Editing Seismic wave (section)

==== Normal modes ====
[[File:Fundametal toroidal oscillation Earth.gif|thumb|right|The sense of motion for toroidal <sub>0</sub>T<sub>1</sub> oscillation for two moments of time.]]
[[File:Fundamental spheroidal oscillation Earth.gif|thumb|right|The scheme of motion for spheroidal <sub>0</sub>S<sub>2</sub> oscillation. Dashed lines give nodal (zero) lines. Arrows give the sense of motion.]]
Free oscillations of the Earth are [[standing wave]]s, the result of interference between two surface waves traveling in opposite directions. Interference of Rayleigh waves results in ''spheroidal oscillation S'' while interference of Love waves gives ''toroidal oscillation T''. The modes of oscillations are specified by three numbers, e.g.,  <sub>n</sub>S<sub>l</sub><sup>m</sup>, where ''l'' is the angular order number (or ''spherical harmonic degree'', see [[Spherical harmonics]] for more details). The number ''m'' is the azimuthal order number. It may take on 2''l''+1 values from −''l'' to +''l''. The number ''n'' is the ''radial order number''. It means the wave with ''n'' zero crossings in radius. For spherically symmetric Earth the period for given ''n'' and ''l'' does not depend on ''m''.

Some examples of spheroidal oscillations are the  "breathing" mode <sub>0</sub>S<sub>0</sub>, which involves an expansion and contraction of the whole Earth, and has a period of about 20 minutes; and the "rugby" mode <sub>0</sub>S<sub>2</sub>, which involves expansions along two alternating directions, and has a period of about 54 minutes. The mode <sub>0</sub>S<sub>1</sub> does not exist because it would require a change in the center of gravity, which would require an external force.<ref name=Shearer2009ch8/>

Of the fundamental toroidal modes, <sub>0</sub>T<sub>1</sub> represents changes in Earth's rotation rate; although this occurs, it is much too slow to be useful in seismology. The mode <sub>0</sub>T<sub>2</sub> describes a twisting of the northern and southern hemispheres relative to each other; it has a period of about 44 minutes.<ref name=Shearer2009ch8/>

The first observations of free oscillations of the Earth were done during the great [[1960 Valdivia earthquake|1960 earthquake in Chile]]. Presently the periods of thousands of modes have been observed. These data are used for constraining large scale structures of the Earth's interior.