72. Bird, P., and M. M. C. Carafa: Improving deformation
models by discounting transient signals in geodetic data, 1: Concept and
synthetic examples, *J. Geophys. Res., 121*(7), 5538-5556, doi:
10.1002/2016JB013056.

**Abstract**. 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
multi-thousand-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.