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: Eigentone
Other articles related to "earth":
... Main article Earth in culture The standard astronomical symbol of the Earth consists of a cross circumscribed by a circle ... humankind did not begin to view the Earth as a moving object in orbit around the Sun until the 16th century ... Earth has often been personified as a deity, in particular a goddess ...
... abduct her, bursting through a cleft in the earth ... Demeter, when she found her daughter had disappeared, searched for her all over the earth with torches ... In most versions she forbids the earth to produce, or she neglects the earth and in the depth of her despair she causes nothing to grow ...
... also known by the temporary name AL00667, is a near-Earth asteroid, first discovered on January 13, 2004, by the LINEAR project ... Center (MPC) suggesting an imminent collision with Earth on or about January 15 with a likelihood of 14 ... The asteroid passed at a distance of 12 Gm (or 32 times the distance from the Earth to the Moon), posing no threat ...
... the gravitational constant and the mass of a given astronomical body such as the Sun or the Earth—is known as the standard gravitational parameter and is denoted ... Also, for celestial bodies such as the Earth and the Sun, the value of the product GM is known more accurately than each factor independently ... For Earth, using M⊕ as the symbol for the mass of the Earth, we have Calculations in celestial mechanics can also be carried out using the unit of solar mass rather than the standard SI unit kilogram ...
2004 FH is a near-Earth asteroid that was discovered on March 15, 2004, by the NASA-funded LINEAR asteroid survey ... just 43,000 km (27,000 mi) above the Earth's surface on March 18, 2004, at 2208 UTC making it the 11th closest approach to Earth recorded as of 21 November 2008 (2008 -11-21) (see ... For comparison, geostationary satellites orbit Earth at 35,790 km ...
Famous quotes containing the word earth:
“Words whispered on Earth are heard in Heaven like thunder; evil done in dark places the gods see like lightning.”
“The earth is the very quintessence of the human condition.”
—Hannah Arendt (19061975)
“Earth laughs in flowers, to see her boastful boys
Earth-proud, proud of the earth which is not theirs;
Who steer the plough, but cannot steer their feet
Clear of the grave.”
—Ralph Waldo Emerson (18031882)