# Dictionary:Dispersion

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1. Variation of velocity with frequency. Dispersion distorts the shape of a wavetrain; peaks and troughs advance toward (or recede from) the beginning of the wave as it travels. Leads to the concept of group velocity U distinct from phase velocity V. Where $\lambda$ =wavelength, f=frequency, and V=phase velocity,

$V=f\lambda ={\frac {f}{1/\lambda }}$ .
$U={\frac {df}{d(1/\lambda )}}$ .

The dispersion of seismic body waves is very small under most circumstances, but surface waves may show appreciable dispersion in the presence of near-surface velocity layering. See Figure D-16. The dispersion of electromagnetic body waves is large in most earth materials. For ground roll and channel waves (see Figure C-2c, d), phase velocity decreases with frequency, sometimes called normal dispersion, and where velocity increases with frequency, anomalous dispersion.

2. A statistical term for the amount of deviation of a value from the norm. See statistical measures.

3. Angular dispersion is variation of velocity with direction, as in an anisotropic medium. Leads to the concept of ray velocity distinct from phase velocity; see Figure A-14a.