Summary Geodetic measurements of ground deformation are crucial to identifying and interpreting geophysical processes. We develop a method to fuse data streams from multiple geodetic techniques into a single, three-component deformation field with quantified uncertainties, and without invoking a geophysical model. The fusion is formulated as a semi-parametric latent factor model: a linear mapping ties each observation to the underlying 3-D displacement, while the displacement components are represented nonparametrically with multi-output Gaussian process priors. To achieve practical performance at regional scale, we deploy two complementary sparse GP engines: an Informative Vector Machine (IVM) that selects a small, most-informative active set for fast subset-of-data inference, and a Sparse Variational GP (SVGP) that summarizes the full dataset with inducing points and optimizes a global variational bound. Together, these reduce the scaling of the computation to near-linear in data size and cubic only in the active/inducing set, enabling the potential of fusion of dense geodetic data while maintaining rigorous uncertainty quantification. We demonstrate the approach on coseismic deformation from the 2020 Sparta, NC, USA and 2016 Meinong, Taiwan earthquakes, fusing interferometric synthetic aperture radar (InSAR) with either light detection and ranging (LiDAR) or global navigation satellite system (GNSS) data, respectively. The fused solutions show marked improvements in the precision and coherence of the resolved deformation field and deliver robust, spatially explicit uncertainty estimates. The methodology is readily extensible to time-varying observations to produce four-dimensional (space-time) deformation fields, offering a scalable path to richer characterization of transient geophysical phenomena.
Szymanski et al. (Thu,) studied this question.