The difference between Bleistein's DMO and Black/Zhang's DMO results from
a philosophical difference about the definition of ``true-amplitude''.
While the goal in the synthetic tests was to preserve the peak amplitude of
each reflection event, Bleistein's algorithm is based on preserving the
spectral density of the image wavelet. A second difference results from
the sequence in the processing flow surrounding DMO. A divergence
correction must be applied to the input prior to applying Black/Zhang's DMO,
whereas both input and output of Bleistein's DMO decay
with spherical divergence
factors of and and , respectively
These two differences account for the *A ^{2}* factor between the two Jacobians
leading to higher weights on Bleistein's DMO,
which results in higher peak amplitudes than those on
the predicted curve.

On the other hand, the difference between Black/Zhang's DMO and Hale's DMO results from the fact that the former algorithm accounts for the reflection point smear and, therefore, correctly positions input events at their true zero-offset locations. The two Jacobians differ by a factor of

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Consequently, to be consistent with the original definition of preserving the peak amplitudes of reflection events, I define the amplitude function of AMO in terms of Black/Zhang's DMO and its asymptotic inverse.

1/18/2001