Coastal Louisiana is affected by sea level rates compounded by subsidence rates, leading to flooding and land loss. Subsidence in the region is caused by natural and anthropogenic processes that vary spatially and temporally across the Gulf of Mexico. Here, we quantify modern vertical and horizontal displacement using InSAR time-series and LiDAR differencing with data spanning between 1999-2020. Our study area is in Baton Rouge (BR), LA. It encompasses two Quaternary faults that cut cemented Pleistocene sediments. We test the ability of these methods to detect millimetric changes in an urban area with extraction and injection wells. Both methods indicate that the footwall of the BR fault has larger subsidence values (InSAR time series x̄=-0.552 to -0.732 mm/y) than the hanging wall of the fault (x̄=1.94 mm/y). LiDAR differencing accurately detects displacement trends, although it can overestimate the displacements. There are areas of uplift that spatially correlate to the locations of injection wells. Our results indicate that subsidence follows the spatial pattern of groundwater level changes proposed by previous studies, suggesting volumetric changes caused by fluid extraction and injection. The correlation of the BR fault zone with the boundary between blocks subsiding at different rates indicates that creep occurs along some sectors of the fault zone at rates of ~3 mm/y, similar to estimates from displaced structures. The creep may be accommodating changes in groundwater level rather than gravity and salt dynamics. The fault zones may be more permeable than surrounding areas, and more susceptible to hydrological and anthropogenic processes.