VTI migration velocity analysis using RTM |

Now we can define the gradient by the back-projection of a unit perturbation in the objective function:

Let's analyze the first term in equation 17 in detail, and the second term follows the same reasoning.

where

and

Plugging equation 19 and 20 into equation 18, we can rewrite equation 18 explicitly as follows:

Similarly, we can obtain the explicit form for the second term in equation 17:

Substituting equation 21 and equation 22 for the corresponding terms in equation 17, we now have derived the explicit form for the DSO gradient.

VTI migration velocity analysis using RTM |

2012-05-10