Introduction

Given the relative simplicity of the Radon method applied in the image space, as shown in chapter 2, extending its application to account for the effect of crossline offset seems attractive. The first step in that direction is to understand the moveout of the multiples on 3D Subsurface-Offset-Domain Common-Image Gathers (SODCIGs) and Angle Domain Common Image Gathers (ADCIGs). In 3D, the ADCIGs are function of the aperture angle and the reflection azimuth (, ).

I show in this chapter that the residual moveout equation of a 3D specular water-bottom multiple from a flat water-bottom in 3D ADCIGs is a direct extension of the 2D equation presented in Chapter  after a simple rotation of coordinates to account for the source-receiver azimuth. The raypath of the specular water-bottom multiple in this case is confined to one vertical plane and is therefore essentially a 2D multiple. For a water-bottom that dips in the inline direction only, the raypath of the multiple is contained in a vertical plane only if the source-receiver azimuth is in the inline direction. For other directions, and for all directions if the water-bottom dips in the crossline direction, however, the propagation of the multiple is not contained in a plane.

In this chapter I concentrate on the mapping of the multiples to image space and leave their attenuation for later chapters. I will illustrate the mapping of the water-bottom multiple from a water-bottom dipping in the crossline direction using a very simple 3-D synthetic prestack dataset provided by ExxonMobil.