The envelopes of high-frequency seismograms from earthquakes in New York State, South Africa, and southern California are analyzed to determine how much of the observed attenuation of shear waves in the crust is caused by anelasticity and how much is produced by scattering from small-scale heterogeneities. For seismograms from New York and South Africa, there is a systematic enrichment of high-frequency energy that develops in the coda relative to the direct S or Lg waves. This enrichment of high frequencies in the coda grows larger with increasing source-receiver distance. This implies that high-frequency energy is scattered from the direct wave into the coda as the shear wave propagates in the crust. I use the growth with source-receiver distance of the high-frequency energy in the coda relative to the direct wave to estimate the scattering attenuation of the crust. For seismograms from New York, it is consistently observed that the time decay of high-frequency energy in the coda, when compared to the low-frequency coda decay, is less than the relative decay of high-frequency energy with travel time in the Lg wave. These observations supports the idea that the time decay of the coda is controlled mainly by the anelastic attenuation and is insensitive to the energy flux model. I use the relative time decay of high-frequency energy in the coda to determine the anelastic attenuation. This analysis indicates that the observed attenuation of 15-Hz Lg waves in New York State (Δ=100--400 km) is caused about equally by scattering and anelasticity.

Using the estimate of Lg wave Q as a constraint, I find that the scattering Q in the crust of New York is either independent of frequency or increases with frequency f slower than f0.3. This implies that the one-dimensional power spectrum of spatial velocity variations in the crust of New York decays with increasing wavenumber k more slowly than k-1.3, for length scales of about 0.2 to 1 km. A similar analysis for South Africa indicates that scattering is the major cause of the observed S wave attenuation of high-frequency energy (30 Hz) at local distances (<100 km). For southern California, the extent of the scattering attenuation is unclear from the data, although the relatively steep coda decay of southern California implies that the anelastic attenuation is stronger there than in New York or South Africa. At 3 Hz, the coda decays for lapse times of 10--45 s are similar to the decay of S wave amplitudes with travel time for the three regions. However, the 30-Hz coda decays are susbstantially less than the 30-Hz S wave decays with travel time, producing coda Q values that are much higher than the S wave Q in each area. For southern California and New York State, the 3-Hz coda Q taken from the late coda (50--110 s) is comparable to the Lg wave Q. However, the 3-Hz coda Q for South Africa over these lapse times is about 5 times the estimated Lg wave Q. For all three areas, the frequency dependence of the coda Q does not match the frequency dependence of the S wave Q, and for New York and South Africa, it changes with lapse time.