New constrains on the thickness of the Semail Ophiolite in the Northern Emirates

Near-critical angle and refraction studies were performed at IFP as piggyback studies during a wider programme of crustal imagery operated by WesternGeco on behalf of the Ministry of Energy of the United Arab Emirates. The main objective is to illuminate the base of the Semail Ophiolite along part of a regional transect (D1) crossing the Northern Emirates from the Gulf of Oman in the east up to the Arabian Gulf in the west. Results confirm that the sole thrust of the ophiolite has been folded during the Miocene stacking of the underlying Arabian Platform. The thickness of the ophiolite grades from zero in the core of the Masafi tectonic window, up to a maximum of 1.7 km below the axial part of a successor basin which has been preserved on top of the serpentinite west of the current exposure of the main ultramafic bodies. Apatite grains extracted from plagiogranites of the Semail ophiolite also provide evidences for an early unroofing of the gabbros and plagiogranites during the Late Cretaceous, with cooling ages of 72-76 Ma at the top of the ophiolite in the east (not far from the Fujairah coast line), which are coeval and also consistent with the occurrence of Late Cretaceous paleo-soils, rudists and paleo-reef deposits on top of serpentinized ultramafics in the west. Younger cooling ages of 20 Ma have been also found at the base of the ophiolite near Masafi, in the core of the nappe anticline, thus providing a Neogene age for the refolding of the allochthon and stacking of underlying parautochthonous platform carbonate units. These results, together with the occurrence of a thick sedimentary pile illuminated below the metamorphic sole along the north-trending, strike-profile D2 running parallel to the axis of the Masafi window, should stimulate a renewal of the exploration in the central part of the Emirate foothills, where the ophiolite thickness is currently limited, and was already drastically reduced by the end of its Late Cretaceous obduction. © 2010 Saudi Society for Geosciences

Universal regularity estimates for solutions to fully nonlinear elliptic equations with oblique boundary data

In this work, we establish universal moduli of continuity for viscosity solutions to fully nonlinear elliptic equations with oblique boundary conditions, whose general model is given by \left\{ \begin{array}{rcl} F(D^2u,x) &=& f(x) \quad \mbox{in} \,\, \Omega\\ \beta(x) \cdot Du(x) + \gamma(x) \, u(x)&=& g(x) \quad \mbox{on} \,\, \partial \Omega. \end{array} \right. Such regularity estimates are achieved by exploring the integrability properties of $f$ based on different scenarios, making a $\text{VMO}$ assumption on the coefficients of $F$, and by considering suitable smoothness properties on the boundary data $\beta, \gamma$ and $g$. Particularly, we derive sharp estimates for borderline cases where $f \in L^n(\Omega)$ and $f\in p-\textrm{BMO}(\Omega)$. Additionally, for source terms in $L^p(\Omega)$, for $p \in (n, \infty)$, we obtain sharp gradient estimates. Finally, we also address Schauder-type estimates for convex/concave operators and suitable H\"{o}lder data