Geoscience Reference
In-Depth Information
12
02
03
00
02
03
Figure 4.7.
Free oscillation modes and periods:
0
T
2
(44 min),
0
T
3
(28 min),
1
T
2
(13 min),
0
S
0
(20 min),
0
S
2
(54 min) and
0
S
3
(36 min). In mode
0
T
2
, the opposite
hemispheres twist in opposite directions. In mode
1
T
2
the outside part of the sphere
twists as in mode
0
T
2
, but the inner sphere twists in the opposite direction. (After
Bullen and Bolt (1985).) To view some animations for harmonic degree 3, see
http://earth.leeds.ac.uk/∼greg/Sphar/index.html (from G. Houseman).
displacement). The simplest spheroidal oscillation is a purely radial motion,
0
S
0
,
the so-called 'breathing' or 'balloon' mode of the Earth, which has a period of
about 20 min (Fig. 4.7). Mode
0
S
2
, termed the 'football' mode of the Earth, is the
lowest-frequency oscillation, with a period of almost an hour. Free oscillations
can be detected by strainmeters (both S and T modes) and gravimeters used
for measuring Earth tides (only S modes, since T modes do not involve radial
motion, compression or dilatation), as well as by modern digital seismometers
and accelerometers capable of recording very-long-period data.
The fundamental spheroidal modes are equivalent to the standing wave result-
ing from interference amongst all the Rayleigh waves, whereas the fundamental
toroidal modes are equivalent to the standing wave resulting from interference
amongst all the Love waves. This means that the periods of free oscillations can
be used to extend the dispersion curves for surface waves out to the maximum
