by particular velocity-
depth structures), calculated by computer, is often used to obtain a velocity-depth
structure appropriate for particular dispersion curves. Figure 4.6(a) shows stan-
dard continental and oceanic dispersion curves. Notice that, over much of the
frequency range, oceanic paths are faster than continental paths. In Fig. 4.6(b)
notice the low S-wave velocities starting at approximately 50-100 km depth.
This low-velocity region is generally identified with the asthenosphere, the zone
beneath the lithospheric plates, where the temperatures approach the solidus of
mantle material and thus the material ceases to behave rigidly, becoming more
ductile and able to creep.
4.1.4 Free oscillations of the Earth
Any mechanical system has a natural oscillation that can be excited, and the
Earth is no exception. The Earth can oscillate in an indefinite number of
normal
modes
of oscillation, rather like a giant bell. These free oscillations are standing
waves: vibrations of the whole Earth with periods between about 100 s and 1 h.
Although such oscillations had been predicted theoretically at the beginning
of the twentieth century, the first definite measurement did not take place until
22 May 1960, when a large earthquake in Chile excited the oscillations sufficiently
for them to be detected. Modern instrumentation is such that now free oscillations
excited by large earthquakes can be recorded about twenty times each year. Free
oscillations from the 1994
M
w
=
8.3 earthquake in Bolivia were recorded for
months afterwards.
There are two independent types of free oscillations:
spheroidal oscillations
(S) and
toroidal
or
torsional oscillations
(T). The general displacement for
spheroidal oscillations has both radial and tangential components. The displace-
ment for toroidal oscillations is always perpendicular to the radius vector and so
is confined to the surfaces of concentric spheres within the Earth. Such oscil-
lations, which involve only the crust and mantle (the outer core is liquid and
so cannot sustain shear), do not change the shape or volume of the Earth. Both
spheroidal and toroidal oscillations have an infinite number of modes (or, as in
music, overtones). The notation used to describe free oscillations is
n
S
l
and
n
T
l
.
The first subscript,
n
, indicates the overtone:
n
=
0isthe fundamental mode
while higher-frequency modes with
n
0 are overtones. The second subscript,
l
,
the harmonic degree, indicates the number of nodes in latitude (places with zero
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