We have developed a method of nonstationary sparse reflectivity inversion (NSRI) that directly retrieves the reflectivity series from nonstationary seismic data without the intrinsic instability associated with inverse filtering methods. We have investigated the NSRI performance in the presence of input error (e.g., the phase shift and the peak frequency of the wavelet), which determined that NSRI results are reasonable in the case of moderate error. NSRI was then applied to data collected from a laboratory physical model made of highly attenuating media, for which true reflectivities were known, but the wave propagation and the filtering mechanism were not. Analysis of data from the physical model, therefore, represented a blind test for evaluating the effectiveness and accuracy of NSRI. The physical model had a specified spatial scale of 1:5000 (relative to the field scale) and an approximate 1:1 velocity scale. Because the input is required by NSRI, attenuation of the P-wave was measured in the laboratory at ultrasonic frequencies with a pulse transmission technique and the spectral ratio method. Although multiples, side reflections from the model boundaries, diffractions, and other event types were clearly observed from the raw data, no preprocessing was done to avoid affecting the filtering effects. Results from the physical modeling data demonstrated that the derived formula for an attenuated seismogram was correct and estimated values were reliable. The functions and advantages of NSRI were confirmed. The compensated seismogram generated by NSRI was superior to that generated using gain-limited inverse filtering. We have also investigated NSRI’s capabilities in analyzing a marine data set from the Gulf of Suez. These examples provided a basis for discussing assumptions and limitations of NSRI.