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Monitoring the evolution of freshwater water resources worldwide is challenging yet essential to prevent severe water scarcity. In that regard, the Gravity Recovery and Climate Experiment and Follow-On satellite missions (GRACE/-FO) have successfully proven to complement in-situ hydrological observations by giving access to variations in continental water storage through measurements of the Earth’s gravity field since 2002.However, the measurement noise and errors inherent to the GRACE/-FO missions design and data processing cause estimation bias and spatial leakage that limit applications to large-scale hydrological basins and complicate geophysical interpretation. Moreover, missing observations during and between the missions, and in particular the 11-month gap between missions make if difficult to monitor long-term mass variations. To overcome these issues, we build a procedure, based on a spectral analysis by Multichannel – Singular Spectrum Analysis (M-SSA), that uses spatio-temporal correlations of the GRACE/-FO time series to fill data gaps and reduce a significant portion of the distinctive noise pattern while maintaining the best possible spatial resolution. This processing reveals hydrological signals that are less well or not resolved by other processing strategies.We seek validation of the GRACE/-FO M-SSA solution by comparison with independent estimates of regional hydrological mass balance. We first develop a new forward modeling approach to derive regional hydrological balance that accounts for potential bias caused by necessary filtering of the GRACE/-FO data. In particular, we account for signal leakage of a known source while estimating regional mass balance.The Caspian Sea, due to its relative isolation, large size and significant mass variations over the past decades, offers an interesting example to validate mass balance derived from GRACE/-FO measurements. We compare space-gravity derived hydrological mass balance with independent altimetry data, accounting for thermosteric effects using in-situ data and ground deformation caused by mass redistribution, and show consistent results on the long term variations. However, we also discuss potential causes of a significant discrepancy in seasonal amplitude.

Ever since the Maule earthquake (Mw8.8, 2010), a quick vertical uplift is measured thanks to GNSS in the Andes, facing the rupture zone (~250 km to the trench). Models built for the Maule earthquake [Klein et al. 2016] have highlighted that a low-viscosity channel is required to explain the post-seismic uplift. This channel is located along the slab between 50 km and 130 km depth and has a viscosity of a few 1017 Pa.s - lower than in the asthenosphere, 1018 Pa.s. After the Illapel earthquake (Mw8.3, 2015), simple observations on GNSS time-series show that no uplift occurred in the Andes at an equivalent distance to the trench than in the case of the Maule earthquake. The subduction in the Illapel region is characterized by a flat-slab (called the Pampean flat-slab) in contrast with the normal-dipping subduction in the region of Maule.Here, we investigate what is the impact of the Pampean flat-slab on the post-seismic deformations of the Illapel earthquake. In particular, we try to understand whether the presence of the flat-slab inhibits the effect of the low-viscosity channel. For that purpose we compare GNSS vertical displacements with predictions in both regions of Maule and Illapel from a 3D spherical finite-element model that accounts for the slab geometry of the Chilean subduction zone.

Thanks to space geodesy we know with a millimetric precision how the lithosphere deforms at each stage of the seismic cycle. In particular, during the post-seismic phase, it can deform over thousands of kilometers and for decades. These deformations are partly due to viscoelastic relaxation of the asthenosphere.In a previous work, we have shown that at the temporal and spatial scale of the seismic cycle, the viscoelastic relaxation can be modeled by a linear creep law [Boulze et al. 2022]. Therefore, because of the linearity of the creep law, the superposition principle applies and the present day deformation is simply the sum of the post-seismic deformations induced by past earthquakes. Based on this result, the objective of our work is to determine what slip history is needed on the Chilean subduction interface to reproduce the current deformation of South America, which is well measured by GNSS.To investigate this challenging problem, we first develop a 3D spherical finite-element model of the Chilean subduction zone. This model covers the entire South American continent and incorporates a slab with a geometry described by Slab2.0 model [Hayes et al. 2018]. Then, we compare different ways to model the seismic cycle using the backslip theory [Savage 1983]. Finally, by comparing GPS time-series with our seismic cycle model prediction, we discuss many ingredients of the model: e.g. the viscosity of the asthenosphere (Maxwell, Burgers), the impact of a flat slab and low viscosity zones, the magnitude and extent of historical earthquakes.

