Azimuth moveout (AMO) was introduced by Biondi and Chemingui as an operator that transforms common-azimuth common offset seismic data from one vector offset to another. The time-and-space (Kirchhoff) formulation of AMO Fomel and Biondi (1995a,b) leads to a three-dimensional stacking operator, which includes four major components: the curvilinear surface of the summation path, the associated amplitude, the time filter, and the surface aperture (the range of integration). In this paper, we analyze two additional issues that are required for a successful practical implementation of the method: the operator parameterization and operator antialiasing.
The problem of parameterization arises because of the complicated time-dependent shape of the AMO aperture described in Fomel and Biondi (1995a). In this paper we show that the expressions for the summation path, the amplitudes, and the integration range have simple analytical forms when defined in the coordinate system of the input and output offset vectors.
The operator aliasing problem is common for a wide variety of integral (stacking) operators Lumley et al. (1994). It is caused by the spatial undersampling of the summation path. When the integration path is parametrized in the spatial coordinate, as it is commonly done, the steeper part of the summation path becomes undersampled. The error introduced by the undersampling of the summation path is usually controlled by limiting the rate of change in the integrand (the input data) either by low-pass filtering Gray (1992), or by triangular filtering Claerbout (1992a). Unfortunately, in the case of AMO this simple methods are suboptimal because of the rapid changes in the summation path gradient that are encountered along the ``ridges'' of the AMO saddle. We therefore propose a new antialiasing method derived from the time-slice technique, which was developed by Dave Hale for DMO Hale (1991). Synthetic examples show the superiority of the new method compared with the triangle filtering.