A continuous/discontinuous Galerkin framework for modeling coupled subsurface and surface water flow

We consider conjunctive surface-subsurface flow modeling, where surface water flow is described by the shallow water equations and ground water flow by Richards’ equation for the vadose zone. Coupling between the models is based on the continuity of flux and water pressure. Numerical approximation of the coupled model using the framework of discontinuous Galerkin (DG) methods is formulated. In the subsurface, the local discontinuous Galerkin (LDG) method is used to approximate ground water velocity and hydraulic head; a DG method is also used to approximate surface water velocity and elevation. This approach allows for a weak coupling of the models and the use of different approximating spaces and/or meshes within each regime. A simplified LDG method based on continuous approximations to water head is also described. Numerical results that investigate physical and numerical aspects of surface–subsurface flow modeling are presented. This work was supported by National Science Foundation grant DMS-0411413.     

A coupling of mixed and discontinuous Galerkin finite-element methods for poroelasticity

In this paper, we formulate a finite-element procedure for approximating the coupled fluid and mechanics in Biot’s consolidation model of poroelasticity. We approximate the flow variables by a mixed finite-element space and the displacement by a family of discontinuous Galerkin methods. Theoretical convergence error estimates are derived and, in particular, are shown to be independent of the constrained specific storage coefficient, c _o . This suggests that our proposed algorithm is a potentially effective way to combat locking, or the nonphysical pressure oscillations, which sometimes arise in numerical algorithms for poroelasticity.     

Groundwater resources in the Jabal Al Hass region,northwest Syria: an assessment of past use and future potential

In many cases, the development of groundwater resources to boost agricultural production in dry areas has led to a continuous decline in groundwater levels; this has called into question the sustainability of such exploitation. In developing countries, limited budgets and scarce hydrological data often do not allow groundwater resources to be assessed through groundwater modeling. A case study is presented of a low-cost water-balance approach to groundwater resource assessments in a 1,550 km² semi-arid region in northwestern Syria. The past development of irrigated agriculture and its effect on the groundwater system were studied by analysis of Landsat images and long-term groundwater level changes, respectively. All components of the groundwater balance were determined. Groundwater recharge was estimated using the chloride mass balance method. Over the past three decades, groundwater levels have declined, on average, 23 m, coinciding with a two-fold increase in the groundwater-irrigated area. Groundwater resources are currently depleted by a value that lies between 9.5×10⁶ and 118×10⁶ m³ year^?1, which is larger than can be compensated for by a future decrease in natural discharge or changes in boundary conditions. However, groundwater resources are likely to be sufficient to supply domestic and livestock needs in the area.     

Fractional crystallization models and B–Be–Li systematics at Mt Somma-Vesuvius volcano (Southern Italy)

A compilation of B–Be–Li data on rocks that cover the entire eruptive history of Somma-Vesuvius is presented and interpreted in the light of evolution models for the Somma-Vesuvius rocks. Using major and trace element data, fractional crystalllization models are presented for different geochemical units. These data were used to constrain the source mineralogy of the Somma-Vesuvius rocks (ol-opx-cpx-gar-amp of 0.4-0.3-0.1-0.1-0.1), the amount of sediment added (5–10%) and the melt fraction from batch partial melting computations (0.05–0.1). From the B–Li data it is inferred that the main process responsible for the B isotopic signature is sediment recycling. However, the B–Li data show a major variation in Li abundances respect to B which is explained with Li dehydration before the fluid enriched the mantle wedge that produced the arc magmas. The Somma-Vesuvius B isotope composition is intermediate between that of the Campi Flegrei and the broad field of the Eolian Island arc. A low Be isotopes in the recent volcanic rocks can be explained as: (a) the top 1–22 m of the incoming sediment is accreted, (b) large amounts of sediment erosion, (c) a slow rate of subduction which have provoked a long magmatic history for the Vesuvius magma, (d) the sediment component takes several Myr longer than the subducting plate to reach the magma source region beneath Italy.     

Heat flow and crustal thermal structure in the Late Archaean Closepet Granite batholith,south India

The Late Archaean Closepet Granite batholith in south India is exposed at different crustal levels grading from greenschist facies in the north through amphibolite and granulite facies in the south along a ∼400 km long segment in the Dharwar craton. Two areas, Pavagada and Magadi, located in the Main Mass of the batholith, best represent the granitoid of the greenschist and amphibolite facies crustal levels respectively. Heat flow estimates of 38 mW m⁻² from Pavagada and 25 mW m⁻² from Magadi have been obtained through measurements in deep (430 and 445 m) and carefully sited boreholes. Measurements made in four boreholes of opportunity in Pavagada area yield a mean heat flow of 39 ± 4 (s.d.) mW m⁻², which is in good agreement with the estimate from deep borehole. The study, therefore, demonstrates a clear-cut heat flow variation concomitant with the crustal levels exposed in the two areas. The mean heat production estimates for the greenschist facies and amphibolite facies layers constituting the Main Mass of the batholith are 2.9 and 1.8 μW m⁻³, respectively. The enhanced heat flow in the Pavagada area is consistent with the occurrence of a radioelement-enriched 2-km-thick greenschist facies layer granitoid overlying the granitoid of the amphibolite facies layer which is twice as thick as represented in the Magadi area. The crustal heat production models indicate similar mantle heat flow estimates in the range 12–14 mW m⁻², consistent with the other parts of the greenstone-granite-gneiss terrain of the Dharwar craton.     

