Modeling sea level changes and geodetic variations by glacial isostasy: the improved SELEN code

We describe the basic features of SELEN, an open source Fortran 90 program for the numerical solution of the so-called "Sea Level Equation" for a spherical, layered, non-rotating Earth with Maxwell viscoelastic rheology. The Sea Level Equation was introduced in the 70s to model the sea level variations in response to the melting of late-Pleistocene ice-sheets, but it can be also employed for predictions of geodetic quantities such as vertical and horizontal surface displacements and gravity variations on a global and a regional scale. SELEN (acronym of SEa Level EquatioN solver) is particularly oriented to scientists at their first approach to the glacial isostatic adjustment problem and, according to our experience, it can be successfully used in teaching. The current release (2.9) considerably improves the previous versions of the code in terms of computational efficiency, portability and versatility. In this paper we describe the essentials of the theory behind the Sea Level Equation, the purposes of SELEN and its implementation, and we provide practical guidelines for the use of the program. Various examples showing how SELEN can be configured to solve geodynamical problems involving past and present sea level changes and current geodetic variations are also presented and discussed

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

Relationship between the moment of inertia and the k2k_2 Love number of fluid extra-solar planets

Context: Tidal and rotational deformation of fluid giant extra-solar planets may impact their transit light curves, making the $k_2$ Love number observable in the upcoming years. Studying the sensitivity of $k_2$ to mass concentration at depth is thus expected to provide new constraints on the internal structure of gaseous extra-solar planets. Aims: We investigate the link between the mean polar moment of inertia $N$ of a fluid, stably layered extra-solar planet and its $k_2$ Love number, aiming at obtaining analytical relationships valid, at least, for some particular ranges of the model parameters. We also seek a general, approximate relationship useful to constrain $N$ once observations of $k_2$ will become available. Methods: For two-layer fluid extra-solar planets, we explore the relationship between $N$ and $k_2$ by analytical methods, for particular values of the model parameters. We also explore approximate relationships valid over all the possible range of two-layer models. More complex planetary structures are investigated by the semi-analytical propagator technique. Results: A unique relationship between $N$ and $k_2$ cannot be established. However, our numerical experiments show that a `rule of thumb' can be inferred, valid for complex, randomly layered stable planetary structures. The rule robustly defines the upper limit to the values of $N$ for a given $k_2$, and agrees with analytical results for a polytrope of index one and with a realistic non-rotating model of the tidal equilibrium of Jupiter.Comment: Accepted for publication on Astronomy & Astrophysic

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

Palaeo-Shoreline Configuration of the Adventure Plateau (Sicilian Channel) at the Last Glacial Maximum

The Adventure Plateau, located in the NW sector of the Sicilian Channel, experienced several episodes of exposure/erosion and subsequent drowning, with the most recent occurring after the Last Glacial Maximum (LGM). Unlike other parts of the Sicilian Channel, the Adventure Plateau is relatively tectonically stable and is therefore best suitable for reconstructing its coastal configuration before the post-LGM marine transgression. Here, we use high-resolution seismic data to identify and map the palaeo-coastline at the LGM on the basis of the internal architecture of the prograding wedges (i.e., the location of the subaqueous clinoform rollover point) and the erosional markers such as the subaerial unconformities and the wave ravinement surfaces. These data, which show an extreme variability in the palaeo-morphology of the coastal margins of the Adventure Plateau, have been complemented with vintage seismic profiles in order to entirely cover its perimeter. The mapped LGM coastline has then been compared to predictions from glacial isostatic adjustment (GIA) modeling, which considers the horizontal migration of the shorelines in response to sea level rise and to Earth's rotational and deformational effects associated with deglaciation. The two shorelines (i.e., the coastline derived from the marine data interpretation and the one derived from the GIA model) are in good agreement at 21 kyears BP, although some discrepancies occur in the southern part of the plateau, where the seabed slope is extremely gentle, which makes the clinoform rollover points and the buried erosional unconformities difficult to detect. After 20 kyears BP, an acceleration in the rate of the sea level rise occurred. The results of this study indicate the importance of comparing experimental data with model predictions in order to refine and calibrate boundary parameters and to gain a better picture of the evolution of sea level rise over various time scales

Impact of Sumatra earthquake on CMB topography and core ellipticity

Characterization of the global impact of 2004 Sumatra earthquake event through the investigation of its effects on core-mantle boundary (CMB) shape and on the elliptical part of the gravity field (J2

Did the September 2010 (Darfield) earthquake trigger the February 2011 (Christchurch) event?

