A robust approach to time-to-depth conversion and interval velocity estimation from time migration in the presence of lateral velocity variations |

We continue the derivation of the Fréchet derivative matrix from equation
12. Using the same notations as introduced in equation 10, after discretization equation
12 becomes

Because is in time-domain , we need to apply the chain-rule for its derivative with respect to
, i.e.,

Another differentiation of equation 6 leads to

Finally, by inserting equations B-2 through B-4 into B-1, we complete the
derivation of the Fréchet derivative matrix:

A robust approach to time-to-depth conversion and interval velocity estimation from time migration in the presence of lateral velocity variations |

2015-03-25