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The standard one-way wave equation Claerbout (1971) produces the correct phase
of the wavefield, but it is not equivalent to the acoustic wave equation in terms of amplitude.
Zhang (1993) suggests that to improve the dynamics information of one-way wave equation,
an amplitude correction term should be included into the standard one-way wave equation.
Zhang et al. (2001) apply the one-way wave equation with the amplitude correction
to shot-profile migration and shows that it can provide the same amplitude
as an image produced by the true amplitude Kirchoff migration Hanitzsch (1997) by asymptotic analysis.
Vlad et al. (2003) compare the amplitude of one-way wave equation with amplitude correction
with acoustic wave equation and WKBJ amplitude correction, and concludes that it has the same effect as the
WKBJ correction Clayton and Stolt (1981). In this short note, we will demonstrate in theory that the one-way wave equation with the amplitude correction term is
equivalent to the first order approximation of WKBJ amplitude correction.

** Next:** Amplitude preserving one-way wave
** Up:** Shan and Biondi: Residual
** Previous:** Shan and Biondi: Residual
Stanford Exploration Project

10/14/2003