- 1.
- We can, again, ignore the spatial variability of the slowness function for
the terms of the summation, and
,which gives the following linear mixed-domain migration equation, known in the literature
as the
*extended local Born-Fourier*method Huang et al. (1999):(10) - 2.
- We can consider Equation (10) as a Taylor series expansion, therefore we can write it
in a more compact, but equivalent, form as
(11) *local Born-Fourier*a.k.a.*pseudo-screen*method Huang and Wu (1996).The extended local Born-Fourier method, Equation (10), is preferable in practice, since Equation (11) can lead to instability when the denominator vanishes. Another way of avoiding the instability is to add a small complex quantity, , to the denominator, method that is known as the

*complexified local Born-Fourier*or*complexified pseudo-screen*method de Hoop and Wu (1996):(12)

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