Stacked seismic data are modeled as a superposition of simple-interface and thin layer reflections. This parameterization permits a parsimonious blocky model of the impedance. The method is an alternative to the classical least-mean-squared-error approach and is similar in spirit to minimum-entropy deconvolution and sparse-spike inversion, although much different, and simpler, in implementation. A specified number of events on a seismic trace are modeled (inverted) independently. The selected set of basis functions used to represent the data includes a simple interface and a suite of high and low impedance layers covering a range of layer thickness. The simple interface basis function is the seismic wavelet, which is presumed to be known. Each event is classified using a normalized zero-lag crosscorrelation of the basis functions with the seismic trace. Modeled events are prevented from overlapping, thereby ensuring a sparse earth model. Real data results show that a portion of a shallow-marine data set can be well modeled in the context of a sparse earth model. A maximum of 30 simple-interface and thin-layer reflections (per trace) model 65 stacked traces over the time range of 0.8-1.9 s. We use a time and space invariant, statistically derived, autoregressive, seismic wavelet estimate. Wavelet polarity is chosen such that the inversion correctly models the fluid anomaly signals as low impedance layers. For wavelet A, we make the common assumption of white reflectivity and achieve a data misfit that is 7.8 dB down. For wavelet B, we assume a blue reflectivity that has a 3 dB/octave increase with frequency and achieve an improved fit to the data. Wavelet B also produces a more accurate estimate of the layer thickness of a known gas reservoir (10-12 ms average thickness) than does wavelet A (15-17 ms average thickness). Our results are competitive with other approaches to impedance estimation and are obtained in a much simpler fashion.