Due to the multiple bottom reflections encountered in shallow water environments, the spatial structure of the ambient noise field depends strongly on the geoacoustic properties of the seabed, which are invariant over time scales associated with most measurements. The vertical directionality and coherence are relatively stable features of the noise that are determined primarily by the seabed, rather than temporal variations in the surface source distribution. In this paper, estimates of the compressional and shear wave speeds are determined from ambient noise measurements over shear supporting seabeds. Using a model of wind-generated noise over an elastic seabed, it is shown that the noise is sensitive to the compressional and shear wave speeds in the upper few meters of seabed. An inversion procedure is developed based on a matched field of the complex, broadband coherence from a single hydrophone pair. Using ambient noise data from two shear supporting sites, compressional and shear wave estimates are obtained that are in good agreement with independent surveys. For one site where the bedrock is exposed, a half-space model of the seabed yields reasonable estimates of the seabed parameters. For the other site, the presence of a thin sedimentary layer results in a low estimate from the half-space model. However, when the layer is included in the model, the estimates of the underlying bedrock are in good agreement with a seismic survey.