We examine the canonical source/Green's function separation problem in the context of teleseismic P wave scattering from receiver-side crust and upper mantle structure. Conventional receiver function analysis affords a leading order approximation to the S component of the Green's function but provides no information on P-to-P scattering. We demonstrate that an improved estimate of the three-dimensional Earth's Green's function, including scattered P contributions, can be achieved through consideration of its theoretical spectral properties. Under conditions typical of the real Earth the P component of the Green's function is shown to be minimum phase. This behavior is responsible for the success of receiver functions in mantle studies. The minimum-phase property is used here to normalize the source signature on P wave seismograms, thereby facilitating implementation of multichannel, multicomponent deconvolution of both Green's function and source signature within the log spectral domain. Examples using both synthetic simulations and seismograms recorded on the Canadian National Seismograph Network illustrate the recovery of accurate and reproducible estimates of the P wave Green's function. Our approach can be adapted to a range of source-receiver configurations. In particular, it may prove useful in the recovery of compressional properties beneath portable, field arrays where calibration is provided by nearby, permanent installations.