Using the method of characteristics, we can derive a system of ordinary differential equations that define the ray trajectories. To do so, we need to transform equation (9) to the following form:

(14) |

(15) |

where *s* is a running parameter along the rays, related to the traveltime *t* as follows:

Using equation (9), we obtain

(18) |

(19) |

and

where and and , and the same holds for and .
To trace rays, we must first
identify the initial values *x _{0}*, ,

The raytracing system of equations (18-21) describes the ray-theoretical aspect of wave propagation in the -domain, and can be used as an alternative to the eikonal equation. Numerical solutions of the raytracing equations, as opposed to the eikonal equation, provide multi-arrival traveltimes and amplitudes. In the numerical examples, we use raytracing to highlight some of the features of the -domain coordinate system.

10/9/1997