The AMO operator introduced in this dissertation is a new partial prestack imaging operator that can be efficiently applied to 3-D prestack data to transform their effective offset and azimuth. By including AMO in the processing flow, we can reduce the computational costs of 3D imaging and, in many applications, improve the quality of the final image. I demonstrate in Chapter 2 how the size of 3D prestack dataset can be largely reduced by coherent partial stacking using AMO, which preserves the high-frequency, steeply-dipping energy. AMO is also a modeling operator that maps seismic data into equivalent data with different offset and azimuth. Therefore, it can be effectively employed for data regularization and for wave-equation interpolation to overcome spatial aliasing. These two applications are fully explored in Chapters 3 and 4.
Biondi and Chemingui 1994 defined AMO as the cascade of a 3D prestack imaging operator with its corresponding modeling operator. To derive analytical expressions for the AMO impulse response, we used both constant velocity DMO and its inverse, as well as constant-velocity migration and modeling. The two derivations yield to an equivalent, velocity-independent definition for the kinematics of AMO. Similar to DMO processing Deregowski and Rocca (1981); Hale (1984), the first order effects of velocity variation are removed by applying a normal moveout correction (NMO) to the data prior to AMO. Given the irregular spatial sampling of 3D data, AMO is implemented as an integral operator. Its impulse response is a skewed saddle in the time-midpoint space. The shape of the saddle depends on the amount of azimuth rotation and offset continuation applied to the data. For small azimuthal rotations and offset continuation, the AMO impulse response is compact and its application as an integral operator is inexpensive compared to 3D prestack migration.
In the context of amplitude preserving processing, I developed a true amplitude function for AMO so that amplitude variations as a function of offset and azimuth are not distorted by the transformation. I restricted the definition of ``true-amplitude'' to be consistent with the definition of most interpreters for preserving peak amplitudes of reflection events. The derivation is based on chaining a ``true-amplitude'' DMO with its amplitude preserving ``true''-inverse. I use a general formulation for inverting integral solutions, Beylkin (1985); Cohen and Hagin (1985) to derive an integral inverse DMO that is asymptotically valid. Detailed derivation of AMO amplitudes are provided in Chapter 3 which illustrates an example of a ``true-amplitude'' algorithm.