An analysis of 2D and 3D multiple attenuation for a canonical example

Three-dimensional formulations of free-surface multiple attenuation for multioffset seismic data are well known. They are not yet used in practice because they require very dense source-receiver coverage, which is still out of reach with existing seismic-acquisition systems. The development of alternative solutions based on 2D algorithms depends on our understanding of the relationship between 2D and 3D free-surface multiple-attenuation methods. This paper attempts to enhance this understanding by establishing the relationship between 2D and 3D inverse scattering free-surface multiple attenuation. A 3D model consisting of three scattering points (one scattered point located in the vertical plane containing the shooting line and the other two points outside this plane) in a homogeneous medium (for which the exact pressure field is analytically known) is used to show that the 2D inverse scattering multiple-attenuation algorithm predicts all free-surface multiples as does its 3D counterpart but with some traveltime and amplitude errors. One implication of this result is that the current 2D inverse scattering multiple-attenuation algorithm, with an appropriate 2D-to-3D correction, can be used to predict the free-surface multiples for data containing out-of-plane scattering.