Analysis of Dip-Dependent Operator Relating Migration Velocities and Interval Velocities
, by Paul J. Fowler
In previous papers in SEP-44 and SEP-48 I derived a linear operator
that relates perturbations in interval slownesses to the resultant changes
in the slownesses used for prestack time migration.
This operator is suitable only for point diffractors; the
migration slowness change for a continuous reflector will not in general
be the same as the migration slowness change for a point diffractor.
In this paper
I show how to decompose the point-diffractor operator into dip
components and from this, how to derive an operator suitable for continuous
beds of any specified dip.
This dip-specific operator, like the all-dip point-diffractor operator,
is derived using a two-step procedure of first tomographically
estimating traveltime perturbations, and then finding a least-squares
fit for a diffraction pyramid to the perturbed traveltimes.
This fitting now uses not the whole pyramid,
but only that part of it illuminated by a family of rays
symmetric around the normal-incidence ray.
For flat beds, the dipping-bed migration-
slowness operator reduces to Toldi's flat-bed stacking-slowness operator.
STANFORD