Description: The problem of compressibility in modelling of viscoelastic deformations of planetary bodies is still a topic under discussion. Studies facing this topic discuss the error when considering a stratification of layers with constant material parameters. But homogeneous compressible layers imply that the initial state is not stable. So, any perturbation method applied to this type of state results in an ill-posed problem, evident in a denumerable infinite set of modes in the spectral representation of the solution. Based on the analytic solution of Cambiotti and Sabadini, we discuss any violation from the stable Adams–Williamson condition to result in unphysical behaviour where we concentrate here on the consequences for the horizontal displacement and deformation within the mantle due to surface loading. This focus motivates to revisit the Longman paradox, which discusses the boundary conditions for a compressible fluid core.

Description: Global navigation satellite systems (GNSSs) have revealed that a mega-thrust earthquake that occurs in an island-arc trench system causes post-seismic crustal deformation. Such crustal deformation data have been interpreted by combining three mechanisms: afterslip, poroelastic rebound and viscoelastic relaxation. It is seismologically important to determine the contribution of each mechanism because it provides frictional properties between the plate boundaries and viscosity estimates in the asthenosphere which are necessary to evaluate the stress behaviour during earthquake cycles. However, the observation sites of GNSS are mostly deployed over land and can detect only a small part of the large-scale deformation, which precludes a clear separation of the mechanisms. To extend the spatial coverage of the deformation area, recent studies started to use satellite gravity data that can detect long-wavelength deformations over the ocean. To date, compared with theoretical models for calculating the post-seismic crustal deformation, a few models have been proposed to interpret the corresponding gravity variations. Previous approaches have adopted approximations for the effects of compressibility, sphericity and self-gravitation when computing gravity changes. In this study, a new spectral-finite element approach is presented to consider the effects of material compressibility for Burgers viscoelastic earth model with a laterally heterogeneous viscosity distribution. After the basic principles are explained, it is applied to the 2004 Sumatra–Andaman earthquake. For this event, post-seismic deformation mechanisms are still a controversial topic. Using the developed approach, it is shown that the spatial patterns of gravity change generated by the above three mechanisms clearly differ from one another. A comparison of the theoretical simulation results with the satellite gravity data obtained from the Gravity Recovery and Climate Experiment reveals that both afterslip and viscoelastic relaxation are occurring. Considering the spatial patterns in satellite gravity fields is an effective method for investigating post-seismic deformation mechanisms.

Description: The ability of any satellite gravity mission concept to monitor mass transport processes in the Earth system is typically tested well ahead of its implementation by means of various simulation studies. Those studies often extend from the simulation of realistic orbits and instrumental data all the way down to the retrieval of global gravity field solution time-series. Basic requirement for all these simulations are realistic representations of the spatio-temporal mass variability in the different sub-systems of the Earth, as a source model for the orbit computations. For such simulations, a suitable source model is required to represent (i) high-frequency (i.e., subdaily to weekly) mass variability in the atmosphere and oceans, in order to realistically include the effects of temporal aliasing due to non-tidal high-frequency mass variability into the retrieved gravity fields. In parallel, (ii) low-frequency (i.e., monthly to interannual) variability needs to be modelled with realistic amplitudes, particularly at small spatial scales, in order to assess to what extent a new mission concept might provide further insight into physical processes currently not observable. The new source model documented here attempts to fulfil both requirements: Based on ECMWF’s recent atmospheric reanalysis ERA-Interim and corresponding simulations from numerical models of the other Earth system components, it offers spherical harmonic coefficients of the time-variable global gravity field due to mass variability in atmosphere, oceans, the terrestrial hydrosphere including the ice-sheets and glaciers, as well as the solid Earth. Simulated features range from sub-daily to multiyear periods with a spatial resolution of spherical harmonics degree and order 180 over a period of 12 years. In addition to the source model, a de-aliasing model for atmospheric and oceanic high-frequency variability with augmented systematic and random noise is required for a realistic simulation of the gravity field retrieval process, whose necessary error characteristics are discussed. The documentation of the updated ESA Earth System Model (updated ESM) for gravity mission simulation studies is organized as follows: The characteristics of the updated ESM along with some basic validation is presented in Volume 1. A detailed comparison to the original ESA ESM (Gruber et al., 2011) is provided in Volume 2, while Volume 3 contains the description of a strategy to derive realistic errors for the de-aliasing model of high-frequency mass variability in atmosphere and ocean.

Description: The strong lithospheric dichotomy between eastern and western Antarctica origins from the West Antarctic Rift. The rheological implications are therefore a reduction of elastic-lithosphere thickness by more than a factor of 2 from East to West Antarctica, and strongly reduced mantle viscosities below West Antarctica and the Antarctic Peninsula. We apply a spectral finite element model which enables the consideration of lateral viscosity variations in the upper mantle. Variations in seismic velocity are transformed to viscosity variations applying scaling laws, and the glaciation model IJ05 (Ivins & James, 2005, Ant. Sci.) is used for parameterizing the deglaciation of Antarctica. Considering different parameterizations of lithosphere structure we study the implications of lateral variability on the glacial-isostatic adjustment of Antarctica.

Description: Lateral heterogeneities in the Earth’s crust and mantle are demanded from seismic tomographic models, surface data and constraints derived from mantle dynamics. Nevertheless, such structural features are often neglected in GIA and only a 1D structure is assumed for the prediction of the earth’s response to glacial loading as for the inversion of mantle viscosity. 1D model assumption is valid when focussing on vertical motions which are less sensitive to lateral variations in mantle structure but it is questionable for the prediction of horizontal motions. In this presentation, we discuss the consequences which arise for the deformational behaviour of the Earth’s interior if we consider lateral viscosity variations. In particular, our study focusses on viscosity variations in the upper mantle including the mantle lithosphere and implications for plate motions as for the global gravity field are discussed.

Description: We present regional-scale mass balances for 25 drainage basins of the Antarctic Ice Sheet (AIS) from satellite observations of the Gravity and Climate Experiment (GRACE) for the years 2002–2011. Satellite gravimetry estimates of the AIS mass balance are strongly influenced by mass movement in the Earth interior caused by ice advance and retreat during the last glacial cycle. Here, we develop an improved glacial-isostatic adjustment (GIA) estimate for Antarctica using newly available GPS uplift rates, allowing us to more accurately separate GIA-induced trends in the GRACE gravity fields from those caused by current imbalances of the AIS. Our revised GIA estimate is considerably lower than previous predictions, yielding an (upper) estimate of apparent mass change of 48 ± 18 Gt yr−1. Therefore, our AIS mass balance of −103 ± 23 Gt yr−1 is considerably less negative than previous GRACE estimates. The Northern Antarctic Peninsula and the Amundsen Sea Sector exhibit the largest mass loss (−25 ± 6 Gt yr−1 and −126 ± 11 Gt yr−1, respectively). In contrast, East Antarctica exhibits a slightly positive mass balance (19 ± 16 Gt yr−1), which is, however, mostly the consequence of compensating mass anomalies in Dronning Maud and Enderby Land (positive) and Wilkes and George V Land (negative) due to interannual accumulation variations. In total, 7% of the area constitute more than half of the AIS imbalance (53%), contributing −151 ± 9 Gt yr−1 to global mean sea-level change. Most of this imbalance is caused by long-term ice-dynamic speed up expected to prevail in the future.