References

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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.