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:
“We are the party of all labor.
The whole earth shall be ours to share
And every race and craft our neighbor.
No idle class shall linger there
Like vultures on the wealth we render
From field and factory, mill and mine.
Tomorrow’s sun will rise in splendor
And light us till the end of time.”
—Eugène Pottier (1816–1887)
“What I would like to write is a book about nothing, a book without exterior attachments, which would be held together by the inner force of its style, as the earth without support is held in the air—a book that would have almost no subject or at least in which the subject would be almost invisible.”
—Gustave Flaubert (1821–1880)
“The Indians knew that life was equated with the earth and its resources, that America was a paradise, and they could not comprehend why the intruders from the East were determined to destroy all that was Indian as well as America itself.”
—Dee Brown (b. 1908)