Discussion

This section briefly compares Huygens wavefront tracing with the other major traveltime computation methods: paraxial ray tracing (PRT) Cervený (1987), eikonal solvers (ES) Fomel (1997); Popovici and Sethian (1997); Vidale (1990); van Trier and Symes (1991), and wavefront construction (WC) Vinje et al. (1993). Table 1 summarizes the comparison.

HWT has its output in ray coordinates, the same domain as PRT. However, PRT is done by solving a system of ordinary differential equations (ODE) in the physical domain, while in HWT the solution is obtained by solving a system of partial differential equations (PDE) using finite-differences in the ray coordinate domain.

Both HWT and ES are finite-difference methods. However, HWT represents a finite-difference method in the ray domain, while ES represent finite-difference methods in the Cartesian domain. Also, HWT generates all the arrivals, while the ES generate only one arrival, typically the first.

Finally, HWT is similar to WC in that both compute each wavefront from the preceding one. However, WC involves ray tracing from one wavefront to the next, while in HWT one wavefront is generated from the preceding by finite-differences in the ray domain.

   

finds the solution to a system of PDEs finds the solution to a system of ODEs Eikonal Solvers

gives the output in ray coordinates gives the output in Cartesian coordinates

computes multiple arrivals computes one arrival Wavefront Construction

finds a new wavefront by finite-differences finds a new wavefront by ray tracing