More than 7 years of observations of postseismic relaxation after the 2004 Sumatra‐Andaman earthquake provide an improving view on the deformation in the wide vicinity of the 2004 rupture. We include both Gravity Recovery and Climate Experiment (GRACE) gravity field data that show a large postseismic signal over the rupture area and GPS observations in the back arc region. With increasing time GPS and GRACE show contrasting relaxation styles that were not easily discernible on shorter time series. We investigate whether mantle creep can simultaneously explain the far‐field surface displacements and the long‐wavelength gravity changes. We interpret contrasts in the temporal behavior of the GPS‐GRACE observations in terms of lateral variations in rheological properties of the asthenosphere below and above the slab. Based on 1‐D viscoelastic models, our results support an (almost) order of magnitude contrast between oceanic lithosphere viscosity and continental viscosity, which likely means that the low viscosities frequently found from postseismic deformation after subduction earthquakes are valid only for the mantle wedge. Next to mantle creep, we also consider afterslip as an alternative mechanism for postseismic deformation. We investigate how the combination of GRACE and GPS data can better discriminate between different mechanisms of postseismic relaxation: distributed deformation (mantle creep) versus localized deformation (afterslip). We conclude that the GRACE‐observed gravity changes rule out afterslip as the dominant mechanism explaining long‐wavelength deformation even over the first year after the event.

Large earthquakes do not only heavily deform the crust in the vicinity of the fault, they also change the gravity field of the area affected by the earthquake due to mass redistribution in the upper layers of the Earth. Besides that, for sub-oceanic earthquakes deformation of the ocean floor causes relative sea level changes and mass redistribution of water that have again a significant effect on the gravity field. To model these deformations, sea level changes and gravity field perturbations self-consistently we use an adapted version of the sea level equation (SLE) that has been used for glacial isostatic adjustment studies. The sea level equation, next to our normal mode model for seismic solid earth modelling, allows us to compute a gravitationally self-consistent solution for the co-seismic relative sea level, surface deformation and geoid height changes. We apply our geographically detailed models to the case of the 2004 December 26 Sumatra-Andaman earthquake. Recent studies that have modelled the ocean mass effect on co-seismic gravity change for this specific earthquake show model results that indicate a broad negative change in geoid height around the fault due to ocean water redistribution [5], [13]. Our model results for the ocean contribution to geoid height differ from these studies in the sense that we find a pattern similar to the elongated dipole pattern of the solid earth model outputs for gravity and vertical deformation, together with a relatively small broad negative geoid height change. We explain the relation between outcomes for geoid height, relative sea level and vertical deformation of the ocean floor and we confront our model results with a least squares estimation of the co-seismic discontinuity in GRACE-derived gravity field time series. We show that taking into account the contribution of ocean water redistribution to the co-seismic geoid height change next to a compressible solid earth model is essential to explain the predominant negative co-seismic geoid anomalies from the GRACE gravity field solutions. Besides, we introduce a detailed approach to modelling an earthquake in a normal mode model that better approximates realistic continuous slip on the fault plane than models that do not distribute slip with depth. To demonstrate the importance of the slip distribution we show the differences in outcomes for modelled geoid height and vertical deformation.

Recent megathrust events in Tohoku (Japan), Maule (Chile), and Sumatra (Indonesia) were well recorded. Much has been learned about the dominant physical processes in megathrust zones: (partial) locking of the plate interface, detailed coseismic slip, relocking, afterslip, viscoelastic mantle relaxation, and interseismic loading. These and older observations show complex spatial and temporal patterns in crustal deformation and displacement, and significant differences among different margins. A key question is whether these differences reflect variations in the underlying processes, like differences in locking, or the margin geometry, or whether they are a consequence of the stage in the earthquake cycle of the margin. Quantitative models can connect these plate boundary processes to surficial and far‐field observations. We use relatively simple, cyclic geodynamic models to isolate the first‐order geodetic signature of the megathrust cycle. Coseismic and subsequent slip on the subduction interface is dynamically (and consistently) driven. A review of global preseismic, coseismic, and postseismic geodetic observations, and of their fit to the model predictions, indicates that similar physical processes are active at different margins. Most of the observed variability between the individual margins appears to be controlled by their different stages in the earthquake cycle. The modeling results also provide a possible explanation for observations of tensile faulting aftershocks and tensile cracking of the overriding plate, which are puzzling in the context of convergence/compression. From the inversion of our synthetic GNSS velocities we find that geodetic observations may incorrectly suggest weak locking of some margins, for example, the west Aleutian margin.

The Japan Tohoku‐Oki earthquake (9.0 Mw) of 11 March 2011 has left signatures in the Earth's gravity field that are detectable by data of the Gravity field Recovery and Climate Experiment (GRACE) mission. Because the European Space Agency's (ESA) satellite gravity mission Gravity field and steady‐state Ocean Circulation Explorer (GOCE)—launched in 2009—aims at high spatial resolution, its measurements could complement the GRACE information on coseismic gravity changes, although time‐variable gravity was not foreseen as goal of the GOCE mission. We modeled the coseismic earthquake geoid signal and converted this signal to vertical gravity gradients at GOCE satellite altitude. We combined the single gradient observations in a novel way reducing the noise level, required to detect the coseismic gravity change, subtracted a global gravity model, and applied tailored outlier detection to the resulting gradient residuals. Furthermore, the measured gradients were along‐track filtered using different gradient bandwidths where in the space domain Gaussian smoothing has been applied. One‐year periods before and after earthquake occurrence have been compared with the modeled gradients. The comparison reveals that the earthquake signal is well above the accuracy of the vertical gravity gradients at orbital height. Moreover, the obtained signal from GOCE shows a 1.3 times higher amplitude compared with the modeled signal. Besides the statistical significance of the obtained signal, it has a high spatial correlation of ~0.7 with the forward modeled signal. We conclude therefore that the coseismic gravity change of the Japan Tohoku‐Oki earthquake left a statistically significant signal in the GOCE measured gravity gradients.

