Velocity analysis using similarity-weighted semblance |

where and come from two least-squares minimization problems:

where is a diagonal operator composed from the elements of : and is a diagonal operator composed from the elements of : . Least-squares problems 5 and 6 can be solved with the help of shaping regularization with a smoothness constraint:

where is a smoothing operator, and and are two parameters controlling the physical dimensionality and enabling fast convergence when inversion is implemented iteratively. These two parameters can be chosen as the least-squares norms of and , respectively.

syn,weights
A demonstration of similarity-weighted semblance. (a) NMO corrected gather. (b) Weights applied to each trace for semblance calculation based on the local similarity between each trace and a reference trace.
Figure 1. |
---|

Velocity analysis using similarity-weighted semblance |

2015-06-25