Acoustic propagation in an ocean surface duct is computed using Feynmann path integral techniques. The surface duct index of refraction, n = c0/c(z), is modeled by a quartic anharmonic-oscillator potential, n2 = aq2 + bq4, with a pressure release boundary condition at the surface. A closed form expression for the acoustic pressure field is obtained for all values of the coupling parameter b and which implicitly includes all virtual and continuum modes.