GNSS-Based Kinematic Reference Frames: The ADELA Model for Subduction Zones

GNSS reference frames in high-seismicity regions struggle to accurately represent nonlinear crustal deformation, as traditional linear velocity models fail to account for post-seismic transients. This research presents ADELA (Analysis of DEformation beyond Los Andes), a kinematic framework engineered to model complex surface displacements in subduction zones. We analyzed time series from 874 GNSS stations across South America (SIRGAS-CON and REDGEOMIN networks) from 2009-2024, including 12 major earthquakes (Mw \((\geq)\) 7.0). Our methodology applies parametric modeling to GNSS trajectories, combining secular trends, seasonal signals, and co-seismic/post-seismic components using logarithmic and exponential functions. We spatially interpolated the resulting coordinates through Kriging, Thin Plate Spline (TPS), and Cubic Spline techniques to produce a continuous deformation field. Comparisons with the linear VEMOS model showed that ADELA reduced RMSE by 38-45% in seismically active areas, maintaining millimeter-level precision during post-seismic phases. Euler pole analysis across VEMOS realizations (2009-2022) exposed rotational inconsistencies above 0.15°/Myr within identical geographic domains, confirming systematic limitations of linear approaches. ADELA offers a complementary framework for maintaining kinematic reference frames in complex geodynamics settings, supporting infrastructure monitoring, precise navigation, and tectonic research. This methodology advances GNSS applications in global subduction zones and can be adapted to any region experiencing nonlinear crustal deformation.