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.
|Wavefront Tracing||Ray Tracing|
|finds the solution to a system of PDEs||finds the solution to a system of ODEs|
|Wavefront Tracing||Eikonal Solvers|
|gives the output in ray coordinates||gives the output in Cartesian coordinates|
|computes multiple arrivals||computes one arrival|
|Wavefront Tracing||Wavefront Construction|
|finds a new wavefront by finite-differences||finds a new wavefront by ray tracing|