Time-to-depth conversion and seismic velocity estimation using time-migration velocity |

**Step 1.**- Compute the geometrical spreading of the image rays in the time-domain coordinates from the Dix velocity by solving equation 14 in 2-D and 20 in 3-D. Then find from equation 10 in 2-D and equation 17 in 3-D.
**Step 2.**- Convert the seismic velocity in the time-domain coordinates to the depth-domain coordinates using the time-to-depth conversion algorithm, which was presented by Cameron et al. (2007). It is a fast and robust Dijkstra-like solver motivated by the Fast Marching method (Sethian, 1999,1996).

We performed step 1 in two ways: a finite difference method and a spectral Chebyshev method.

2013-07-26