Improving deformation models by discounting transient signals in geodetic data: 1. Concept and synthetic examples

GPS geodesy provides very precise velocities of benchmarks on decadal timescales, and geodesists often describe their uncertainties with a velocity covariance matrix. However, those who model neotectonic deformation to estimate long‐term seismic hazard want constraints on the interseismic velocities of stable bedrock on multithousand‐year timescales. When the former (available data) are used as proxies for the latter (desired constraints), it is necessary to increase uncertainties to characterize a variety of transient and/or surficial noise processes, including magma chamber recharge, postseismic relaxation, pore fluid motion, extremely slow landsliding, and glacial isostatic adjustment. The effects of transient noise on distant reference benchmarks also add to uncertainty of the long‐term velocity reference frame. We augment the reported velocity covariance matrix with transpose products of velocity perturbation vectors from simple models approximately describing anticipated transient and surficial noise sources. No artifacts are introduced by this method because the velocity‐vector data are unchanged. When the inverse of the augmented covariance matrix (the “diminished normal matrix”) is used in the objective function of a neotectonic deformation model partially driven by GPS data, the perturbing effects of transient and surficial signals are greatly reduced. Improvement occurs even when the prior estimates of noise processes are rather crude. We present two examples computed with synthetic data.