<title>Migration to zero-offset in variable velocity media</title>

Abstract

ABSTRACT As a condition for further generalization of the migration to zero-offset in variable velocity media, I develop the theory for 2-D migration to zero offset (MZO) in constant velocity media, starting from prestack migration in midpoint-offset coordinates. Iarrive at an integral formulation for the MZO operator, analytically derived from the double square root (DSR) prestack migration equation. The integral formulationfor the MZO is similar in form to the DSR equation, suggesting a generalization tovariable velocity media using a. phase-shift algorithm. Isolating the zero-offset migration The basic concept for analytically deriving the MZO from prestack migration isto separate the latter into two processes:. Migration to zero-offset.. Zero-offset migration.Once we extract the zero-offset migration from the prestack migration operator, it isassumed that what remains is in fact an operator that transforms the common-offsetdata into zero-offset data, hence the name of the operator: migration to zero-offset. Idefine migration to zero-offset as the operation that converts a common-offset sectioninto a zero-offset section. For a. constant velocity medium this operation is equivalentto the sequence of normal moveout (NMO) followed by dip moveout (DM0).