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LOCAL SNELL PARAMETER, AND PROPAGATION DIRECTION.

Inversion methods which use the directional dependence of the reflection
coefficient to estimate the elastic parameters of the medium (AVO inversion)
use in general an angular functionality to express such a dependence.
This choice is not always convenient because the angle estimation
may be strongly dependent on the macro model that was used in the estimation
process. Moreover, the propagation angles are affected by the elastic
perturbations that one wishes to estimate, using the angular dependence
of the reflectivities. I claim that a more appropriate choice for expressing
the directional dependence of the reflection coefficient is the *local
Snell parameter*, which is defined as the component of the slowness
parallel to the ``local reflector plane" at each position of the subsurface.
Evidently, not all points of the subsurface can be considered
as a reflector, but at all points of interest, where the
the upcoming wavefronts intercept the downgoing wavefront, a ``reflector
plane" can be defined. As defined, the local Snell parameter is conserved
for first order perturbations in the local elastic parameters. Although
its estimated value will be still dependent on the macro model, it will
be much less sensitive to errors in the model than the angle of incidence.

11/18/1997