S U M M A R YDuring megathrust earthquakes, great ruptures are accompanied by large scale mass redistribution inside the solid Earth and by ocean mass redistribution due to bathymetry changes. These large scale mass displacements can be detected using the monthly gravity maps of the GRACE satellite mission. In recent years it has become increasingly common to use the long wavelength changes in the Earth's gravity field observed by GRACE to infer seismic source properties for large megathrust earthquakes. An important advantage of space gravimetry is that it is independent from the availability of land for its measurements. This is relevant for observation of megathrust earthquakes, which occur mostly offshore, such as the M w ∼ 9 2004 Sumatra-Andaman, 2010 Maule (Chile) and 2011 Tohoku-Oki (Japan) events. In Broerse et al., we examined the effect of the presence of an ocean above the rupture on long wavelength gravity changes and showed it to be of the first order.Here we revisit the implementation of an ocean layer through the sea level equation and compare the results with approximated methods that have been used in the literature. One of the simplifications usually lies in the assumption of a globally uniform ocean layer. We show that especially in the case of the 2010 Maule earthquake, due to the closeness of the South American continent, the uniform ocean assumption is not valid and causes errors up to 57 per cent for modelled peak geoid height changes (expressed at a spherical harmonic truncation degree of 40). In addition, we show that when a large amount of slip occurs close to the trench, horizontal motions of the ocean floor play a mayor role in the ocean contribution to gravity changes. Using a slip model of the 2011 Tohoku-Oki earthquake that places the majority of slip close to the surface, the peak value in geoid height change increases by 50 per cent due to horizontal ocean floor motion. Furthermore, we test the influence of the maximum spherical harmonic degree at which the sea level equation is performed for sea level changes occurring along coastlines, which shows to be important for relative sea level changes occurring along the shore. Finally, we demonstrate that ocean floor loading, self-gravitation of water and conservation of water mass are of second order importance for coseismic gravity changes.When GRACE observations are used to determine earthquake parameters such as seismic moment or source depth, the uniform ocean layer method introduces large biases, depending on the location of the rupture with respect to the continent. The same holds for interpreting shallow slip when horizontal motions are not properly accounted for in the ocean contribution. In both cases the depth at which slip occurs will be underestimated.

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One of the primary observational data sets of sea level is represented by the tide gauge record. We propose a new method to estimate variability on decadal time scales from tide gauge data by using a state space formulation, which couples the direct observations to a predefined state space model by using a Kalman filter. The model consists of a time‐varying trend and seasonal cycle, and variability induced by several physical processes, such as wind, atmospheric pressure changes and teleconnection patterns. This model has two advantages over the classical least‐squares method that uses regression to explain variations due to known processes: a seasonal cycle with time‐varying phase and amplitude can be estimated, and the trend is allowed to vary over time. This time‐varying trend consists of a secular trend and low‐frequency variability that is not explained by any other term in the model. As a test case, we have used tide gauge data from stations around the North Sea over the period 1980–2013. We compare a model that only estimates a trend with two models that also remove intra‐annual variability: one by means of time series of wind stress and sea level pressure, and one by using a two‐dimensional hydrodynamic model. The last two models explain a large part of the variability, which significantly improves the accuracy of the estimated time‐varying trend. The best results are obtained with the hydrodynamic model. We find a consistent low‐frequency sea level signal in the North Sea, which can be linked to a steric signal over the northeastern part of the Atlantic.

The Gravity Recovery and Climate Experiment (GRACE) mission (launched 2002) and the Gravity Field and Steady‐State Ocean Circulation Explorer (GOCE) mission (March 2009 to November 2013) collected spaceborne gravity data for the preseismic and postseismic periods of the 2011 Tohoku‐Oki earthquake. In addition, the dense Japan GeoNet Global Navigation Satellite Systems (GNSS) network measured with approximately 1050 stations the coseismic and postseismic surface displacements. We use a novel combination of GNSS, GRACE, and GOCE observations for a distributed fault slip model addressing the issues with gravimetric and geometric change over consistent time windows. Our model integrates the coseismic and postseismic effects as we include GOCE observations averaged over a 2 year interval, but their inclusion reveals the gravity change with unprecedented spatial accuracy. The gravity gradient grid, evaluated at GOCE orbit height of 265 km, has an estimated formal error of 0.20 mE which provides sensitivity to the mainly coseismic and integrated postseismic‐induced gravity gradient signal of −1.03 mE. We show that an increased resolution of the gravity change provides valuable information, with GOCE gravity gradient observations sensitive to a more focused slip distribution in contrast to the filtered GRACE equivalent. The 2 year averaging window of the observations makes it important to incorporate estimates of the variance/covariance of unmodeled processes in the inversion. The GNSS and GRACE/GOCE combined model shows a slip pattern with 20 m peak slip at the trench. The total gravity change (≈200 μGal) and the spatial mapping accuracy would have been considerably lower by omitting the GOCE‐derived fine‐scale gravity field information.