We present an inversion scheme allowing estimates of the thickness of a layer and its parameters from traveltimes of the wave reflected from the bottom of the layer. We concentrate on unconverted P wave reflected in a homogeneous layer of arbitrary anisotropy symmetry and orientation. The inversion scheme is based on the approximate travel-time formula derived under the assumption of weak anisotropy. For the description of anisotropy, the so-called A-parameters, which represent an alternative to standard elastic moduli specifying anisotropic media, are used. Nine of fifteen P-wave A-parameters, which describe P-wave propagation in weak-anisotropy approximation, can be determined. The thickness of the layer may be either a sought or known quantity. If an additional information about the orientation of symmetry elements is available for higher-symmetry anisotropy, the corresponding phase-velocity surface can be reconstructed. Synthetic tests indicate that the inversion scheme works very well for weak anisotropy (less than 10%), yields reasonable results even for anisotropy stronger than 20%. The scheme has tendency to overestimate the thickness of the layer if it is a sought parameter.
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