We have investigated the possible cause-and-effect relationship due to stress transfer between two earthquakes that occurred near Christchurch, New Zealand, in September 2010 and in February 2011. The Mw 7.1 Darfield (Canterbury) event took place along a previously unrecognized fault. The Mw 6.3 Christchurch earthquake, generated by a thrust fault, occurred approximately five months later, 6 km south-east of Christchurch's city center. We have first measured the surface displacement field to retrieve the geometries of the two seismic sources and the slip distribution. In order to assess whether the first earthquake increased the likelihood of occurrence of a second earthquake, we compute the Coulomb Failure Function (CFF). We find that the maximum CFF increase over the second fault plane is reached exactly around the hypocenter of the second earthquake. In this respect, we may conclude that the Darfield earthquake contributed to promote the rupture of the Christchurch fault

Effects of transient water mass redistribution associated with a tsunami wave on Earth's pole path

We have quantified the effects of a water mass redistribution associated with the propagation of a tsunami wave on the Earths pole path and on the Length-Of-Day (LOD) and applied our modeling results to the tsunami following the 2004 giant Sumatra earthquake. We compared the result of our simulations on the instantaneous rotational axis variations with the preliminary instrumental evidence on the pole path perturbation (which has not been confirmed) registered just after the occurrence of the earthquake. The detected perturbation in the pole path showed a step-like discontinuity that cannot be attributed to the effect of a seismic dislocation. Our results show that the tsunami induced instantaneous rotational pole perturbation is indeed characterized by a step-like discontinuity compatible with the observations but its magnitude is almost one hundred times smaller than the detected one. The LOD variation induced by the water mass redistribution turns out to be not significant because the total effect is smaller than current measurements uncertainties

Sensitivity analysis of polar orbiter motion to lunar viscoelastic tidal deformation

We investigate the impact of viscoelastic tidal deformation of the Moon on the motion of a polar orbiter. The dissipative effects in the Moon’s interior, i.e., tidal phase lags, are modeled as Fourier series sampled at given frequencies associated with linear combinations of Delaunay arguments, the fundamental parameters describing the lunar motion around the Earth and the Sun. We implement the tidal model to evaluate the temporal lunar gravity field and the induced perturbation on the orbiter. We validate the numerical scheme via a frequency analysis of the perturbed orbital motion. We show that, in the case of the Lunar Reconnaissance Orbiter at a low altitude of less than 200 km, the main lunar tides and hence the potential Love numbers around the monthly and some multiple frequencies are dynamically separable. The omission of those effects in practice introduces a position error at the level of a few decimeters within 10 days

Search for heavy particles decaying into a top-quark pair in the fully hadronic final state in pp collisions at s =13 TeV with the ATLAS detector

A search for new particles decaying into a pair of top quarks is performed using proton-proton collision data recorded with the ATLAS detector at the Large Hadron Collider at a center-of-mass energy of s=13 TeV corresponding to an integrated luminosity of 36.1 fb-1. Events consistent with top-quark pair production and the fully hadronic decay mode of the top quarks are selected by requiring multiple high transverse momentum jets including those containing b-hadrons. Two analysis techniques, exploiting dedicated top-quark pair reconstruction in different kinematic regimes, are used to optimize the search sensitivity to new hypothetical particles over a wide mass range. The invariant mass distribution of the two reconstructed top-quark candidates is examined for resonant production of new particles with various spins and decay widths. No significant deviation from the Standard Model prediction is observed and limits are set on the production cross-section times branching fraction for new hypothetical Z′ bosons, dark-matter mediators, Kaluza-Klein gravitons and Kaluza-Klein gluons. By comparing with the predicted production cross sections, the Z′ boson in the topcolor-assisted-technicolor model is excluded for masses up to 3.1-3.6 TeV, the dark-matter mediators in a simplified framework are excluded in the mass ranges from 0.8 to 0.9 TeV and from 2.0 to 2.2 TeV, and the Kaluza-Klein gluon is excluded for masses up to 3.4 TeV, depending on the decay widths of the particles.Peer Reviewe