Introduction

The imaging operator transforms the data, which is in data-midpoint position, data-offset, and time coordinates [(m_D,h_D,t)], into an image that is in image-midpoint location, offset, and depth coordinates [($m_{\xi},h,z_{\xi}$)]. This image provides information about the accuracy of the velocity model. This information is present in the redundancy of the prestack seismic image, (i.e. non-zero-offset images). The subsets of this image for a fixed image point ($m_\xi$) with coordinates $(z_\xi,h)$ are known as common-image gathers (CIGs), or common-reflection-point gathers (CRPs). If the CIGs are a function of $(z_\xi,h)$, the gathers are also referred as offset-domain common-image gathers (ODCIGs). The common-image gathers can also be expressed in terms of the opening angle $\theta$, by transforming the offset axis (h) into the opening angle ($\theta$) to obtain a common-image gather with coordinates ($z_\xi$,$\theta$); these gathers are known as Angle-Domain Common-Image Gathers (ADCIGs) (, , , , , ).

There are two kinds of ODCIGs: those produced by Kirchhoff migration, and those produced by wave-equation migration. There is a conceptual difference in the offset dimension between these two kinds of gathers. For Kirchhoff ODCIGs, the offset is a data parameter (h=h_D), and involves the concept of flat gathers. For wave-equation ODCIGs, the offset dimension is a model parameter ($h=h_\xi$), and involves the concept of focused events. In this chapter, I will refer to these gathers as subsurface offset-domain common-image gathers (SODCIGs). Imaging artifacts due to multipathing are present in ODCIGs. However, an event in an angle section uniquely determines a ray couple, which in turn uniquely locates the reflector. Hence, the image representation in the angle domain does not have artifacts due to multipathing (, ). Unlike ODCIGs, ADCIGs produced with either Kirchhoff methods or wave-equation methods have similar characteristics, since the ADCIGs describe the reflectivity as a function of the reflection angle.

This chapter also presents the option to transform the PS-ADCIGs into two angle-domain common-image gathers. The first angle-gather is function of the P-incidence angle, the second one is function of S-reflection angle. I refer to these two angle gathers as P-ADCIGs and S-ADCIGs, respectively. Throughout this process, the ratio between the different velocities plays an important role in the transformation. I present the equations for this mapping and show results on a synthetic data set. I also present results on a 2-D real data set from the Mahogany field in the Gulf of Mexico. For this exercise a comparison between the PZ-ADCIGs and the PS-ADCIGs yield information to improved the PS image.