We have estimated P-wave and S-wave anelastic attenuation coefficients for the thick, unconsolidated sediments of the Mississippi embayment, central United States, using the spectral distance decay of explosion P and Rayleigh waves. The sediment-trapped P wave, P_sed, is observed to ranges of 80 km at 10 Hz, and 1-Hz Rayleigh waves are observed out to 130 km from a 5000-lb borehole explosion in the northern part of the embayment. Rayleigh waves of 4 Hz are seen to distances of 3 km from a smaller 50-lb explosion. Analysis of the group velocity and amplitude-distance decay of both waves yields an average Q_s of 100 and Q_p of 200 for embayment sediments that are independent of frequency. Scatter in the Q estimates comes from interference of multiple P-wave reverberations and Rayleigh-wave modes. The attenuation model is self-consistent in that it is the same as obtained by the analysis of synthetic seismograms using the inferred Q-values. Inferred Q_p and Q_s values are more than three times higher than previous estimates and imply that unconsolidated sediments of the embayment do not significantly attenuate small-strain earthquake ground motions. These estimates represent a lower bound to Q of the sediments since significant scattering is observed in the waveform data that contributes to the distance decay of wave amplitude. Higher Q values also imply that the unconsolidated sediments of the embayment will form an efficient wave guide for surface waves radiated from shallow earthquakes or large earthquakes that rupture into the sediments, producing high-amplitude, long-duration wave trains that should be considered in earthquake hazard assessments.