Decoding the origins of vertical land motions observed today at coasts

In recent decades, geodetic techniques have allowed detecting vertical land motions and sea-level changes of a few millimetres per year, based on measurements taken at the coast (tide gauges), on board of satellite platforms (satellite altimetry) or both (Global Navigation Satellite System). Here, contemporary vertical land motions are analysed from January 1993 to July 2013 at 849 globally distributed coastal sites. The vertical displacement of the coastal platform due to surface mass changes is modelled using elastic and viscoelastic Green's functions. Special attention is paid to the effects of glacial isostatic adjustment induced by past and present-day ice melting. Various rheological and loading parameters are explored to provide a set of scenarios that could explain the coastal observations of vertical land motions globally. In well-instrumented regions, predicted vertical land motions explain more than 80 per cent of the variance observed at scales larger than a few hundred kilometres. Residual vertical land motions show a strong local variability, especially in the vicinity of plate boundaries due to the earthquake cycle. Significant residual signals are also observed at scales of a few hundred kilometres over nine well-instrumented regions forming observation windows on unmodelled geophysical processes. This study highlights the potential of our multitechnique database to detect geodynamical processes, driven by anthropogenic influence, surface mass changes (surface loading and glacial isostatic adjustment) and tectonic activity (including the earthquake cycle, sediment and volcanic loading, as well as regional tectonic constraints). Future improvements should be aimed at densifying the instrumental network and at investigating more thoroughly the uncertainties associated with glacial isostatic adjustment models.This research benefited from financial support from the CNES (Centre National d’Etudes Spatiales, France) through the TOSCA committee fellowship and from the European Research Council within the framework of the SP2-Ideas Program ERC-2013-CoG, under ERC Grant agreement number 617588. GS is supported by a DiSPeA research grant (CUP H32I160000000005) and by Programma Nazionale di Ricerche in Antartide (PNRA 2013/B2.06, CUP D32I14000230005). AM was supported by an Australian Research Council Super Science Fellowship (FS110200045)

Convergence in measure under Finite Additivity

We investigate the possibility of replacing the topology of convergence in probability with convergence in $L^1$. A characterization of continuous linear functionals on the space of measurable functions is also obtained

Fractional backward stochastic differential euqations and fractional backward variational inequalities

In the framework of fractional stochastic calculus, we study the existence and the uniqueness of the solution for a backward stochastic differential equation, formally written as: [{[c]{l}% -dY(t)= f(t,\eta(t),Y(t),Z(t))dt-Z(t)\delta B^{H}(t), \quad t\in[0,T], Y(T)=\xi,.] where $\eta$ is a stochastic process given by $\eta(t)=\eta(0) +\int_{0}^{t}\sigma(s) \delta B^{H}(s)$, $t\in[0,T]$, and $B^{H}$ is a fractional Brownian motion with Hurst parameter greater than 1/2. The stochastic integral used in above equation is the divergence-type integral. Based on Hu and Peng's paper, \textit{BDSEs driven by fBm}, SIAM J Control Optim. (2009), we develop a rigorous approach for this equation. Moreover, we study the existence of the solution for the multivalued backward stochastic differential equation [{[c]{l} -dY(t)+\partial\varphi(Y(t))dt\ni f(t,\eta(t),Y(t),Z(t))dt-Z(t)\delta B^{H}(t),\quad t\in[0,T], Y(T)=\xi,.] where $\partial\varphi$ is a multivalued operator of subdifferential type associated with the convex function $\varphi$.Comment: 41 page

A new MRI rating scale for progressive supranuclear palsy and multiple system atrophy: validity and reliability

AIM To evaluate a standardised MRI acquisition protocol and a new image rating scale for disease severity in patients with progressive supranuclear palsy (PSP) and multiple systems atrophy (MSA) in a large multicentre study. METHODS The MRI protocol consisted of two-dimensional sagittal and axial T1, axial PD, and axial and coronal T2 weighted acquisitions. The 32 item ordinal scale evaluated abnormalities within the basal ganglia and posterior fossa, blind to diagnosis. Among 760 patients in the study population (PSP = 362, MSA = 398), 627 had per protocol images (PSP = 297, MSA = 330). Intra-rater (n = 60) and inter-rater (n = 555) reliability were assessed through Cohen's statistic, and scale structure through principal component analysis (PCA) (n = 441). Internal consistency and reliability were checked. Discriminant and predictive validity of extracted factors and total scores were tested for disease severity as per clinical diagnosis. RESULTS Intra-rater and inter-rater reliability were acceptable for 25 (78%) of the items scored (≥ 0.41). PCA revealed four meaningful clusters of covarying parameters (factor (F) F1: brainstem and cerebellum; F2: midbrain; F3: putamen; F4: other basal ganglia) with good to excellent internal consistency (Cronbach α 0.75-0.93) and moderate to excellent reliability (intraclass coefficient: F1: 0.92; F2: 0.79; F3: 0.71; F4: 0.49). The total score significantly discriminated for disease severity or diagnosis; factorial scores differentially discriminated for disease severity according to diagnosis (PSP: F1-F2; MSA: F2-F3). The total score was significantly related to survival in PSP (p<0.0007) or MSA (p<0.0005), indicating good predictive validity. CONCLUSIONS The scale is suitable for use in the context of multicentre studies and can reliably and consistently measure MRI abnormalities in PSP and MSA. Clinical Trial Registration Number The study protocol was filed in the open clinical trial registry (http://www.clinicaltrials.gov) with ID No NCT00211224

