Uniqueness for SQG patch solutions

This paper is about the evolution of a temperature front governed by the surface quasi-geostrophic equation. The existence part of that program within the scale of Sobolev spaces was obtained by the third author (2008). Here we revisit that proof introducing some new tools and points of view which allow us to conclude the also needed uniqueness result.Ministerio de Economía y CompetitividadJunta de AndalucíaEuropean Research Counci

The Rayleigh-Taylor condition for the evolution of irrotational fluid interfaces

For the free boundary dynamics of the two-phase Hele-Shaw and Muskat problems, and also for the irrotational incompressible Euler equation, we prove existence locally in time when the Rayleigh-Taylor condition is initially satisfied for a 2D interface. The result for water waves was first obtained by Wu in a slightly different scenario (vanishing at infinity), but our approach is different because it emphasizes the active scalar character of the system and does not require the presence of gravity.Ministerio de Educación y CienciaEuropean Research Counci

Interface evolution: water waves in 2-D

We study the free boundary evolution between two irrotational, incompressible and inviscid fluids in 2-D without surface tension. We prove local-existence in Sobolev spaces when, initially, the difference of the gradients of the pressure in the normal direction has the proper sign, an assumption which is also known as the Rayleigh-Taylor condition. The well-posedness of the full water wave problem was first obtained by S. Wu. Well-posedness in Sobolev spaces of the full water wave problem in 2-D. Invent. math. 130, 39-72, 1997. The methods introduced in this paper allows us to consider multiple cases: with or without gravity, but also a closed boundary or a periodic boundary with the fluids placed above and below it. It is assumed that the initial interface does not touch itself, being a part of the evolution problem to check that such property prevails for a short time, as well as it does the Rayleigh-Taylor condition, depending conveniently upon the initial data. The addition of the pressure equality to the contour dynamic equations is obtained as a mathematical consequence, and not as a physical assumption, from the mere fact that we are dealing with weak solutions of Euler’s equation in the whole space.Ministerio de Educación y CienciaMinisterio de Ciencia e InnovaciónEuropean Research Counci

Porous media: the Muskat problem in 3D

The Muskat problem involves filtration of two incompressible fluids throughout a porous medium. In this paper we shall discuss in 3-D the relevance of the RayleighTaylor condition, and the topology of the initial interface, in order to prove its local existence in Sobolev spaces.Ministerio de Ciencia e InnovaciónEuropean Research CouncilNational Science Foundatio

Riemann y el análisis matemático

Factoria FM

Seismic crustal structure in the southwest of the Iberian Peninsula and the Gulf of Cadiz

The crust under the southwestern Iberian Peninsula and the Gulf of Cadiz has been sampled by 1200 km of deep seismic refraction=wide-angle reflection profiles, together with many seismic reflection lines and bore-holes. Wide-angle seismic data were collected during the last three decades. Commercial multichannel data provide a detailed image of the uppermost crust, improving the confidence about the models of the deeper structures. P-wave velocities within the thick column of sediments in the Gulf of Cadiz range from 2.0 to 3.8 km=s, while the Algarve and the Sines areas have higher velocities of 4.3 to 4.8 km=s. The top of the Palaeozoic basement rises to the northwest, outcropping in the South Portuguese zone of the Iberian Massif, and is characterized by P-wave velocities of 5.7–5.9 km=s. High velocities of 6.4 km=s have been found at shallow depths of 7 to 10 km in the South Portuguese zone, that could be related to the mafic and ultramafic rocks in the Beja-Acebuches zone. Lower crustal velocities are in the range of 6.7–6.9 km=s. The crustal thickness shows important lateral changes from 29 km beneath the Guadalquivir Basin=Iberian Massif contact to 35 km in the southeastern part of the South Portuguese zone. From the interpretation of these seismic data, a geodynamic model of the evolution of the crust in Southwestern Iberia and the Gulf of Cadiz is proposed. The Guadalquivir Basin, and its continuation at sea, the Gulf of Cadiz, is a flexure area of the crust that could be related to the overloading due to the overthrusting of the Alboran Domain over the Iberian plate

Survey explores active tectonics in Northeastern Caribbean

There is renewed interest in studying the active and complex northeastern Caribbean plate boundary to better understand subduction zone processes and for earthquake and tsunami hazard assessments [e.g., ten Brink and Lin, 2004; ten Brink et al., 2004; Grindlay et al, 2005]. To study the active tectonics of this plate boundary, the GEOPRICO-DO (Geological, Puerto Rico-Dominican) marine geophysical cruise, carried out between 28 March and 17 April 2005 (Figure 1), studied the active tectonics of this plate boundary. Initial findings from the cruise have revealed a large underwater landslide, and active faults on the seafloor (Figures 2a and 2c). These findings indicate that the islands within this region face a high risk from tsunami hazards, and that local governments should be alerted in order to develop and coordinate possible mitigation strategies. The cruise collected multibeam bathymetry, gravity, magnetic, high-resolution seismic, deep seismic sounding, and multichannel seismic reflection data, which are currently being processed and interpreted (Table 1). In early November 2005, 10 ocean-bottom seismometers (OBS) that had been deployed northeast of Puerto Rico and the Virgin Islands (Figure 1) during the cruise were recovered. These OBS recorded data during the cruise and the local seismicity between April and October 2005

