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Inversion of velocity parameters for the walkaway VSP data in a multilayered medium can be impeded by velocity gradients and anisotropy in some layers. A problem occurs if we compare velocities obtained from borehole seismic profiling which are equal to their vertical components with the velocities calculated with paths coming from far offsets where the horizontal component plays an important role, especially when the vertical gradient exists and the ray paths are curve-shaped. In this contribution we present the results of velocity model inversion for VSP data considering velocity gradient and elliptical anisotropy. The algorithm consists of two steps, optimization of velocity parameters and optimization of ray paths for the given model. Both procedures use the Nelder-Mead simplex method which finds local minima. Due to the character of optimization we performed also multistart analysis which can provide information about possible equivalences between parameters. Analysis was conducted for different parameterizations, in some cases allowing introduction of additional parameters: vertical gradient and elliptical anisotropy coefficient. The optimal model for a specific set of data is chosen with the help of Bayesian Information Criterion to balance complexity of model with quality of approximation of traveltimes.

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In this paper, we discuss five parameters that indicate the inhomogeneity of a stack of parallel isotropic layers. We show that, in certain situations, they provide further insight into the intrinsic inhomogeneity of a Backus medium, as compared to the Thomsen parameters. Additionally, we show that the Backus average of isotropic layers is isotropic if and only if γ = 0 . This is in contrast to parameters δ and , whose zero values do not imply isotropy.

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