A nonlinear waveform inversion procedure derived from Tarantola and Valette's inversion formalism has been implemented in the horizontal slowness and intercept time (p-tau ) domain. It infers simultaneously the velocity (bulk modulus) and density profiles of layered acoustic media. An arbitrary partition of the full wavefield information, i.e., an arbitrary selection of traces (and time ranges) of the whole p-tau seismic section is used as input to the inversion procedure. To explore its applicability and limitations, the algorithm has been tested against a series of 'noise-free' and noisy minimum-phase band-limited p-tau data sets synthesized from models of many microlayers which are meant to emulate the behavior of well logs.For a given data covariance, we confirmed that the specification of the starting model covariance determines the 'generalized' damping factor which predicts the resolution of the final inverted model and the convergence rate of the inversion procedure. We found three major obstacles in this type of inversion: underparameterization of the model space with fixed thickness, large variation in material properties of the model, and lack of low-wavenumber information from observed seismic signals. Underparameterization of the model space introduces substantial noise and artifacts into an inversion procedure, and large variations in material properties cause severe multiples which cause strong nonlinearity in an inversion. For multichannel seismic reflection data, the best low-wavenumber information for the model is provided by the moveout of the signals. A well-estimated starting model from any available source helps in stabilizing the inversion in two aspects; it provides necessary low-wavenumber information to reconstruct the correct model profiles, and it reduces the magnitude of model parameter perturbations (with respect to the starting model) to suppress the strong nonlinearity. With proper inversion parameters, using limited data traces (less than 15 p values), the procedure is capable of reconstructing the velocity and density profiles simultaneously and satisfactorily.