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The effect of dispersion on the morphology of impulsive acoustic radiation force induced shear waves propagating in viscoelastic (VE) media is investigated. Change in shear wave morphology was quantified by calculating its spatial coherence. The magnitude of the slope of the spatial coherence as a function of propagation distance, or decorrelation rate, was used to compare the VE behavior of different materials. Shear waves in VE media with a range of material properties were simulated using Finite Element Method (FEM) models and a three parameter standard linear solid model of viscoelasticity. Shear wave decorrelation rate increased with the amount of stress relaxation occurring within the temporal extent of the shear wave. Shear wave decorrelation rate can therefore be used to discriminate ranges of VE behavior. In experimental data collected using a modified Siemens AntaresTM scanner, the shear wave decorrelation rate was significantly higher for a VE phantom than one constructed of an elastic material. In preliminary in vivo human liver data, shear wave decorrelation was found to be present and variable among different patients. The relationship between liver viscosity as quantified by shear wave spatial coherence and disease states is being investigated.