Surface generated ambient noise can be used to infer sediment properties. Here, a passive geoacoustic inversion method that uses noise recorded by a drifting vertical array is adopted. The array is steered using beamforming to compute the noise arriving at the array from various directions. This information is used in two different ways: Coherently (cross-correlation of upward/downward propagating noise using a minimum variance distortionless response fathometer), and incoherently (bottom loss vs frequency and angle using a conventional beamformer) to obtain the bottom properties. Compressive sensing is used to invert for the number of sediment layer interfaces and their depths using coherent passive fathometry. Then the incoherent bottom loss estimate is used to refine the sediment thickness, sound speed, density, and attenuation values. Compressive sensing fathometry enables automatic determination of the number of interfaces. It also tightens the sediment thickness priors for the incoherent bottom loss inversion which reduces the search space. The method is demonstrated on drifting array data collected during the Boundary 2003 experiment.