Before geodetically derived strain and rotation rates can be robustly compared to geological or seismological observations, we need reliable strain rate uncertainties. Various methods exist to compute strain rates from GNSS-derived interseismic velocities, but a realistic representation of interpolation uncertainties has remained a challenge. The main problem is that commonly used deterministic interpolation methods do not account for uncertainty resulting from the absence of information in between observation sites. We apply stochastic interpolation by means of ordinary kriging to propagate errors both from discontinuous data coverage as well as from observation uncertainties to our strain rate estimates. However, interseismic horizontal surface velocities in tectonically active regions are spatially highly non-stationary, with high spatial variability around active faults and lower velocity variability in tectonically more stable regions. This requires an extension of traditional ordinary kriging approaches. For interpolation uncertainties that reflect the local variability and spatial correlation of the observed surface velocities, we apply a novel method that incorporates the spatially variable statistics of the underlying data. We estimate realistic uncertainties and covariances of the interpolated velocity field. For regions with a high spatial velocity variability, we find a large increase in uncertainty with increasing distance from observation sites, while in areas with little spatial variability, we estimate a small increase in uncertainty with distance. Subsequently, we propagate interpolated velocity covariance to strain rate uncertainties, such that we can assess the statistical significance of the interpolated strain rate field. Applied to a number of actively deforming regions, including the Pacific coast of North America and Japan, we show to what degree we can robustly determine strain rates based on available GNSS-derived velocities. Realistic uncertainties assist the community to better discriminate continuous or localized deformation on active faults from the available geodetic data.@en

We aim to better understand the overriding plate deformation during the megathrust earthquake cycle. We estimate the spatial patterns of interseismic GNSS velocities in South America, Southeast Asia and northern Japan and the associated uncertainties due to variations in network density and observation uncertainties. Interseismic velocities with respect to the overriding plate generally decrease with distance from the trench with a steep gradient up to a ‘hurdle’, beyond which the gradient is distinctly lower and velocities are small. The hurdle is located 500–1000 km away from the trench for the trench-perpendicular velocity component, and either at the same distance or closer for the trench-parallel component. Significant coseismic displacements were observed beyond these hurdles during the 2010 Maule, 2004 Sumatra–Andaman, and 2011 Tohoku earthquakes. We hypothesize that both the interseismic hurdle and the coseismic response result from a mechanical contrast in the overriding plate. We test our hypothesis using physically consistent, generic, 3-D finite element models of the earthquake cycle. Our models show a response similar to the interseismic and coseismic observations for a compliant near-trench overriding plate and an at least five times stiffer overriding plate beyond the contrast. The model results suggest that hurdles are more prominently expressed in observations near strongly locked megathrusts. Previous studies inferred major tectonic or geological boundaries and seismological contrasts located close to the observed hurdles in the studied overriding plates. The compliance contrast probably results from thermal, compositional and thickness contrasts and might cause the observed focusing of smaller-scale deformation like backthrusting.@en

Geodetic observations of vertical land motion following a megathrust earthquake are key to a better understanding of processes and parameters controlling the dynamics at subduction margins. The relative contributions of dominant drivers during the postseismic phase, such as viscoelastic relaxation, afterslip and relocking, remain difficult to estimate individually and are often derived at the end of an observation period. Data assimilation can provide the means to estimate model parameters by combining physical models with observations whilst taking their uncertainties into account. We use Bayesian inference in the form of an ensemble smoother to estimate geodynamic parameters during the postseismic phase of the megathrust earthquake cycle. The ensemble smoother uses a Monte Carlo approach to represent the probability density distribution (pdf) of model states with a finite number of realizations. Prior estimates of the imperfect physical model are combined with the likelihood of noisy observations to estimate the posterior pdf of model parameters. We discuss a synthetic data experiment where observations are sampled from a 3D finite element model with noise added to represent errors in the data. With a smoother, observations at all time steps are assimilated in one go, to ensure consistency between estimated parameters and model outputs. We assimilate vertical and horizontal surface displacements into a 2D finite element viscoelastic earthquake cycle model with a power-law rheology. We incorporate heterogeneity into the viscoelastic structure and estimate the viscosity field based on a heterogeneous temperature field and experimental flow laws. Preliminary results show that model parameters, such as the extent of the cold nose, maximum depth of afterslip and flow law parameters can be recovered remarkably well by assimilating synthetic on- and offshore surface observations. We will apply the smoother to postseismic surface displacements of the Tohoku 2011 earthquake to estimate model parameters and driving processes across spatio-temporal domains.@en

In Southeast Alaska, extreme uplift rates are primarily caused by glacial isostatic adjustment (GIA), as a result of ice thickness changes from the Little Ice Age to the present combined with a low-viscosity asthenosphere. Previous GIA models adopted a 1-D Earth structure. However, the actual Earth structure is likely more complex due to the long history of subduction and tectonism and the transition from a continental to an oceanic plate. Seismic evidence indeed shows a laterally heterogenous Earth structure. In this study, a numeral model is constructed for Southeast Alaska, which allows for the inclusion of lateral viscosity variations. The viscosity follows from scaling relationships between seismic velocity anomalies and viscosity variations. We use this scaling relationship to constrain the thermal effect on seismic variations and investigate the importance of lateral viscosity variations. We find that a thermal contribution to seismic anomalies of 10% is required to explain the GIA observations. This implies that non-thermal effects control seismic anomaly variations in the shallow upper mantle. Due to the regional geologic history, it is likely that hydration of the mantle impact both viscosity and seismic velocity. The best-fit model has a background viscosity of 5.0 × 10¹⁹ Pa-s, and viscosities at ∼80 km depth range from 1.8 × 10¹⁹ to 4.5 × 10¹⁹ Pa-s. A 1-D averaged version of the 3-D model performed slightly better, however, the two models were statistically equivalent within a 2σ measurement uncertainty. Thus, lateral viscosity variations do not contribute significantly to the uplift rates measured with the current accuracy and distribution of sites.

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