The nuclear events Rulison and Rio Blanco in western Colorado generated short-period Rayleigh waves which traversed numerous paths across North America. Average Rayleigh wave attenuation coefficient values were determined for periods between 5 and 40 s. Large standard deviations for the observed values at periods less than 7 or 8 s and abnormally low values at periods of 12--14 s can be explained by regional variations in the values of the shear wave quality factor. The average Rayleigh wave attenuation coefficient values decrease from about 0.8¿10-3 km-1 at a period of 5 s to very small or negative values at periods of 12--14 s. Roughly constant values of about 0.5¿10-4 km-1 occur at longer periods. At periods of 5 s and less, equalized amplitudes recorded at eastern North American stations are at least 5 times greater than amplitudes recorded at western stations. The disparity in observed amplitudes decreases rapidly with increasing period, and only small differences occur at periods greater than 16 s. A Backus-Gilbert inversion method was developed to determine the contribution of various portions of the crust to the regional variation in attenuation. For purposes of computation the North American continent was assumed to consist of two superprovinces, eastern North America and the North American Cordillera. Qβ-1 values in the upper crust of the cordillera are about twice those in the upper crust of eastern North America. On the other hand, differences in Qβ-1 for the lower crust were much smaller and could be negligible. At periods less than 5 s, amplitudes are strongly attenuated by the presence of a layer of low velocity surface sediments. The smallness of the areas over which western North American earthquakes are felt, compared with the size of such areas in eastern North America for a given maximum intensity, may be entirely explained by this difference in velocity structure. Regional variations in shear wave quality factor do not seem to be directly related to regional temperature variations. Lateral variation of the volume of water in pore spaces within the crust is suggested as an alternative way to explain the attenuation data.