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

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**).

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