Q estimates are made from in situ measurements of energy loss per cycle from transmitted P and S waves, as a function of frequency, for data from active-source experiments. Assuming that intrinsic Q is frequency-independent and scattering Q is frequency-dependent over the frequencies of interest, the relative contributions of each, to a total observed Q, are estimated. Test examples are produced by computing viscoelastic synthetic seismograms using a pseudospectral solution with inclusion of relaxation mechanisms (for intrinsic Q) and a fractal distribution of scatterers (for scattering Q). The composite theory implies that when the total Q for S waves is smaller than that for P waves, intrinsic Q is dominant; when it is larger, scattering Q is dominant. In the inverse problem, performed by a global least squares search, intrinsic Q estimates are reliable as long as their values are sufficiently low so that their effects are measurable in the data. Estimates of scattering Q parameters are most reliable if the frequency bandwidth of the data corresponds to wavelengths both larger and smaller than the dominant scatterer size, and the estimates exhibit nonuniqueness if all the data are on one side or the other. In situ measurements are made from small-scale linear array data from the North Sea, the New Madrid seismic zone, Turkey, and north Texas. All provide internally consistent and geologically reasonable results. For the P waves in all four data sets, intrinsic and scattering contributions are of approximately the same importance; for S waves the intrinsic contributions dominate. ¿ American Geophysical Union 1994