Viscosity contrasts in the Venus mantle from tidal deformations

The tidal deformations of a planet are often considered as markers of its inner structure. In this work, we use the tide excitations induced by the Sun on Venus for deciphering the nature of its internal layers. In using a Monte Carlo Random Exploration of the space of parameters describing the thickness, density and viscosity of 4 or 5 layer profiles, we were able to select models that can reproduce the observed mass, total moment of inertia, $k_2$ Love number and expected quality factor $Q$. Each model is assumed to have homogeneous layers with constant density, viscosity and rigidity. These models show significant contrasts in the viscosity between the upper mantle and the lower mantle. They also rather favor a S-free core and a slightly hotter lower mantle consistent with previous expectations.Comment: Accepted for publication in Planetary and Space Science

Generalized Maxwell Love numbers

By elementary methods, I study the Love numbers of a homogeneous, incompressible, self–gravitating sphere characterized by a generalized Maxwell rheology, whose mechanical analogue is represented by a finite or infinite system of classical Maxwell elements disposed in parallel. Analytical, previously unknown forms of the complex shear modulus for the generalized Maxwell body are found by algebraic manipulation, and studied in the particular case of systems of springs and dashpots whose strength follows a power–law distribution. We show that the sphere is asymptotically stable for any choice of the mechanical parameters that define the generalized Maxwell body and analytical forms of the Love numbers are always available for generalized bodies composed by less than five classical Maxwell bodies. For the homogeneous sphere, “real” Laplace inversion methods based on the Post–Widder formula can be applied without performing a numerical discretization of the n–th derivative, which can be computed in a “closed–form” with the aid of the Fa`a di Bruno formula

SELEN 4 (SELEN version 4.0): a Fortran program for solving the gravitationally and topographically self-consistent sea-level equation in glacial isostatic adjustment modeling

Abstract. We present SELEN4 (SealEveL EquatioN solver), an open-source program written in Fortran 90 that simulates the glacial isostatic adjustment (GIA) process in response to the melting of the Late Pleistocene ice sheets. Using a pseudo-spectral approach complemented by a spatial discretization on an icosahedron-based spherical geodesic grid, SELEN4 solves a generalized sea-level equation (SLE) for a spherically symmetric Earth with linear viscoelastic rheology, taking the migration of the shorelines and the rotational feedback on sea level into account. The approach is gravitationally and topographically self-consistent, since it considers the gravitational interactions between the solid Earth, the cryosphere, and the oceans, and it accounts for the evolution of the Earth's topography in response to changes in sea level. The SELEN4 program can be employed to study a broad range of geophysical effects of GIA, including past relative sea-level variations induced by the melting of the Late Pleistocene ice sheets, the time evolution of paleogeography and of the ocean function since the Last Glacial Maximum, the history of the Earth's rotational variations, present-day geodetic signals observed by Global Navigation Satellite Systems, and gravity field variations detected by satellite gravity missions like GRACE (the Gravity Recovery and Climate Experiment). The "GIA fingerprints" constitute a standard output of SELEN4. Along with the source code, we provide a supplementary document with a full account of the theory, some numerical results obtained from a standard run, and a user guide. Originally, the SELEN program was conceived by Giorgio Spada (GS) in 2005 as a tool for students eager to learn about GIA, and it has been the first SLE solver made available to the community

Shallow upper mantle rheology and secular ice sheet fluctuations

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A Sea Level Equation for seismic perturbations

Large earthquakes are a potentially important source of relative sea level variations, since they can drive global deformation and simultaneously perturb the gravity field of the Earth. For the first time, we formalize a gravitationally self-consistent, integral sea level equation suitable for earthquakes, in which we account both for direct effects by the seismic dislocation and for the feedback from water loading associated with sea level changes. Our approach builds upon the well-established theory first proposed in the realm of glacio-isostatic adjustment modelling. The seismic sea level equation is numerically implemented to model sea level signals following the 2004 Sumatra–Andaman earthquake, showing that surface loading from ocean water redistribution (so far ignored in post-seismic deformation modelling) may account for a significant fraction of the total computed post-seismic sea level variatio

Creep, Relaxation and Viscosity Properties for Basic Fractional Models in Rheology

The purpose of this paper is twofold: from one side we provide a general survey to the viscoelastic models constructed via fractional calculus and from the other side we intend to analyze the basic fractional models as far as their creep, relaxation and viscosity properties are considered. The basic models are those that generalize via derivatives of fractional order the classical mechanical models characterized by two, three and four parameters, that we refer to as Kelvin-Voigt, Maxwell, Zener, anti-Zener and Burgers. For each fractional model we provide plots of the creep compliance, relaxation modulus and effective viscosity in non dimensional form in terms of a suitable time scale for different values of the order of fractional derivative. We also discuss the role of the order of fractional derivative in modifying the properties of the classical models.Comment: 41 pages, 8 figure

