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

External links

find literature about
Eikonal equation
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