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In this paper we present a one-dimensional normal-incidence inversion procedure for reflection seismic data. A lossless layered system is considered which is characterized by reflection coefficients and traveltimes. A priori knowledge for the unknown parameters, in the form of statistics, is incorporated into a nonuniform layered system, and a maximum a posteriori estimation procedure is used for the estimation of the system's unknown parameters (i.e., we assume a random reflector model) from noisy and band-limited data. Our solution to the inverse problem includes a downward continuation procedure for estimation of the states of the system. The state sequences are composed of overlapping wavelets. We show that estimation of the unknown parameters of a layer is equivalent to estimation of the amplitude and detection of the time delay of the first wavelet in the upgoing state sequence of the layer. A suboptimal maximum-likelihood deconvolution procedure is employed to perform estimation and detection. The most desirable features of the proposed algorithm are its layer-recursive structure and its ability to process noisy and band-limited data.