# Difference between revisions of "Dictionary:Eikonal equation"

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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 is written in terms of medium velocity only <math> V(\mathbf{x} ) </math> | ||

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

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

## 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 , as

**Failed to parse (syntax error): {\displaystyle \left(\nabla V(\mathbf{x}} \right) = \frac{1}{V^2(\mathbf{x})} . }**