We have developed a case study of amplitude variation with azimuth (AVAZ) analysis applied to quantify the amount of the azimuthal anisotropy present in the Lower Paleozoic shales of the Baltic Basin (northern Poland). The challenges encountered here are related to thin (up to 25 m) deeply buried (approximately 3 km) targets, characterized by a weak average azimuthal anisotropy (1%–2% from cross-dipole sonic data). Synthetic AVAZ modeling confirms the applicability of the method. We used data after full-azimuth angle-domain prestack depth migration (PSDM) processed by a contractor and in-house sectored prestack time migration (PSTM). Application of AVAZ on full-azimuth PSDM data provided results that were further corroborated by the available calibration data. Anisotropy azimuths from AVAZ correlate with natural fracture direction from image logs (x-tended range microimager [XRMI]) interpretation, especially at the wells with only one dominant fracture system present. Fracture strikes inferred from AVAZ also correspond with fracture strikes inverted from the microseismic S-wave splitting analysis. Hudson’s crack densities calculated from the AVAZ anisotropic gradients matched crack densities from cross-dipole sonic as well as followed the same trend as the fracture intensities from XRMI data. Part of the success in this case should be attributed to the high-end processing of the input data because such obvious correlations are absent for AVAZ results on sectored PSTM data.