Minimum traveltime calculation in 3-D graph theory

摘要

In this short note, graph theory is applied to traveltime calculations in three dimensions. The computational memory requires two 3-D arrays to store the velocity model and traveltime results, plus two temporary arrays for searching the minimum traveltime. We found that the quick-sort algorithm is more efficient than the heap sort. We have to balance between accuracy and computing speed when choosing number of layer connections. Graph theory provides the most robust numerical scheme for traveltime calculations. It accurately captures head waves from curved interfaces as well as caustics.