# Ecuación Eikonal

(ī kōn’ ∂l) (from Greek (ikon) meaning *image*. An equation derived from the wave equation through the substitution of a harmonic wave trial solution into the wave equation. In one form of the eikonal equation seen in physics literature, the local velocity is compared to a reference velocity (analogous to comparing a velocity to the speed of light in vacuum):

where is an index of refraction and the quantity is identified as wave
propagation phase advance function, which is the *travel time* of a point on a wave front. The use of index of refraction reflects
the physicists' desire to work in dimensionless coordinates.

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.

Another form of the eikonal equation is written in terms of the ray direction vector where the gradient of traveltime (or *slowness*) vector
for

por lo tanto son las "coordenadas generalizadas" y son el "momento generalizado" de la mecanica Hamiltoniana, y la ecuación eikonal corresponde a la función Hamiltoniana o la ecuación Hamilton-Jacobi de la mecanica analitica.