# Difference between revisions of "Dictionary:Eikonal equation"

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where ''n'' is an index of refraction and [[File:Fgr.gif]] is the wave function. Valid only where the variation of properties is small within a wavelength, sometimes called the ‘‘high-frequency condition.’’ | where ''n'' is an index of refraction and [[File:Fgr.gif]] is the wave function. Valid only where the variation of properties is small within a wavelength, sometimes called the ‘‘high-frequency condition.’’ | ||

− | More commonly in geophysical literature, the eikonal equation is written in terms of medium velocity only <math> V(\mathbf{x} ) </math> | + | More commonly in geophysical literature, the eikonal equation (for scalar waves) is written in terms of medium velocity only <math> V(\mathbf{x} ) </math> |

where <math> \mathbf{x} = (x_1,x_2,x_3) </math>, as | where <math> \mathbf{x} = (x_1,x_2,x_3) </math>, as | ||

− | <center> <math> \left(\nabla | + | <center> <math> \left(\nabla \phi(\mathbf{x}) \right)^2 = \frac{1}{V^2(\mathbf{x})} . </math> </center> |

+ | |||

+ | Solutions to the eikonal equation yield a high-frequency or large-wavenumber asymptotic representation of the wave field as a family of rays, represented by ray position and ray direction---the so-called ''kinematic'' aspect of wave propagation. | ||

==External links== | ==External links== | ||

{{search}} | {{search}} |

## Revision as of 11:38, 10 June 2015

(ī kōn’ ∂l) A form of the wave equation for harmonic waves in which the local velocity is compared to a reference velocity (analogous to comparing a velocity to the speed of light in vacuum):

where *n* is an index of refraction and is the wave function. Valid only where the variation of properties is small within a wavelength, sometimes called the ‘‘high-frequency condition.’’

More commonly in geophysical literature, the eikonal equation (for scalar waves) is written in terms of medium velocity only where , as

Solutions to the eikonal equation yield a high-frequency or large-wavenumber asymptotic representation of the wave field as a family of rays, represented by ray position and ray direction---the so-called *kinematic* aspect of wave propagation.