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The main papers discussing aspects of solving the FEAVO problem are
Kjartansson (1979), Woodward (1987),
Claerbout (1993), Bevc (1994), and
Harlan (1994). All are iterative inversions that try to find
the velocity model that will result in the given raw data.
With the exception of Harlan (1994),
this operator is some form of plane-wave decomposition
using a straight-ray assumption; none uses an actual differential
(``wave-equation'') operator.
Woodward (1987) applies corrections in order to account
for differences between infinite-frequency rays and the ``fat rays''
associated with the physics of wave propagation.
All of them, with the exception of Harlan (1994),
invert either for the traveltime effects associated with AVO, or for
the amplitudes, but not for both simultaneously.
None of the previous attempts is completely successful in producing a velocity
model that satisfies the initial goals of the problem.
Using only a
two-dimensional midpoint-offset map of FEAVO effects, instead of
recognizing that they correlate across depth (as equation
3 and Figure
9 show), they introduced too many degrees of freedom
in the inversions. Considering only straight rays
was incorrect even in the case of the universally encountered v(z)
variation.
All methods require some form of picking, which results in endless
headaches. None makes successful use of the entire quantity of information by
simultaneously considering both the traveltimes and the amplitudes for
all the reflectors. Only one Harlan (1994) incorporates the
information given by standard velocity analysis (which is not
significantly affected by FEAVO effects).

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Stanford Exploration Project

11/11/2002