Dictionary:Eikonal equation

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(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 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 (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.

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Eikonal equation
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