# Dictionary:Eikonal equation

(ī kōn’ ∂l) A form of the wave equation for harmonic waves in which the local velocity ${\displaystyle V}$ is compared to a reference velocity ${\displaystyle V_{R}}$(analogous to comparing a velocity to the speed of light in vacuum):
${\displaystyle \left(\nabla \phi \right)^{2}=\left({\frac {V}{V_{R}}}\right)^{2}=n^{2}}$,
More commonly in geophysical literature, the eikonal equation is written in terms of medium velocity only ${\displaystyle V(\mathbf {x} )}$ where ${\displaystyle \mathbf {x} =(x_{1},x_{2},x_{3})}$, as
$\displaystyle \left(\nabla V(\mathbf{x}} \right) = \frac{1}{V^2(\mathbf{x})} .$