Estimation of Reflection Coefficient Under Migration of Converted and Monotype Waves

Algorithms providing restoring reflection coefficients in true-amplitude migration have been developed quite recently. The results were obtained for the zero-offset pattern as well as for the common shot pattern in the class of monotype waves. The paper generalizes these results, first, for the case of the arbitrary type pattern and, second, for the case of reflected waves of the arbitrary type. A solution is sought as a product of a stacking-type operator with a specially chosen weight function and correcting filters which contain powers of operators of the Hilbert transformation and differentiation. The problem of the correcting filtration during migration has not been put forward up to date. The signal shape needs correction in the presence of caustics and focusing points in the medium. The problem seems to be difficult because the mentioned singularities are due to different factors, with the reflector geometry, which is not assumed to be known, playing an important role among them. The main result of this work is that, irrespective of the used pattern, the stacking operator itself compensates the influence of the caustics which are due to the reflector geometry. An additional correction is needed only for compensating the caustics, whose presence is quite determined by the structure of the overlying strata, which is considered to be known.