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The anisotropy of an equivalent medium resulting from the Backus (1962)average is induced by the vertical inhomogeneity among its constituent layers.The velocity field of the constituent isotropic layers increases linearly withdepth, which is assumed to be a good seismological description of sedimentarylayers Slotnick (1959). We derive an analytical relationship between theanisotropy, characterized by the Thomsen (1986) parameters, and the linearinhomogeneity parameters, which forms a system of three equations for nineunknowns. To obtain well-posedness, we constrain the problem by considering twoseismological methods applied to field data. We use the results from the twomethods, for a particular region of interest, to assess the validity of theanalytical relation.

On relations of anisotropy and linear inhomogeneity using Backus average