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

Nonetheless, we found two ways for solving these PDEs numerically on the required, and relatively short, interval of time: namely, a finite difference scheme inspired by the Lax-Friedrichs method and a spectral Chebyshev method. A detailed analysis of the problem shows that our methods work thanks to

- the special input , corresponding to a positive finite seismic velocity;
- the special initial conditions , corresponding to the image rays;
- the fact that our finite difference method contains error terms which damp the high harmonics; truncation of the polynomial series in the spectral Chebyshev method which is similar to truncation of the high harmonics; and
- the short interval of time, in which we need to compute the solution, so that the growing low harmonics fail to develop significantly.

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

2013-07-26