A method for the determination of a local Vp/Vs is described. Given P and S arrival times at a network of stations for a set of local earthquakes, Wadati’s method is generalized to solve for origin times for all the events and for a common P to S velocity ratio. The joint inversion results in a more tightly constrained estimate for Vp/Vs than can be achieved through averaging Vp /Vs values from a set of Wadati diagrams. Applying the method to data from the Sharpsburg, Kentucky, aftershock sequence yields a value for Vp/Vs of 1.70 ± 0.01. In comparison, the estimated error is an order of magnitude larger when Vp/Vs values from a set of Wadati diagrams are averaged. This Vp/Vs value combined with estimated values for Vp ranging from 6.1 to 6.9 km/sec is compatible with an upper crustal composition dominated by granite and basalt.