We explore the use of elastic Green’s functions in inversions of one-dimensional Interferometric Synthetic Aperture Radar (InSAR) observations to recover three-dimensional displacement fields. This approach enforces coupling of the horizontal displacements and limits the need for prior assumptions about the subsurface sources, driving the deformation or explicit damping of a given dimension of the full 3D deformation field. We apply these methods to data from the Coachella Valley, California, where artificial groundwater recharge in 2017 and the associated increases in pore pressure resulted in ground displacements of up to 12 cm. This area is covered by Sentinel-1a/b data for two overlapping paths from both ascending and descending orbits, as well as an east-west flight line from the Uninhabited Aerial Vehicle Synthetic Aperture Radar (UAVSAR), providing five unique line-of-sight geometries. The regularization approaches applied to the Sentinel data alone agree in most respects, with the elastically coupled approach producing a slightly better fit to the independent UAVSAR observations. Our results suggest that the 2017 groundwater entrainment in the Coachella Valley is likely associated with significant horizontal displacements that led to contraction across the fault bounding the northern side of the basin, as well as increases in right-lateral sense of strain in some areas along the fault.