The transverse isotropy (TI) parameters epsilon and delta control amplitude variation with offset (AVO) response at most angles of incidence used in exploration, although the value of delta is not usually known and is difficult to measure. Published measurements on TI materials show that there is a useful empirical correlation between V P /V S and delta . The relationship between delta and V P /V S can be simplified by assuming a linear relationship between C 13 /C 44 and V P /V S . Anellipticity parameter eta also shows a useful empirical correlation with V P /V S . The correlations imply that knowledge of V P /V S is sufficient to make an estimate of the anellipticity of the P-and S-wavefronts in a rock, regardless of the lithology. In this way, the effect of TI on the AVO response of a particular interface may be estimated in the absence of any more accurate data. The empirical relationship indicate that rocks tend to become more anelliptic with increasing V P /V S . Rocks with V P /V S smaller than about 1.8 tend to have zero to small positive values of delta , while rocks with V P /V S larger than around 2 tend to have zero to medium negative delta values. Most previous work has assumed a positive value of delta in shales, but this is not necessarily true. If in fact the delta of a shale is negative (V P /V S is around 2 or higher), and overlies a sandstone, the positive change in delta across the interface could cause a false negative AVO gas indicator. If shale with V P /V S less than 1.8 as measured in organic-rich and overpressured shales, overlies a water-filled sandstone, this could cause a false positive AVO gas indicator. However, if the effect of TI can be estimated, then the chances of success for AVO analysis in correctly predicting the presence of hydrocarbons can be increased.