A time-space implementation of AMO as a time-variant operator is still not practical for 3D data because of its computing costs. Several authors Bale and Jakubowicz (1987); Biondi and Ronen (1986); Bolondi et al. (1984); Notfors and Godfrey (1987) have described a logarithmic stretching of the time axis that can convert a non-Fourier transform implementation to a Fourier transform combined with a phase shift.
The log-stretch transform makes AMO a time-invariant operator,
which means it only depends on the difference between the input and
output time. A transformation of the log-stretched data to the Fourier
domain is then a convenient way to process the data in the 
space.
Furthermore, since each frequency inversion is completely independent,
one needs to solve many small systems instead of solving one huge
system of equations. The inversions can be done in parallel by as many
processing units as number of frequencies. In practice, several
frequency bands from a useful bandwidth of the data are carried
in parallel.