Stacking velocity for various single-layer models: 1-D stratified layer, 2-D stratified plane dipping layer, and 2-D homogeneous curved layer. Numerical experiments show that a highly stratified medium can lead to a large error in the estimates of the layer thickness if the stratification effect is ignored. This error can be reduced in part by approximating the medium with an elliptically anisotropic one. In the homogeneous but curved layer case, the conventional stacking velocity analysis yields an increased bias in velocity with increasing curvature of the reflecting interface and with increasing local dip of the interface at the normal incidence point. Unless this bias is corrected, the common Dix-type velocity estimation technique can lead to a significant error in the depth estimates.--Modified journal abstract.