Weak-anisotropy approximation is used to determine seismic anisotropy of rocks from laboratory measurements of P- and S-wave traveltimes. In the weak-anisotropy approximation, one can invert P-wave traveltimes alone. In such a case, one obtains 15 P-wave weak-anisotropy (WA) parameters, which allow an approximate reconstruction of the P-wave phase-velocity surface. In order to obtain all 21 WA parameters, S-wave traveltimes must also be included in the inversion process. We test both types of inversion, with P-wave data only and with both P- and S-wave data, first on synthetic, then on laboratory data. The proposed inversion procedure is non-iterative, it does not require analysis of the type (phase or ray) of the velocity used. It requires knowledge of S-wave traveltimes only without their association with the polarization.
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