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Extended Stolt F-K Migration

Craig Beasley, Walt Lynn, Ken Larner, Hung V. Nguyen

Despite our understanding that depth migration is a more powerful imaging tool than time migration, time migration still constitutes the majority of migration done today. In selecting a time-migration algorithm, three primary criteria are of concern: accuracy in imaging steep dips, accuracy in the presence of vertical velocity variation, and computational effort. The ideal algorithm would be efficient and unlimited in its ability to image steep dips in arbitrary vertical velocity structures. It would also accommodate gentle lateral velocity variations deemed acceptable for time-migration methods.

A particularly attractive algorithm to consider is Stolt's f-k method: it is computationally efficient and has unlimited dip accuracy for constant-velocity media. Although Stolt's method can handle moderate vertical variations, errors become unacceptable for steep dips in the presence of large vertical velocity variation. An extension to Stolt migration removes its restrictions on vertical velocity variation, yielding accuracy comparable to phase-shift migration at only a fraction of the computational time.

This extended Stolt method is based on partitioning the velocity field in a manner analogous to that in cascaded finite-difference migration and performing a number of stages of Stolt migrations. In each stage, the migration velocity field is closer to a constant--the ideal situation for Stolt migration--than when the migration is done conventionally (i.e., in just one stage). Empirical results and error analyses show that four stages of extended Stolt migration are sufficient to migrate steeply dipping events accurately in nearly any vertically varying velocity field. In fact, for a wide range of velocity fields and dips, as few as two stages will produce phase-shift quality images. The method can be used for two-dimensional, two-pass three-dimensional, and single-pass three-dimensio al migrations.

AAPG Search and Discovery Article #91035©1988 AAPG-SEPM-SEG Pacific Sections and SPWLA Annual Convention, Santa Barbara, California, 17-19 April 1988.