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.


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