Conclusions

This paper has introduced a method for tracing phase-rays through monochromatic wavefield solutions of the Helmholtz equation. The resulting phase-rays exhibit a number of attractive characteristics, including: i) a triplication-free ray-field; ii) an ability to shoot rays forward or backward from areas of strong or weak wavefield amplitude alike; and iii) an ability to easily infill rays to ensure adequate phase-ray density. Phase-rays may then be successfully used as a coordinate system on which to extrapolate wavefields. These coordinates avoid coordinate system triplication that can debilitate wavefields extrapolated using conventional ray-field coordinates.

The phase-ray formulation, though, cannot unwrap individual triplicating phases, and chooses a weighted average between interfering phases. Because of this fact phase-ray coordinates represent a trade off between introducing inaccuracy associated with triplicating coordinates and inaccuracy of wavefield extrapolation at greater angles to the ray direction. However, before a critical comparison of the relative merits and drawbacks of phase-ray and conventional ray coordinate extrapolated wavefields is attempted, phase-ray extrapolated wavefields need to be better sampled so that their Cartesian maps are more comparable.