Interval velocity estimation from beam-stacked data -- 2-D gradient operator
, by Biondo Biondi
The theory that I described in SEP-57 (Biondi, 1988) can be applied to com-
pute the gradient of energy in beam-stacks with respect to the velocity model
when the model is two-dimensional (2-D). The computation of the gradient uses
a linear operator that relates perturbations in the velocity model to resulting
changes of beam-stack's parameters. To evaluate this operator I developed a
new ray-tracking algorithm that computes the gradient of raypaths and travel-
times with respect to the velocity model. The resulting back-projection
operator is spatially localized around the down-going and up-going rays. The
operator should resolve well local velocity anomalies. The 2-D inversion is
untested, but the 1-D method sucessfully reonstructed the velocity above a
dipping reflector.
STANFORD