Partial differential equation for migration to zero-offset

Alexander M. Popovici

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ABSTRACT

Starting from prestack migration in offset-midpoint coordinates I obtain a partial differential equation (PDE) for migration to zero-offset in constant velocity. The PDE allows migration to zero-offset (MZO) to be performed via an algorithm similar to phase-shift migration. Since the velocity is isolated on depth intervals, this equation could theoretically be used for variable velocity migration to zero-offset. I show synthetic examples of depth variable velocity MZO which match perfectly the zero-offset section.