Huygens wavefront tracing: A robust alternative to conventional ray tracing

Conclusions

The results obtained so far have led us to the following conclusions:

1. Stability: The HWT method is a lot more stable in rough velocity media than the PRT method. The increased stability results from the fact that HWT derives the points on the new wavefronts from three points on the preceding wavefront, compared to only one in the usual PRT, which also means that a certain degree of smoothing is already embedded in the method. This feature allows us to use the HWT method in media of very sharp velocity variation and still obtain results that are reasonable from a geophysical point of view.

2. Coverage: Being more stable and giving smoother rays than the PRT method, enables the HWT method to provide a better coverage of the shadow zones. The idea is that since the wavefront is traced from one ray to the other, it is very easy to introduce in the code a condition to decrease the shooting angle as soon as the wavefront length exceeds a specified upper limit.

3. Speed: Both methods were tested on an SGI 200. The execution time for shooting 90 rays of 130 samples for each ray was 1.31s for the PRT method and 0.22 s for the HWT method. Even though in the current implementation of HWT we do not compute the amplitudes of the waves, our method has still yielded a big improvement in speed for the 2-D case, which gives us hope of doing even better in the 3-D case.

In our future work, we will implement the 3-D Huygens wavefront tracing method. We expect to preserve its stability, while making it run even faster in comparison to other conventional 3-D ray tracing methods.

Huygens wavefront tracing: A robust alternative to conventional ray tracing