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The amplitude scheme that I use for the MZO operator is naive.
It is roughly equal to Zhang's (1988) true amplitude DMO operator minus
the phase correction.
I plan to develop a fast algorithm to
calculate the amplitudes along the MZO operator.
The principle of the algorithm is based on the definition of
the MZO operator, which is an operator that transforms constant-offset data
to zero-offset data. Given a single diffractor in a velocity
model, we can model the zero-offset diffraction, convolving the
kinematic curve with a particular wavelet. We do the same for a
constant-offset section and obtain the flat top pseudo-hyperbola.
The MZO operator applied to the flat top pseudo-hyperbola should
transform the section into a zero-offset section. We know the
kinematics of the MZO operator, which implies we know the input
samples from the constant-offset section which are summed together
in an output point in the zero-offset section.
For each point in the zero-offset section, we have a number of
input values along a particular impulse response of the MZO operator.
To determine the amplitude for the input points along the MZO operator,
we have to solve a linear system of equations, or a least-squares
problem by taking as many output values as necessary from the
zero-offset section and the corresponding input values along a
particular MZO operator in the constant-offset section.
We don't have to solve the system of equations for each output
time sample, as we can later interpolate for the full operator.

** Next:** CONCLUSIONS
** Up:** MIGRATION TO ZERO-OFFSET
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Stanford Exploration Project

12/18/1997