Construction of three-phase data to model multiphase flow in porous media: Comparing an optimization approach to the finite element approach

Multiphase flow modelling is a major issue in the assessment of groundwater pollution. Three-phase flows are commonly governed by mathematical models that associate a pressure equation with two saturation equations. These equations involve a number of secondary variables that reflect the fluid behaviour in a porous medium. To improve the computational efficiency of multiphase flow simulators, several simplified reformulations of three-phase flow equations have been proposed. However, they require the construction of new secondary variables adapted to the reformulated flow equations. In this article, two different approaches are compared to quantify these variables. A numerical example is given for a typical fine sand.     

Conjugate Points in the Gravitational n-Body Problem

In an effort to understand the nature of almost periodic orbits in the n-body problem (for all time t) we look first to the more basic question of the oscillatory nature of solutions of this problem (on a half-line, usually taken as R ⁺). Intimately related to this is the notion of a conjugate point(due to A. Wintner) of a solution. Specifically, by rewriting the mass unrestricted general problem of n-bodies in a symmetric form we prove that in the gravitational Newtonian n-body problem with collisionless motions there exists arbitrarily large conjugate points in the case of arbitrary (positive) masses whenever the cube of the reciprocal of at least one of the mutual distances is not integrable at infinity. The implication of this result is that there are possibly many Wintner oscillatorysolutions in these cases (some of which may or may not be almost periodic). As a consequence, we obtain sufficient conditions for all continuable solutions (to infinity) to be either unbounded or to allow for near misses (at infinity). The results also apply to potentials other than Newtonian ones. Our techniques are drawn from results in systems oscillation theory and are applicable to more general situations. Dedicated to the memory of Robert M. (Bob) Kauffman, formerly Professor of the University of Alabama in Birmingham     

Leucogranite intruding the South Tibetan Detachment in western Nepal: implications for exhumation models in the Himalayas

The most popular models regarding the exhumation of the Greater Himalayan Sequence (GHS), such as extrusion, channel flow, critical taper and wedge extrusion, require prolonged activity of the two bounding shear zones and faults, the Main Central Thrust (MCT) and the South Tibetan Detachment (STD). We present the crystallization age of an undeformed leucogranite that intrudes both the GHS and the Tethyan Himalaya Sequence (THS). Zircon and monazite U‐Pb ages in the leucogranite give ages between 23 and 25 Ma constraining, at that time, the end of shearing along the STD. Our results limit the contemporaneous activity of the MCT and STD to a short period of time (~1–2 Ma) and thus argue against exhumation models requiring prolonged contemporaneous activity of the MCT and STD.     

A GIS-based approach for gully erosion susceptibility modelling: a test in Sicily, Italy

The aim of this study is to analyze the susceptibility conditions to gully erosion phenomena in the Magazzolo River basin and to test a method that allows for driving the factors selection. The study area is one of the largest (225 km²) watershed of southern Sicily and it is mostly characterized by gentle slopes carved into clayey and evaporitic sediments, except for the northern sector where carbonatic rocks give rise to steep slopes. In order to obtain a quantitative evaluation of gully erosion susceptibility, statistical relationships between the spatial distributions of gullies affecting the area and a set of twelve environmental variables were analyzed. Stereoscopic analysis of aerial photographs dated 2000, and field surveys carried out in 2006, allowed us to map about a thousand landforms produced by linear water erosion processes, classifiable as ephemeral and permanent gullies. The linear density of the gullies, computed on each of the factors classes, was assumed as the function expressing the susceptibility level of the latter. A 40-m digital elevation model (DEM) prepared from 1:10,000-scale topographic maps was used to compute the values of nine topographic attributes (primary: slope, aspect, plan curvature, profile curvature, general curvature, tangential curvature; secondary: stream power index; topographic wetness index; LS-USLE factor); from available thematic maps and field checks three other physical attributes (lithology, soil texture, land use) were derived. For each of these variables, a 40-m grid layer was generated, reclassifying the topographic variables according to their standard deviation values. In order to evaluate the controlling role of the selected predictive variables, one-variable susceptibility models, based on the spatial relationships between each single factor and gullies, were produced and submitted to a validation procedure. The latter was carried out by evaluating the predictive performance of models trained on one half of the landform archive and tested on the other. Large differences of accuracy were verified by computing geometric indexes of the validation curves (prediction and success rate curves; ROC curves) drawn for each one-variable model; in particular, soil texture, general curvature and aspect demonstrated a weak or a null influence on the spatial distribution of gullies within the studied area, while, on the contrary, tangential curvature, stream power index and plan curvature showed high predictive skills. Hence, predictive models were produced on a multi-variable basis, by variously combining the one-variable models. The validation of the multi-variables models, which generally indicated quite satisfactory results, were used as a sensitivity analysis tool to evaluate differences in the prediction results produced by changing the set of combined physical attributes. The sensitivity analysis pointed out that by increasing the number of combined environmental variables, an improvement of the susceptibility assessment is produced; this is true with the exception of adding to the multi-variables models a variable, as slope aspect, not correlated to the target variable. The addition of this attribute produces effects on the validation curves that are not distinguishable from noise and, as a consequence, the slope aspect was excluded from the final multi-variables model used to draw the gully erosion susceptibility map of the Magazzolo River basin. In conclusion, the research showed that the validation of one-variable models can be used as a tool for selecting factors to be combined to prepare the best performing multi-variables gully erosion susceptibility model.     

