Earth
Normal modes are generated in the earth from long wavelength seismic waves from large earthquakes interfering to form standing waves.
For an elastic, isotropic, homogeneous sphere, spheroidal, toroidal and radial (or breathing) modes arise. Spheroidal modes only involve P and SV waves (like Rayleigh waves) and depend on overtone number n and angular order l but have degeneracy of azimuthal order m. Increasing l concentrates fundamental branch closer to surface and at large l this tends to Rayleigh waves. Toroidal modes only involve SH waves (like Love waves) and do not exist in fluid outer core. Radial modes are just a subset of spheroidal modes with l=0. The degeneracy doesn’t exists on Earth as it is broken by rotation, ellipticity and 3D heterogeneous velocity and density structure.
We either assume that each mode can be isolated, the self-coupling approximation, or that many modes close in frequency resonant, the cross-coupling approximation. Self-coupling will change just the phase velocity and not the number of waves around a great circle resulting in a stretching or shrinking of standing wave pattern. Cross-coupling can be caused by rotation of Earth leading to mixing of fundamental spheroidal and toroidal modes, or by aspherical mantle structure or Earth’s ellipticity.
Read more about this topic: Normal Mode
Famous quotes containing the word earth:
“That land is like an Eagle, whose young gaze
Feeds on the noontide beam, whose golden plume
Floats moveless on the storm, and in the blaze
Of sunrise gleams when Earth is wrapped in gloom;
An epitaph of glory for the tomb
Of murdered Europe may thy fame be made,
Great People! as the sands shalt thou become;
Thy growth is swift as morn, when night must fade;
The multitudinous Earth shall sleep beneath thy shade.”
—Percy Bysshe Shelley (1792–1822)
“Converse with a mind that is grandly simple, and literature looks like word-catching. The simplest utterances are worthiest to be written, yet are they so cheap, and so things of course, that, in the infinite riches of the soul, it is like gathering a few pebbles off the ground, or bottling a little air in a phial, when the whole earth and the whole atmosphere are ours.”
—Ralph Waldo Emerson (1803–1882)
“[W]e must remember that so long as war exists on earth there will be some danger that even the Nation that most ardently desires peace may be drawn into war.”
—Franklin D. Roosevelt (1882–1945)