We describe a method for measuring the integrated Comptonization (YSZ) of clusters of galaxies from measurements of the Sunyaev-Zeldovich (SZ) effect in multiple frequency bands and use this method to characterize a sample of galaxy clusters detected in South Pole Telescope (SPT) data. We test this method on simulated cluster observations and verify that it can accurately recover cluster parameters with negligible bias. In realistic simulations of an SPT-like survey, with realizations of cosmic microwave background anisotropy, point sources, and atmosphere and instrumental noise at typical SPT-SZ survey levels, we find that YSZ is most accurately determined in an aperture comparable to the SPT beam size. We demonstrate the utility of this method to measure YSZ and to constrain mass scaling relations using X-ray mass estimates for a sample of 18 galaxy clusters from the SPT-SZ survey. Measuring YSZ within a 0.75 radius aperture, we find an intrinsic log-normal scatter of 21+/-11% in YSZ at a fixed mass. Measuring YSZ within a 0.3 Mpc projected radius (equivalent to 0.75 at the survey median redshift z = 0.6), we find a scatter of 26+/-9%. Prior to this study, the SPT observable found to have the lowest scatter with mass was cluster detection significance. We demonstrate, from both simulations and SPT observed clusters, that YSZ measured within an aperture comparable to the SPT beam size is equivalent, in terms of scatter with cluster mass, to SPT cluster detection significance.
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