Updated absolute gravity rate of change associated with glacial isostatic adjustment in Southeast Alaska and its utilization for rheological parameter estimation

In Southeast Alaska (SE-AK), rapid ground uplift of up to 3 cm/yr has been observed associated with post-Little Ice Age glacial isostatic adjustment (GIA). Geodetic techniques such as global navigation satellite system (GNSS) and absolute gravimetry have been applied to monitor GIA since the last 1990s. Rheological parameters for SE-AK were determined from dense GNSS array data in earlier studies. However, the absolute gravity rate of change observed in SE-AK was inconsistent with the ground uplift rate, mainly because few gravity measurements from 2006 to 2008 resulted in imprecise gravity variation rates. Therefore, we collected absolute gravity data at six gravity points in SE-AK every June in 2012, 2013, and 2015, and updated the gravity variation rate by reprocessing the absolute gravity data collected from 2006 to 2015. We found that the updated gravity variation rate at the six gravity points ranged from −2.05 to −4.40 μGal/yr, and its standard deviation was smaller than that reported in the earlier study by up to 88 %. We also estimated the rheological parameters under the assumption of the incompressible Earth to explain the updated gravity variation rate, and their optimal values were determined to be 55 km and 1.2×10¹⁹ Pa s for lithospheric thickness and upper mantle viscosity, respectively. These optimal values are consistent with those independently obtained from GNSS observations, and this fact indicates that absolute gravimetry can be one of the most effective methods in determining sub-surface structural parameters associated with GIA accurately. Moreover, we utilized the gravity variation rates for estimating the ratio of gravity variation to vertical ground deformation at the six gravity points in SE-AK. The viscous ratio values were obtained as −0.168 and −0.171 μGal/mm from the observed data and the calculated result, respectively. These ratios are greater (in absolute) than those for other GIA regions (−0.15 to −0.16 μGal/mm in Antarctica and Fennoscandia), because glaciers in SE-AK have melted more recently than in other regions

Post-seismic stress relaxation with a linear transient rheology

We performed an analysis of post-seismic stress relaxation, taking into account generalized linear rheologies. We compared the stress field (and its derived functions) obtained with a classical Maxwell rheology with that obtained with a transient Burgers body. From a set of synthetic case studies, we have revealed quantitative and qualitative differences both in relaxation times and in local stress values when a transient rheology is introduced. As a practical application, we modeled the time evolution of the Coulomb failure function following the 2009 L'Aquila earthquake, and we show that a transient rheology can lead to non-monotonic time dependence

Post-seismic stress relaxation with a linear transient rheology

We performed an analysis of post-seismic stress relaxation, taking into account generalized linear rheologies. We compared the stress field (and its derived functions) obtained with a classical Maxwell rheology with that obtained with a transient Burgers body. From a set of synthetic case studies, we have revealed quantitative and qualitative differences both in relaxation times and in local stress values when a transient rheology is introduced. As a practical application, we modeled the time evolution of the Coulomb failure function following the 2009 L'Aquila earthquake, and we show that a transient rheology can lead to non-monotonic time dependence

Sea Level Variations from Decades to Millennia: A few Case Studies

The main goals of this Ph.D. study are to investigate the regional and global geophysical components related to present polar ice melting and to provide independent cross validation checks of GIA models using both geophysical data detected by satellite mission, and geological observations from far field sites, in order to determine a lower and upper bound of uncertainty of GIA effect. The subject of this Thesis is the sea level change from decades to millennia scale. Within ice2sea collaboration, we developed a Fortran numerical code to analyze the local short-term sea level change and vertical deformation resulting from the loss of ice mass. This method is used to investigate polar regions: Greenland and Antarctica. We have used mass balance based on ICESat data for Greenland ice sheet and a plausible mass balance for Antarctic ice sheet. We have determined the regional and global fingerprint of sea level variations, vertical deformations of the solid surface of the Earth and variations of shape of the geoid for each ice source mentioned above. The coastal areas are affected by the long wavelength component of GIA process. Hence understanding the response of the Earth to loading is crucial in various contexts. Based on the hypothesis that Earth mantle materials obey to a linear rheology, and that the physical parameters of this rheology can be only characterized by their depth dependence, we investigate the Glacial Isostatic Effect upon the far field sites of Mediterranean area using an improved SELEN program. We presented new and revised observations for archaeological fish tanks located along the Tyrrhenian and Adriatic coast of Italy and new RSL for the SE Tunisia. Spatial and temporal variations of the Holocene sea levels studied in central Italy and Tunisia, provided important constraints on the melting history of the major ice sheets