Prestack migration error in transversely isotropic media

Previous studies have shown the dependence of migration error on reflector dip when poststack migration is done with an algorithm that ignores the presence of anisotropy. Here we do a numerical study of the offset dependence of migration error that can be expected when common-offset data from factorized transversely isotropic media are imaged by an isotropic prestack migration algorithm. Anisotropic ray tracing, velocity analysis and prestack migration in the common-offset domain are the basic tools for this analysis, which we apply to models with constant vertical gradient in velocity that are characterized by a particular combination of Thomsen's anisotropy parameters: 1) == (e - 6)/(1 + 26). The results show that the offset dependence of error in imaged position, and therefore the quality of stacked, imaged data, depends largely, but not completely, on the anisotropy parameter 1). Generally, the larger the value of 11,the larger the problem of mis-stacking. Over a wide range of reflector dip, time-misalignment of imaged features on commonreflection- point gathers is considerably less than the error in imaged position on the zero-offset data. For all the model parameters studied, we expect stacking quality to be worst for reflector dip around 50 degrees. Reflections from horizontal reflectors and those with dip close to 90 degrees should stack well in all cases, and mis-stacking is not severe for overturned reflectors.