The ray tracing method I have implemented is based on the ray tracing system of first-order partial-differential equations, derived from the Eikonal equation by the method of characteristics (see Cerveny1987 for more details):

(37) |

(38) |

The slowness vector is perpendicular to the wavefront (), and must satisfy

(39) |

The system of ray equations together with equation ()
can be solved by a standard numerical integration method.
I use a fourth-order Rungge-Kutta method.
It propagates the properties of the ray (*x*_{i},*p*_{i}, and *t*) over
an increment in arclength by combining the information
from several Euler-style steps (each involving one evaluation of
the right-hand side of equations () and ()),
and then uses the information
obtained to match a fourth-order Taylor series expansion
of the ray variables at the current position.

Figure shows some of rays traced through the reference model shown in Figure .

Figure 15

2/5/2001