My first post on this blog regards Earth's free oscillations, also called normal modes. As a string or a 2 dimensional membrane, also a 3 dimensional sphere has "natural" oscillations such that motion at each point is sinusoidal.

A detailed derivation of the frequency and shape of these oscillations can be found in:

**Woodhouse, J. H., & Deuss, A. (2007)**. Theory and Observations - Earth’s Free Oscillations. Treatise on Geophysics

**Deuss, A., & Woodhouse, J. H. (2004)**. Iteration method to determine the eigenvalues and eigenvectors of a target multiplet including full mode coupling. Geophysical Journal International

**Al-Attar, D. (2007)**. A solution of the elastodynamic equation in an anelastic earth model. Geophysical Journal International

or in:

**Dahlen and Tromp (1998)**. Theoretical global seismology

The following animations show two spheroidal modes. Their surface movement is in radial and also in tangential direction. The tangential direction is either towards or away from the radial peaks, depending upon the shape of the Eigenfunction.

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Spheroidal Mode l=2, m=0 ("Football mode")

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angular motion is towards radial peaks

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Spheroidal Mode l=10, m=5 ("Fundamental Rayleigh Mode")

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angular motion is away from radial peaks

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