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The time-dependent Mueller matrix solution of vector radiative transfer for stratified random media of nonspherical scatterers is presented. Copolarized and cross-polarized bistatic scattering for a polarized pulse incidence are numerically simulated. Numerical results well demonstrate volumetric and surface scattering mechanism and depict the fraction distribution of random scatterers of stratified random media. The peak tails in polarized echoes due to wave reflections from the underlying surface can be identified. Its copolarized peaks in the specular direction are employed for simultaneous retrievals of the underlying surface roughness and moisture with the presence of stratified vegetation canopy.