Initialization

Since I use a triangular grid, the process of wavefront propagation proceeds on an expanding half hexagonal ring centered at the source point. To start the process, the attributes of wavefronts are initialized at the grid points inside and on a half hexagonal ring shown in Figure . The radius of this half hexagonal ring is determined based on the velocity field around the source point. Generally, it is chosen to be the radius of the largest half hexagon within which the velocity field is well approximated by a linear function. Such a choice make it possible to compute analytically the attributes of wavefronts at the grid points inside and on this half hexagonal ring.

 

vpinit
Figure 10 The attributes of wavefronts are initialized at the grid points within and on a half hexagonal ring as indicated with small black dots. The large black dot indicates the source point.