# Difference between revisions of "Dictionary:Eikonal equation"

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{{lowercase}}{{#category_index:E|eikonal equation}} | {{lowercase}}{{#category_index:E|eikonal equation}} | ||

− | (ī kōn’ ∂l) A form of the wave equation for harmonic waves in which the local velocity | + | (ī kōn’ ∂l) A form of the wave equation for harmonic waves in which the local velocity <math> V </math> is compared to a reference velocity <math> V_R </math>(analogous to comparing a velocity to the speed of light in vacuum): |

− | <center><math>\nabla^2 | + | <center><math>\left(\nabla \phi \right)^2 =\left(\frac{V}{V_R}\right)^2=n^2 </math>,</center> |

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> | ||

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

+ | |||

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

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

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

## Revision as of 12:33, 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 is written in terms of medium velocity only

where **Failed to parse (syntax error): {\displaystyle \mathbf{x} = (x_1,x_2,x_3), as <center> <math> \left(\nabla V(\mathbf{x}} \right) = \frac{1}{V^2(\mathbf{x})} . }**