Outer loop over interval slowness models
Migrate the data with
Apply residual NMO+DMO: compute
Estimate dips on the stacked image
Pick important reflector points
Compute the operator
Update reflector position map , ,
The objective function Q is the sum of the semblance
is the relation between changes in the
interval slowness model and changes in the residual slowness of the chosen
reflection events. finds the direction and magnitude
of increasing semblance versus for each reflector.
guides the change
in due to reflector movement. The line searches return
the values and to describe the maxima
of the objective function in their respective search directions.
The conjugate-gradient algorithm I use is
called PARTAN and is described by Luenberger (1984).
The algorithm is robust for nonlinear functions and when line searches
are inexact. This is important because my objective function is non-quadratic
in shape and for values of intermediate to those computed
the objective function has to be computed by interpolation.
The bound on the
magnitude of the change in interval slowness is taken with respect
to the interval slowness model used for migration. is not
meant to be taken as a firm figure; the data should be remigrated once
residual migration can no longer adequately describe the reflector
movement that accumulates as the iterations proceed. Also, the norm measuring
relative change in the slowness model
can be an or norm.