Toward an exact adjoint:\\ semicircle versus hyperbola

Jun Ji

The correctness of an adjoint operator entirely depends on the correctness of the corresponding forward modeling operator. In migration, the input-oriented algorithm implies more correct forward modeling than the output-oriented algorithm does. One big difference between the two algorithms is the domain of interpolation, and this is one of the major sources of migration artifacts. Whereas the input-oriented algorithm requires interpolation in the model space, the output-oriented algorithm requires interpolation in the data space. For Kirchhoff migration, the method of semicircle superposition and the method of hyperbola summation correspond to the input-oriented and output-oriented algorithms, respectively. The same analogy can be applied to Stolt migration. Levin (1994) suggested the input-oriented algorithm that is the counterpart to the output-oriented algorithm suggested by the SEP ``in-time" group (Popovici et al., 1993; Lin et al.,1993; Blondel and Muir, 1993)

SEP-report, vol.80, 499-511 (1994).

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