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 data gaps and velocity uncertainties. The 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, three-dimensional 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 5 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.

Geodetic data provide an opportunity to improve our understanding of the processes and parameters controlling the dynamics of deformation during the earthquake cycle at subduction zones. However, the observations contain noise and are temporally and spatially sparse, whereas dynamical models are unequivocally imperfect. Also, the relative contributions from various drivers of surface deformation are poorly constrained by independent observations. Some drivers may be static or vary slowly in time (e.g., plate motion), whilst others vary significantly during the earthquake cycle (e.g., viscoelastic relaxation). Data assimilation combines prior estimates of dynamical models, with the likelihood of observations into posterior estimates of the state evolution and time-independent parameters of a physical process. We explore the usefulness of data assimilation by using a particle filter to estimate the (spatially variable) elastic thickness of the overriding plate and the extent of the locked zone. We assimilate vertical interseismic surface displacements into a 2D elastic flexural model. The particle filter uses a Monte Carlo approach to represent the state probability distribution by a finite number of realizations (“particles”). We use sequential importance resampling to preserve particles statistically close to the observations and duplicate and perturb them. Synthetic experiments demonstrate that the particle filter effectively estimates 1D elastic thickness from synthetic observations. However, elastic thickness estimates for models with a landward increase in plate thickness show larger uncertainty near the coast as the sensitivity of surface displacements reduces with increasing plate thickness. Interestingly, the effectiveness of the elastic thickness estimation is highly sensitive to network aperture, including GPS/A. Assimilation of interseismic vertical velocities prior to the 2011 Tohoku-Oki earthquake yields estimates of upper plate thickness that agree with previous studies. However, results of the locked zone extent are not as expected, which could be due to missing physics in the relatively conceptual model. These results demonstrate the potential of the particle filter to better understand the geodynamic process parameters of the earthquake cycle at subduction zones.

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 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 5.0×10^19 Pa-s, and viscosities at ~80 km depth range from 1.8×10^19 to 4.5×10^19 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.

We aim to better understand the spatial distribution of interseismic overriding plate deformation at and near subduction zones. To this end, we analyze horizontal GNSS velocities in South America, southeast Asia, and northern Japan, computing and interpolating local trench-normal and -parallel velocity components. Velocities 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 near-zero. The hurdle is located 500–1000 km away from the trench for the trench-perpendicular component and either at the same distance or closer for the trench-parallel. In contrast, significant displacements during large megathrust earthquakes are generally observed beyond the hurdle. To test our hypothesis that the hurdle results from a lateral contrast in overriding plate compliance, we use cyclic three-dimensional finite element models . Our results are consistent with the observed interseismic velocity gradients and far-field coseismic displacement. The gradient in modeled trench-perpendicular velocities depends on the location of the contrast and on the plate compliance on both sides. Trench-parallel velocities have a progressively shallower gradient with distance from the trench and only depend on the near-trench modulus. The inferred contrast probably results from thermal, compositional and thickness contrasts. This interpretation is consistent with the presence, close to the observed hurdle, of major tectonic or geological boundaries separating the plate margin from a distinct, and likely less compliant, plate interior. Stress accumulation on the model’s locked megathrust patches is hardly affected by the distance to the contrast.