where stands for the pressure of the acoustic wave, represents the signal transmitted by the acoustic source, represents the source position and represents the nabla differential operator. Applying a Fourier transform to both sides of Eq.(2.1) one can obtain the so called Helmholtz equation:

where

and

Let's consider a plane wave-like approximation to the solution of Eq.(2.2) and write that [4]

where represents a slowly changing wave amplitude, and stands for a rapidly evolving phase; the surfaces with constant represent the wavefronts; analogously, the surfaces with constant are called timefronts. By placing Eq.(2.3) into the homogeneous form of Eq.(2.2), considering the high frequency approximation

(where ) and separating the real and imaginary terms of the equation, one can obtain the Eikonal equation:

and the transport equation:

The following sections will describe the solution of Eqs.(2.4)-(2.5).

Orlando Camargo Rodríguez 2012-06-21