The weighted-average-based position (244) in the temporal domain is computed based on the sampling of shear wave displacement (226) along the propagation path. The weighting is, for example, by displacement observed at times (230) corresponding to sampling and represents the time of arrival of the shear wave at the shear-wave propagation path location being sampled. In some embodiments, the computed shear-wave times of arrival at respective locations are functionally related to known inter-location distances (250) to derive shear-wave group velocity. The derived velocity can serve as input into known algorithms for estimating shear elasticity of the medium, such as body tissue, for purposes of clinical diagnosis and therapy assessment.