In a layered elastic material, density, shear velocity, and compressional velocity can be found at any depth from broadband surface measurements at two distinct, nonzero, precritical values of plane-wave incidence angle. Layer-stripping inversion uses three-component surface velocity measurements generated by a polarized surface source to determine subsurface properties incrementally. The surface velocity measurements initialize a first-order, nonlinear, matrix Riccati equation (derived from the elastic wave equation) which takes advantage of an attractive fixed-point condition in the complex frequency plane to extract subsurface mechanical impedances. Subsurface density and velocities are recovered from the inverted impedances at two or more plane-wave incidence angles. General properties of the matrix Riccati equation in the complex frequency plane aid in incorporating bandwidth constraints. Inversion of synthetic plane wave data from a piece-wise continuous model illustrates inversion effects when only a finite bandwidth is available and when different compressional and shear wavelength distance scales are present.