On one approach to solving the eikonal equation $f_x^2+f_y^2+f_z^2=\phi^2$

E. D. Moskalenskii

Institute of Computational Mathematics and Mathematical Geophysics (Computing Center), Siberian Branch of the Russian Academy of Sciences

Abstract: The paper offers a new approach to finding a solution to the eikonal equation $f_x^2+f_y^2+f_z^2=\phi^2$ with a variable velocity of the waves propagation $V(x,y,z)(\phi=1/V)$. It is based on a certain change of a dependent variable and reduction of the equation to a system of three quasilinear equations. It is shown that for certain cases of the function $V(x,y,z)$, exact solutions to this equation can be found with the help of the approach proposed.

Key words: wave propagation, inhomogeneous medium, eikonal equation.

UDC: 517.958

Received: 01.11.2006