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):  
+
(&#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>
 +
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 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 (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})} . }

External links

find literature about
Eikonal equation
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