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 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 , as

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

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Eikonal equation
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