Repeat-pass Interferometric Synthetic Aperture Radar (InSAR) provides spatially dense maps of surface deformation with potentially tens of millions of data points. Here we estimate the actual covariance structure of noise in InSAR data. We compare the results for several independent interferograms with a large ensemble of GPS observations of tropospheric delay and discuss how the common approaches used during processing of InSAR data affects the inferred covariance structure. Motivated by computational concerns associated with numerical modeling of deformation sources, we then combine the data-covariance information with the inherent resolution of an assumed source model to develop an efficient algorithm for spatially variable data resampling (or averaging). We illustrate these technical developments with two earthquake scenarios at different ends of the earthquake magnitude spectrum. For the larger events, our goal is to invert for the coseismic fault slip distribution. For smaller events, we infer the hypocenter location and moment. We compare the results of inversions using several different resampling algorithms, and we assess the importance of using the full noise covariance matrix.