Crustal thickness and images of the lithospheric discontinuities in the Gibraltar arc and surrounding areas

The Gibraltar arc and surrounding areas are a complex tectonic region and its tectonic evolution.since Miocene is still under debate. Knowledge of its lithospheric structure will help to.understand the mechanisms that produced extension and westward motion of the Alboran domain,.simultaneously withNW–SE compression driven by Africa–Europe plates convergence..We perform a P-wave receiver function analysis in which we analyse new data recorded at.83 permanent and temporary seismic broad-band stations located in the South of the Iberian.peninsula. These data are stacked and combined with data from a previous study in northern.Morocco to build maps of thickness and average vP/vS ratio for the crust, and cross-sections.to image the lithospheric discontinuities beneath the Gibraltar arc, the Betic and Rif Ranges.and their Iberian and Moroccan forelands. Crustal thickness values show strong lateral variations.in the southern Iberia peninsula, ranging from ∼19 to ∼46 km. The Variscan foreland is.characterized by a relatively flat Moho at ∼31 km depth, and an average vP/vS ratio of ∼1.72,.similar to other Variscan terranes, which may indicate that part of the lower crustal orogenic.root was lost. The thickest crust is found at the contact between the Alboran domain and the.External Zones of the Betic Range, while crustal thinning is observed southeastern Iberia.(down to 19 km) and in the Guadalquivir basin where the thinning at the Iberian paleomargin.could be still preserved. In the cross-sections, we see a strong change between the eastern.Betics, where the Iberian crust underthrusts and couples to the Alboran crust, and the western.Betics, where the underthrusting Iberian crust becomes partially delaminated and enters into.the mantle. The structures largely mirror those on the Moroccan side where a similar detachment.was observed in northern Morocco. We attribute a relatively shallow strong negativepolarity.discontinuity to the lithosphere-asthenosphere boundary. This means relatively thin.lithosphere ranging from ∼50 km thickness in southeastern Iberia and northeastern Morocco.to ∼90–100 km beneath the western Betics and the Rif, with abrupt changes of ∼30 km under.the central Betics and northern Morocco. Our observations support a geodynamic scenario.where in western Betics oceanic subduction has developed into ongoing continental subduction/delamination while in eastern Betics this process is inactive

IBERARRAY: The seismic component of the TopoIberia research Project

Iberarray, componente sísmica del proyecto TopoIberia, está formada por una red densa de estaciones sísmicas de banda ancha y alta resolución a semejanza del USarray del proyecto Earthscope. Los objetivos que se persiguen con la instalación de Iberarray es estudiar la relación que existe entre los procesos que tienen lugar a escala litosférica y en la corteza de la península Ibérica, mar de Alborán y norte de Marruecos. Esta red está dedicada fundamentalmente a generar una base de datos de formas de onda con una resolución sin precedentes en una zona de especial interés geodinámico como es la región del contacto de placas continentales de Eurasia y Africa. Esta red está ya instalada en su primera fase, hasta 38.5º de Latitud, conformando una malla de 50x50 km entre estaciones. Iberarray está constituida por 50 estaciones de banda ancha más las aportaciones de las redes permanentes en la zona (IAG-UGR,ROA) y las redes portátiles del IAG-UGR y del ICT-CSIC. Iberarray es el brazo sísmico del proyecto multidisciplinar TopoIberia.Iberarray, the seismic component of the TopoIberia project, is a dense seismic array deployed following the spirit of the USarray of the US Earthscope project, with the aim of studying the link between the deep lithosphere processes and the crust in the Iberian peninsula, Alboran sea and north of Morocco. This network is dedicated to generate a large waveform and catalogue dataset with an unprecedented resolution in the area of the complex interaction between the Eurasia and Africa continental plates. In their first leg the Iberarray up to 38.5º latitude with a spatial grid of 50x50 km. Iberarrays is constituted by 50 broad band high resolution seismic stations plus the permanent broad band seismic stations of the seismic network operating in the region (IAG-UGR, ROA) and also the portable broad band stations of the IAG-UGR and ICT-CSIC. Iberarrays in the seismic branch of the multidisciplinary TopoIberia poroject.Ministerio de Economía y Competitividad (MINECO)Depto. de Geodinámica, Estratigrafía y PaleontologíaFac. de Ciencias GeológicasTRUEpu