A ray tracing algorithm for first arrival travel times from zero-offset borehole radar is coupled with an analytical solution to the one dimensional unsaturated water flow equation with a constant flux top boundary condition to invert for soil hydraulic properties. The analytical solution for Richards' equation relies on a non dimensional form of Burger's equation using a Broadbridge and White (BW) soil. The BW soil is described with three parameters: saturated hydraulic conductivity (K s), sorptivity (S), and a dimensionless parameter (C). The ray tracing algorithm makes use of the the arrival time of first arriving waves (direct or critically refracted) to track the wetting front through the subsurface during infiltration. From the time series of first arrival travel time data collected from one depth, the K s can be determined, provided that the wetting front was sharp enough to cause critical refraction at its edge. To determine the other parameters uniquely, co-located pressure head data is needed from the dry range.