Moveout-based wave-equation migration velocity analysis |
Notice that here the moveout between the initial image and the new image is characterized by both curvature and constant shift . The parameter does not affect the gather flatness; therefore there is no need to put it into the objective function in () , however is essential to describe the change of image's kinematics.
Since maximize eq (11),
We differentiate the equation (12) with respect to and , which gives
(13) |
Now we need to invert a Jacobian to get . We define the following:
Then
(15) |
There is another way to define the relation between and , leading to the indidirect operator using a weighted least-squares fitting formula. Suppose we have the locations of one event in the ADCIGs at location ( , and we introduce a moveout formula . Now we define the best fitted intercept and curvature ( and ) values as follows:
(16) |
It is easy to find if there is a pertubation of on :
(18) |
Moveout-based wave-equation migration velocity analysis |