Translations:Mathematical foundation of 3-D migration/71/en

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Aside from the application of the McClellan transform, the circular symmetry of the 3-D impulse response can also be attained by applying the correction term by Li [1] to the extrapolated wavefield, intermittently, at some depth steps. The objective is to compensate for the accumulated errors caused by the approximations made to the exact 3-D extrapolation operator given by equation (G-16). Li [1] devised a correction term originally to compensate for the errors caused by the 45-degree split form of the dispersion relation given by equation (G-12). The error incurred during wave extrapolation using an implicit scheme arises from the difference between the exact form of the dispersion relation given by equation (G-13b) and an approximate form such as that given by equation (G-12).

  1. 1.0 1.1 Li (1991), Li., Z, 1991, Compensating finite-difference errors in 3-D migration and modeling: Geophysics, 56, 1650–1660.