Spatial geodesy through GNSS allows to measure with a millimetric precision the displacement of the lithosphere during the seismic cycle. The post-seismic part of this cycle can last for decades, traduced by long-lasting surface deformations. One of the main physical processes involved in the postseismic deformation is the viscoelastic relaxation in the asthenosphere. However, a long term debate persists about the involved rheology of the asthenosphere: Is the viscosity highly variable from one region to the next and is effective viscosity Newtonian (linear) or non-Newtonian (non linear)? To investigate these questions, we compare the horizontal post-seismic deformations induced by three Chilean megathrust earthquakes: Maule Mw8.8 (2010), Illapel Mw8.3 (2015) and Iquique Mw8.1 (2014). For each earthquake, we select permanent GPS stations along profiles perpendicular to the trench, extending as far as 1400 km. We calculate the ratio of the cumulative post-seismic (post) over 5 years and the coseismic (co) displacements for each station. Remarkably, at a given distance to the trench, the post/co ratios from the three earthquakes differ only slightly.What can be the interpretation of this observation in terms of rheology of the asthenosphere? First we can analyse the response of the asthenosphere in the case of homothetic earthquakes of different magnitude. The post/co ratio obeys simple analytical relationships: For a Newtonian rheology, it is simply a function of the (time/viscosity) ratio. For a non-Newtonian viscosity with a stress exponent n=3, the timescale becomes inversely proportional to M**2, where M is the moment of the earthquake. We show that these relationships are only slightly modified when the earthquakes are no longer homothetic and that the post/co ratio is a good proxy to quantify the strain-rate and stress ratio in the underlying asthenosphere. As a conclusion, the post-seismic deformation following the three Chilean earthquakes reveals very similar viscosity. In particular, a Newtonian, rather than a non-Newtonian, effective viscosity is required to explain the post-seismic deformation process.

The evolution of the Greenland Ice Sheet (GIS) is an important indicator of climate change and driver of sea level rise. However, providing accurate GIS ice mass balance remains a challenge today. Here, we propose to combine a unique set of geodetic measurements to improve our knowledge of the GIS spatial and temporal evolution. We attempt at reconciling satellite observations of ice volume with regional GNSS velocities estimates and time variable space gravity measurements over the 2003-2009 and 2011-2015 periods. The GIS mass variations are inferred from satellite altimetry for large ice sheets (IceSat and CryoSat-2; Sorensen et al.,2018, Simonsen et al.,2017) and digital elevation models (DEMs) generated from multiple satellite archives for peripheral glaciers (Hugonnet et al.,2020), associated with IMAU-FDM firn model (Ligtenberg et al., 2011). The spatial and temporal variations of the gravity field are given by the GRACE mission for which we use a solution where smaller wavelength signals are preserved (Prevost et al., 2019).To resolve short wavelengths load variations affecting the displacement of nearby GNSS stations, we use Green’s functions for vertical crustal displacements assuming purely elastic Earth properties (Martens et al., 2019). We first assume that the deformation is entirely due to recent ice melting and show that vertical elastic displacements predicted by our refined ice loading model, while in good agreement with observations in some regions, cannot explain observations overall. In particular, observations and model disagree in the Southeastern and the Northern parts of Greenland.We then explore potential viscoelastic deformation associated with short-term rheology of the asthenosphere induced by recent ice melting that could explain the observed GNSS displacements. We define a history of ice loading from 1900 to 2009 using both in situ and satellite altimetric measurements, compute today’s associated viscoelastic deformation for various mantle rheologies and discuss the potential contribution of ice melting since the little ice age to current observations. Remaining differences between observations and viscoelastic models may reflect a viscoelastic deformation induced by glacial isostatic adjustment. We discuss implications in terms of regional rheological constraints, and impact on estimates of present-day GIS ice mass budget.Hugonnet, R. (2020). A globally complete, spatially, and temporally resolved estimate of glacier mass change: 2000 to 2019. In EGU 2020. Ligtenberg, S. R. M., et al (2011). An improved semi-empirical model for the densification of Antarctic firn. The Cryosphere, 5, 809-819.Martens, H. R.,et al (2019). LoadDef: A Python‐based toolkit to model elastic deformation caused by surface mass loading on spherically symmetric bodies. Earth and Space Science, 6(2), 311-323.Prevost, P., et al (2019). Data-adaptive spatio-temporal filtering of GRACE data. Geophysical Journal International, 219(3), 2034-2055.Simonsen, S. B., & Sørensen, L. S. (2017). Implications of changing scattering properties on Greenland ice sheet volume change from Cryosat-2 altimetry. Remote Sensing of Environment, 190, 207-216.Sørensen, L. S., et al (2018). 25 years of elevation changes of the Greenland Ice Sheet from ERS, Envisat, and CryoSat-2 radar altimetry. Earth and Planetary Science Letters, 495, 234-241.