Strain rates in the Alpine Mediterranean region: insights from advanced techniques of data processing

Strain rates and Euler poles for various subregions of the Alpine Mediterranean region were calculated by using global navigation satellite system data from permanent stations. The main scope of the study is to compare and analyze strain rate maps that were calculated using different approaches. This area presents a complex tectonic setting due to the interaction of the Eurasian and Nubian plates. The horizontal velocity gradient tensor was computed starting from a new set of site velocities determined by using continuous long-series geodetic data, state-of-the-art antenna calibrations and recomputed precise orbits. Geodesy provides velocities for a sparsely distributed, discrete number of sites, while deformation has a spatially continuous distribution. For this reason, the interpolation method and the geometric approach to the problem play a fundamental role in the estimation of the strain rate field. In the present study, principal deformation axes and principal angle were estimated by applying two different approaches: the Delaunay triangulation and a grid solution. Both methods produce results with broad coherence, providing new information about the deformation throughout the entire study area. Moreover, an evaluation and analysis of Euler poles related to the different velocity patterns, give complementary information to reconstruct the active deformation in the Mediterranean area.     

Monitoring, prediction, and early warning using ground-based radar interferometry

In order to define adequate prevention measures and to manage landslide emergencies, real-time monitoring is required. This paper presents two different applications of the remote sensing technique: the ground-based synthetic aperture radar interferometry, here proposed as a monitoring and early warning support for slope instability. Data acquisitions carried out through a ground-based synthetic aperture radar interferometer, operating in K_u band, installed in front of the observed slopes, are discussed. Two case studies, based on the use of the same apparatus (formerly developed by the Joint Research Center of the European Commission and by Ellegi-LiSALab srl), are reported: the first one concerns the monitoring of a large landslide, named Ruinon (Valfurva, Italy). The second one deals with the monitoring of the NW unstable slope in the Stromboli island aimed to implementing an early warning system. Acquired interferometric data are processed to provide displacements and velocity maps of the monitored area. The monitoring services ongoing on the Ruinon landslide and on Stromboli demonstrate the capability of this technique to operate in different operative settings (i.e., different phenomena and geological framework) and for different aims (monitoring for prevention, early warning, and emergency assessment). This methodology has also been proved by national and regional authorities of civil protection in order to provide a real-time monitoring for emergency management.     

Partial melting of ultrahigh-pressure metamorphic rocks at convergent continental margins: Evidences,melt compositions and physical effects

Ultrahigh-pressure(UHP) metamorphic rocks are distinctive products of crustal deep subduction,and are mainly exposed in continental subduction-collision terranes. UHP slices of continental crust are usually involved in multistage exhumation and partial melting, which has obvious influence on the rheological features of the rocks, and thus significantly affect the dynamic behavior of subducted slices. Moreover,partial melting of UHP rocks have significant influence on element mobility and related isotope behavior within continental subduction zones, which is in turn crucial to chemical differentiation of the continental crust and to crust-mantle interaction.Partial melting can occur before, during or after the peak metamorphism of UHP rocks. Post-peak decompression melting has been better constrained by remelting experiments; however, because of multiple stages of decompression, retrogression and deformation, evidence of former melts in UHP rocks is often erased. Field evidence is among the most reliable criteria to infer partial melting. Glass and nanogranitoid inclusions are generally considered conclusive petrographic evidence. The residual assemblages after melt extraction are also significant to indicate partial melting in some cases. Besides field and petrographic evidence, bulk-rock and zircon trace-element geochemical features are also effective tools for recognizing partial melting of UHP rocks. Phase equilibrium modeling is an important petrological tool that is becoming more and more popular in P-T estimation of the evolution of metamorphic rocks; by taking into account the activity model of silicate melt, it can predict when partial melting occurred if the P-T path of a given rock is provided.UHP silicate melt is commonly leucogranitic and peraluminous in composition with high SiO_2,low MgO, FeO, MnO, TiO_2 and CaO, and variable K_2 O and Na_2 O contents. Mineralogy of nanogranites found in UHP rocks mainly consists of plagioclase + K-feldspar + quartz, plagioclase being commonly albite-rich.Trace element pattern of the melt is characterized by significant enrichment of large ion lithophile elements(LILE), depletion of heavy rare earth elements(HREE) and high field strength elements(HFSE),indicating garnet and rutile stability in the residual assemblage. In eclogites, significant Mg-isotope fractionation occurs between garnet and phengite; therefore, Mg isotopes may become an effective indicator for partial melting of eclogites.     

Petrogenesis and geodynamic significance of silicic volcanism in the western Trans-Mexican Volcanic Belt: role of gabbroic cumulates

In the western Trans-Mexican Volcanic Belt voluminous silicic volcanism has been associated with the rifting of the Jalisco block from mainland Mexico. Rhyolitic volcanism started at 7.5 Ma after a major pulse of basaltic volcanism aged 11–8.5 Ma associated with slab detachment. This was followed by a second period, between 4.9 and 2.9 Ma, associated with rhyolitic domes and ignimbrite coexisting with basaltic volcanism. The similarity in rare earth element contents between basalts and rhyolites excludes a simple liquid line of descent. The low Ba and Sr contents and the ferroan character of the rhyolites suggest extensive fractional crystallization. Late Miocene–early Pliocene rhyolite Sr isotope values are only slightly more radiogenic than the basalts, whereas Nd isotope ratios are indistinguishable. We successfully modelled the 7.5–3 Ma silicic magmatism as a result of partial melting of crustal gabbroic complexes that we infer to have formed in the mid-lower crust due to the high-density Fe-enriched composition of the late Miocene basaltic volcanism. Slab rollback since ~7.5 Ma favoured decompression melting and arrival of additional mafic magmas that intruded in the lower crust. These basalts heated and melted the gabbroic complexes forming the silicic magmas, which subsequently underwent assimilation and fractional crystallization processes. The first silicic pulse was emplaced during a period of low tectonic activity. Extensional faulting since the Pliocene favours the eruption of both silicic magma and lesser amount of mafic lavas.