The launch of Sentinel-1A/B satellites in 2014 and 2016 marked a pivotal moment in Synthetic Aperture Radar (SAR) technology, ushering in a golden era for SAR. With a revisit time of 6–12 days, these satellites facilitated the acquisition of extensive stacks of high-resolution SAR images, enabling advanced time series analysis. However, processing these stacks posed challenges like interferometric phase degradation and tropospheric phase delay. This study introduces an advanced Small Baseline Subset (SBAS) algorithm that optimizes interferometric pairs, addressing systematic errors through dyadic downsampling and Delaunay Triangulation. A novel statistical framework is developed for elite pixel selection, considering distributed and permanent scatterers, and a tropospheric error correction method using smooth 2D splines effectively identifies and removes error components with fractal-like structures. Beyond geodetic technique advancements, the research explores geological phenomena, detecting five significant slow slip events (SSEs) along the Southern San Andreas Fault using multitemporal SAR interferometric time series from 2015-2021. These SSEs govern aseismic slip dynamics, manifesting as avalanche-like creep rate variations. The study further investigates Managed Aquifer Recharge (MAR) as a nature-engineering-based solution in the Santa Ana Basin. Analyzing surface deformation from 2004 to 2022 demonstrates MAR's effectiveness in curbing land subsidence within Orange County, CA. Additionally, MAR has the potential to stabilize nearby faults by inducing a negative Coulomb stress change. Projecting into the future, a suggested 2% annual increase in recharge volume through 2050 could mitigate land subsidence and reduce seismic hazards in coastal cities vulnerable to relative sea level rise. This integrated approach offers a comprehensive understanding of geological processes and proposes solutions to associated risks. / Doctor of Philosophy / The launch of Sentinel-1A/B satellites in 2014 and 2016 marked a big step forward in radar technology, especially Synthetic Aperture Radar (SAR). These satellites, which revisit the same area every 6-12 days, allowed us to collect many high-quality radar images. This helped us study changes over time in a more advanced way. However, there were challenges in handling all these images, like errors in the radar signals and delays caused by the Earth's atmosphere. We devised a smart algorithm based on the Small Baseline Subset (SBAS) to tackle these challenges. It helps optimize how we use pairs of radar images, reducing errors. We also developed a new method to pick the best pixels in the images and corrected errors caused by the atmosphere using mathematical methods. Moving beyond just technology, our research also looked at interesting Earth events. We found five major slow slip events along the Southern San Andreas Fault by studying radar data from 2015 to 2021. These events are like slow-motion slips along the fault, influencing how the ground moves. We also explored Managed Aquifer Recharge (MAR) as a solution in the Santa Ana Basin. By studying ground movement from 2004 to 2022, we found that MAR helped prevent the land from sinking in Orange County, California. It even has the potential to make nearby faults more stable. Looking ahead, increasing MAR activities by 2% each year until 2050 could protect against land sinking and reduce earthquake risks in coastal cities facing rising sea levels. This combined approach gives us a better understanding of Earth's processes and suggests ways to tackle related problems.