Solving the Eikonal equation

The Eq.(2.4) can be rewritten as
\left\vert \mbox{\boldmath$\nabla$}\tau \right\vert = \frac{1}{c}  ,
\end{displaymath} (2.6)

which can be further simplified as
\frac{d\tau}{ds} = \frac{1}{c}  ,
\end{displaymath} (2.7)

where $ds$ stands for the distance traveled by the acoustic wave. Therefore, it follows that
d\tau = \frac{ds}{c}  ,
\end{displaymath} (2.8)

stands for the travel time along $ds$. For a wave propagating between two points $A$ and $B$ the total travel time corresponds then to
\tau = \displaystyle{ \int\limits_{A}^{B}} \frac{ds}{c}  .
\end{displaymath} (2.9)


Orlando Camargo Rodríguez 2012-06-21