It is shown that the density and bulk modulus profiles of a layered fluid half-space are uniquely determined from the vertical component of the particle velocity on the surface due to an impulsive point source on the surface. In addition, an estimate of the highest acoustic wave velocity in the layered half-space is required as well. The necessary conditions for the existence of the solution are discussed and a direct (noniterative) inversion algorithm is developed which constructs the density and bulk modulus profiles of the half-space from the surface data. The main limitations of this theory to real seismic data are briefly discussed.