We analyze interferometric synthetic aperture radar (InSAR) data acquired between 2004 and 2014, by the ERS-2, Envisat, ALOS and TerraSAR-X/TanDEM-X satellite missions to measure and characterize time-dependent deformation at the Brady Hot Springs geothermal field in western Nevada due to extraction of fluids. The long axis of the ~4 km by ~1.5 km elliptical subsiding area coincides with the strike of the dominant normal fault system at Brady. Within this bowl of subsidence, the interference pattern shows several smaller features with length scales of the order of ~1 km. This signature occurs consistently in all of the well-correlated interferometric pairs spanning several months. Results from inverse modeling suggest that the deformation is a result of volumetric contraction in shallow units, no deeper than 600 m, likely associated with damaged regions where fault segments mechanically interact. Such damaged zones are expected to extend downward along steeply dipping fault planes, providing a high permeability conduit to the production wells. Using time series analysis, we test the hypothesis that geothermal production drives the observed deformation. We find a good correlation between the observed deformation rate and the rate of production in the shallow wells. We also explore mechanisms that could potentially cause the observed deformation, including thermal contraction of rock, decline in pore pressure and dissolution of minerals over time.