Introduction

Over the past several decades, anisotropy has been recognized as one of the important factors effecting the accuracy of seismic imaging methods. If anisotropy is not taken into account by wavefield extrapolation operators, subsurface reflectors (especially steeply dipping ones) will be mispositioned. Thus, incorporating anisotropy into existing isotropic wavefield continuation operators has gained significant importance over the past several years. Several methods have been developed to handle anisotropy which include both implicit and explicit extrapolation operators. These include anisotropic implicit methods Ristow and Ruhl (1997), anisotropic PSPI Rousseau (1997), explicit operators Uzcategui (1995), Zhang et al. (2001), reference isotropic with explicit correction filters Baumstein and Anderson (2003) and explicit anisotropic correction filters Shan and Biondi (2004). However, no such method has been developed to incorporate anisotropy into the Common Azimuth migration operator. Common Azimuth migration Biondi and Palacharla (1996) is one of the most computationally effective wavefield continuation method for large 3-D marine surveys. The computational effectiveness of this method can be attributed to the stationary path approximation that this method uses which shrinks the computational volume for full 3-D wavefields from a five-dimensional space to a four-dimensional space. This greatly reduces the computations that are involved at each depth step. Thus, it would be extremely beneficial if anisotropy can be incorporated into the existing isotropic Common Azimuth migration downward continuation operator. In this paper, we develop a method for introducing anisotropy into Common Azimuth migration. In the following sections, we develop the anisotropic Common Azimuth migration operator, firstly for the relatively simple elliptically anisotropy media and then for the more complex VTI media. We then perform error analysis for our derived analytical solution for the VTI media and finally compare the 3-D impulse responses of the elliptically anisotropic Common Azimuth operator with that of the isotropic operator.