Difference between revisions of "Dictionary:Eikonal equation"

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{{lowercase}}{{#category_index:E|eikonal equation}}
 
{{lowercase}}{{#category_index:E|eikonal equation}}
(&#x012B; k&#x014D;n&#x2019; &#x2202;l) A form of the wave equation for harmonic waves in which the local velocity ''V'' is compared to a reference velocity ''V''<sub>''R''</sub> (analogous to comparing a velocity to the speed of light in vacuum):  
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(&#x012B; k&#x014D;n&#x2019; &#x2202;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\phi=\left(\frac{V}{V_R}\right)^2=n^2 </math>,</center>
+
<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 &#x2018;&#x2018;high-frequency condition.&#x2019;&#x2019;
 
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 &#x2018;&#x2018;high-frequency condition.&#x2019;&#x2019;
 +
 +
More commonly in geophysical literature, the eikonal equation is written in terms of medium velocity only <math> V(\mathbf{x} ) </math>
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where <math> \mathbf{x} = (x_1,x_2,x_3), as
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 +
<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 11:33, 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 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

where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \mathbf{x} = (x_1,x_2,x_3), as <center> <math> \left(\nabla V(\mathbf{x}} \right) = \frac{1}{V^2(\mathbf{x})} . }

External links

find literature about
Eikonal equation
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