Near-surface properties play an important role in advancing earthquake hazard assessment. Other areas where near-surface properties are crucial include civil engineering and detection and delineation of potable groundwater. From an exploration point of view, near-surface properties are needed for wavefield separation and correcting for the local near-receiver structure. It has been shown that these properties can be estimated for a lossless homogeneous medium using the propagator matrix. To estimate the near-surface properties, we apply deconvolution to passive borehole recordings of waves excited by an earthquake. Deconvolution of these incoherent waveforms recorded by the sensors at different depths in the borehole with the recording at the surface results in waves that propagate upwards and downwards along the array. These waves, obtained by deconvolution, can be used to estimate the P- and S-wave velocities near the surface. As opposed to waves obtained by cross-correlation that represent filtered version of the sum of causal and acausal Green's function between the two receivers, the waves obtained by deconvolution represent the elements of the propagator matrix. Finally, we show analytically the extension of the propagator matrix analysis to a lossy layered medium for a special case of normal incidence. ?? 2007 The Authors Journal compilation ?? 2007 RAS.