Green's function for migration: Continuous recording geometry

Abstract

Abstract Analytical formulas are derived to give the point scatterer responses for the zero-offset and nonzero-offset migration operators. These formulas are derived under the far-field approximation for a continuous distribution of sources and receivers, and are denoted as migration Green's functions. By specifying a homogeneous velocity model with irregular layers, these Green's functions can be used to quickly compute the synthetic migrated sections without having to compute the modeled data. Thus, these formulas provide a fundamental understanding of migration artifacts and their relationship to the image point location and source-receiver configuration. This understanding lays the foundation for the next step, elimination of these artifacts by migration deconvolution.