Shear waves recorded at or near the sea-bed, i.e. a water–sediment interface, may suffer from unwanted phase change, which is detrimental to velocity analysis and processing and degrades the quality of the final stacked or migrated image. In this study, this phenomenon is analysed for P-SV converted waves recorded at the sea-bed. Theoretical analysis shows that phase change does not occur if the converted shear waves always maintain raypaths that lie within the critical angle, provided the subsurface layering is horizontal. A phase change that is asymmetric with offset can readily be explained as being due to dipping layers at targets or the dipping sea-bed. This analysis is extended to multiple layers and anisotropic media and shows that the same conclusions hold. The analysis performed on two sets of ocean-bottom-cable seismic data shows that the majority of observations show little evidence of phase change, and occasionally display the asymmetric phase change with offset. This finding underlines the robustness of converted shear waves for imaging the horizontal subsurfaces and sea-bed as all of the offset information may be used.