An iterative procedure to determine lateral variation of 21 elastic parameters from qP wave travel times is proposed. The procedure consists of two steps. In the first step, an isotropic starting model is updated using formulae for weak anisotropy. In this way, 15 qP wave weak anisotropy (WA) parameters are determined. The WA parameters serve as a basis for an estimate of all 21 elastic parameters, which are iteratively updated until the difference between observed and calculated travel times stops to vary. No a priori assumptions about heterogeneity and anisotropy of a model are made except the variation of elastic parameters with respect to spatial coordinates in the model box is assumed to be trilinear.
The procedure is tested on a synthetic multi-azimuthal multiple-source offset VSP experiment. Travel times were picked from noiseless qP wave synthetics generated by sources distributed along 6 profiles itersecting at the mouth of a borehole with receivers. The model considered is vertically inhomogeneous of hexagonal symmetry, with nearly horizontal axis of symmetry. The model may thus simmulate a cracked medium with a slightly tilted system of vertical parallel cracks. The SVD technique is used for solving the system of linear equations resulting from the condition of minimization of the object function. Due to insufficient illumination of the studied structure, the inversion process is surprisingly slow. At least for qP waves, however, it converges to elastic parameters of the true model. In case of qS waves, the resulting phase velocities roughly show a proper angular variation but the phase velocity surfaces based on inverted data have a nearly constant offset from the true surfaces. The experiment shows that a single iteration is insufficient for accurate recovery of the structure.
The paper is available in PostScript (957 kB, colour figures) and GZIPped PostScript (238 kB, colour figures).