Nowadays, most data processing methods use depth dependent parameters that can not be determined in a direct way but have to be estimated indirectly. On the other hand, data processing in time requires only the knowledge of parameters that can be measured on the surface such as time, offset and horizontal velocity Muir (1993). This is of advantage especially in the case of anisotropy as the vertical velocity does not need to be estimated any longer.
In an attempt to implement an example of time processing, an extended Stolt migration algorithm was developed for general dispersion relations and an exact interpolation scheme Rosenbaum and Boudreaux (1981). Based on Fourier transformation both in time and in space, the Stolt migration () is able to handle the sometimes triplicating behavior of real elastic anisotropy as can be expected, for example, for shear waves in certain shales. Therefore, Stolt migration may be a useful tool in determining the amount of anisotropy in a medium.
As an example, we implement in this study the dispersion relation for the case of anelliptic anisotropy into the migration algorithm which was designed for the use of any dispersion relation. Anelliptic anisotropy is an extension of elliptic anisotropy which retains the convenient symmetry properties of elliptic anisotropy in approximation Dellinger et al. (1993); Karrenbach (1991); Muir and Dellinger (1985). It is especially useful when more independent parameters than vertical and horizontal velocity are needed, but the full complexity of transverse anisotropy is unnecessary. The effect of the anelliptic anisotropy is shown on impulse responses for different grades of anellipticity.