Presentation: Joint Interpolation of 3-component GPS Velocities Constrained by Elasticity
Vertical ground motion at fault systems can be difficult to detect due to their small amplitude and contamination from non-tectonic sources, such as ground water loading. However, it may play an important role in our understanding of the earthquake cycle and the associated seismic hazards. Ground motion measurements from GPS are often sparse and must be interpolated onto a regular grid (e.g., for computing strain rate), ideally taking into account the varying degrees of uncertainty of the data. Traditionally, each vector component is interpolated separately using minimum curvature or biharmonic spline methods. Recently, a joint interpolation of the two horizontal components has been developed using the Green's functions for a point force deforming a thin elastic sheet. The elasticity constraints provide a coupling between the two vector components and lead to improved results because the underlying physics of the method approximately matches that of the GPS observations. We propose an expansion of this method into 3D in order to incorporate vertical GPS velocity measurements. To smooth the model and avoid singularities, we formulate the interpolation as a weighted least-squares inverse problem with damping regularization. Optimal values of the regularization parameter and the Poisson's ratio of the elastic medium are determined through K-fold cross-validation, a technique often used in machine learning for model selection. Additionally, the cross-validation provides a measure of the accuracy of model predictions and eliminates the need for manual configuration. The computational load of the inversion is lessened by imposing a cutoff distance to the Green's functions computations, which makes the sensitivity matrix sparse. We will present preliminary results from an application to EarthScope GPS data from the San Andreas Fault system. In the future, we aim to develop a joint inversion of 3D GPS and InSAR line-of-sight velocities to improve data coverage.