On tightness and stopping times

This paper studies conditions of tightness for sequences of processes, which conditions are mostly based on the use of 'dominating' increasing processes. The results obtained follow in directions initiated by Aldous and Rebolledo and are particularly well-suited for studying sequences of semimartingales. Also obtained are results that extend sufficient conditions of Aldous's type to processes that are not quasi-left-continuous.

Decadal geodetic variations in Ny-Alesund (Svalbard): role of past and present ice-mass changes

The geodetic rates for the gravity variation and vertical uplift in polar regions subject to past and present-day ice-mass changes (PDIMCs) provide important insight into the rheological structure of the Earth. We provide an update of the rates observed at Ny-Ålesund, Svalbard. To do so, we extract and remove the significant seasonal content from the observations. The rate of gravity variations, derived from absolute and relative gravity measurements, is −1.39 ± 0.11 μGal yr−1. The rate of vertical displacements is estimated using GPS and tide gauge measurements. We obtain 7.94 ± 0.21 and 8.29 ± 1.60 mm yr−1, respectively. We compare the extracted signal with that predicted by GLDAS/Noah and ERA-interim hydrology models. We find that the seasonal gravity variations are well-represented by local hydrology changes contained in the ERA-interim model. The phase of seasonal vertical displacements are due to non-local continental hydrology and non-tidal ocean loading. However, a large part of the amplitude of the seasonal vertical displacements remains unexplained. The geodetic rates are used to investigate the asthenosphere viscosity and lithosphere/asthenosphere thicknesses. We first correct the updated geodetic rates for those induced by PDIMCs in Svalbard, using published results, and the sea level change due to the melting of the major ice reservoirs. We show that the latter are at the level of the geodetic rate uncertainties and are responsible for rates of gravity variations and vertical displacements of −0.29 ± 0.03 μGal yr−1 and 1.11 ± 0.10 mm yr−1, respectively. To account for the late Pleistocene deglaciation, we use the global ice evolution model ICE-3G. The Little Ice Age (LIA) deglaciation in Svalbard is modelled using a disc load model with a simple linear temporal evolution. The geodetic rates at Ny-Ålesund induced by the past deglaciations depend on the viscosity structure of the Earth. We find that viscous relaxation time due to the LIA deglaciation in Svalbard is more than 60 times shorter than that due to the Pleistocene deglaciation. We also find that the response to past and PDIMCs of an Earth model with asthenosphere viscosities ranging between 1.0 and 5.5 × 1018 Pa s and lithosphere (resp. asthenosphere) thicknesses ranging between 50 and 100 km (resp. 120 and 170 km) can explain the rates derived from geodetic observations

Ground deformation and gravity variations modelled from present-day ice thinning in the vicinity of glaciers

International audienceThe solid Earth deforms because of post-glacial rebound due to the viscous relaxation following the last deglaciation but also because of present-day elastic deformation induced by ice thinning. In this paper, we compute elastic loading Green's function associated to the tilt of the ground in the vicinity of glaciers using a Love number formalism for a stratified non-rotating spherical Earth model. We compare this global approach with the plane approximation in terms of height, gravity and tilt changes as a function of the distance from the measurement point to the load. We find that Green's functions for the vertical displacement (resp. horizontal displacement, elastic part of the tilt) agree to within 1% up to ∼400 m (resp. 2km, 5km) from the glaciers.Two specific cases of ice thinning are considered:1/ the alpine glaciers of the Mont Blanc region (France) where ice-thickness variations are derived from differential digital elevation model analysis for the period 1979-2003; 2/ the Svalbard (Norway) glaciers by considering the ice model SVAL. We show that the rates of ground tilt are well above the limit of detection of up-todate long base hydrostatic tiltmeters, which, if installed next to the glaciers, could be used to monitor the time evolution of ice thinning. We also show that the topography has a strong influence on the gravity variations near the glaciers