The Meso-Cenozoic thermo-tectonic evolution of the Eastern Pyrenees: an <Superscript>40</Superscript>Ar/<Superscript>39</Superscript>Ar fission track and (U–Th)/He thermochronological study of the Canigou and Mont-Louis massifs

Vertical displacements on the SW–NE Têt fault (Eastern Pyrenees Axial Zone, France), which separates the Variscan Canigou-Carança and Mont-Louis massifs, were constrained using a thermochronologic multi-method approach. ⁴⁰Ar/³⁹Ar data from the granitic Mont-Louis massif record its Variscan cooling history and reveal no ages younger than Early Cretaceous, while the Canigou-Carança gneiss massif records systematically younger ⁴⁰Ar/³⁹Ar ages. These younger ⁴⁰Ar/³⁹Ar ages in the Canigou-Carança gneiss massif are the result of partial to total rejuvenation of argon isotopic systems related to a thermal flow coeval with the Cretaceous HT-BP metamorphism in the North Pyrenean Zone. Only the deepest rocks from the Canigou-Carança suffered this extensive Mid-Cretaceous thermal overprint probably due to differential burial around 4 km at that time. The post Mid-Cretaceous vertical displacements along the Têt fault are recorded by “low” temperature thermochronology using K-feldspar ⁴⁰Ar/³⁹Ar, zircon and apatite fission track and (U–Th)/He datings. The Mont-Louis granite samples experienced a long period of protracted cooling reflecting a lack of thermo-tectonic activity in this area from Late Palaeozoic to Early Cenozoic, followed by cooling from 55–60 Ma to Late Eocene at a mean rate of 15–20°C/Ma in the final stage. This cooling stage corresponds to Têt fault reactivation with a reversed component, promoting exhumation of the Mont-Louis roof zone contemporaneously with the south-vergent Pyrenean thrusting. In the Canigou-Carança massif, the main cooling event occurred from 32 to 18 Ma at a maximum rate of 30°C/Ma during Early Oligocene followed by a more moderate rate of 3°C/Ma from Late Oligocene to Early Burdigalian, coeval with the normal reactivation of the Têt fault in brittle conditions that accommodated the final exhumation of the massif during the opening of the Gulf of Lion.     

Provenance of late Palaeozoic metasediments of the Patagonian proto-Pacific margin (southernmost Chile and Argentina)

In this provenance study of late Palaeozoic metasediments of the Eastern Andean Metamorphic Complex (EAMC) along the south Patagonian proto-Pacific margin of Gondwana, the palaeogeological setting of the continental margin in Devonian–Carboniferous and Permian times is reconstructed. The study is based on detrital heavy mineral contents, chemical compositions of tourmaline grains, and whole rock element and Nd-Sr isotopic compositions. Element and isotopic compositions reveal that Devonian–Carboniferous metaturbidites deposited before the development of a Late Carboniferous–Permian magmatic arc along the margin were mainly fed from felsic, recycled, old continental rocks. The last recycling phase involved erosion of metasediments that were exposed in Patagonia. Feeder systems to the basin cut either through epidote-rich or garnet-rich metasediments. In Permian time, EAMC metaturbidites were deposited next to the evolving magmatic arc and were derived from felsic, crustal rocks. Two provenance domains are recognised. The metasediments of the northern one are chemically similar to those of the Devonian–Carboniferous metasediments. This domain was fed from the metasedimentary host rocks of the magmatic arc. The southern domain probably was fed from the arc proper, as indicated mainly by the dominance of metaplutonic lithic fragments, abundant detrital biotite, and the major element composition of the metasediments.     

High heat flow anomalies on an old oceanic plate observed seaward of the Japan Trench

Thirty-three new measurements on the seaward slope and outer rise of the Japan Trench along a parallel of 38°45′N revealed the existence of high heat flow anomalies on the subducting Pacific plate, where the seafloor age is about 135 m.y.. The most prominent anomaly with the highest value of 114 mW/m² is associated with a small mound on the outer rise, which was reported to be a kind of mud volcano. On the seaward slope of the trench, heat flow is variable: high (70–90 mW/m²) at some locations and normal for the seafloor age (about 50 mW/m²) at others. The spatial variation of heat flow may be related to development of normal faults and horst/graben structures due to bending of the Pacific plate before subduction, with fluid flow along the fault zones enhancing the vertical heat transfer. Possible heat sources of the high heat flow anomalies are intra-plate volcanism in the last several million years like that discovered recently on the Pacific plate east of the Japan Trench.     

Estimates of heat flow and heat production and a thermal model of the São Francisco craton

An updated analysis of geothermal data from the highland area of eastern Brazil has been carried out and the characteristics of regional variations in geothermal gradients and heat flow examined. The database employed includes results of geothermal measurements at 45 localities. The results indicate that the Salvador craton and the adjacent metamorphic fold belts northeastern parts of the study area are characterized by geothermal gradients in the range of 6–17°C/km. The estimated heat flow values fall in the range of 28–53 mW/m², with low values in the cratonic area relative to the fold belts. On the other hand, the São Francisco craton and the intracratonic São Francisco sedimentary basin in the southwestern parts are characterized by relatively higher gradient values, in the range of 14–42°C/km, with the corresponding heat flow values falling in the range of 36–89 mW/m². Maps of regional variations indicate that high heat flow anomaly in the São Francisco craton is limited to areas of sedimentary cover, to the west of the Espinhaço mountain belt. Crustal thermal models have been developed to examine the implications of the observed intracratonic variations in heat flow. The thermal models take into consideration variation of thermal conductivity with temperature as well as change of radiogenic heat generation with depth. Vertical distributions of seismic velocities were used in obtaining estimates of radiogenic heat production in crustal layers. Crustal temperatures are calculated based on a procedure that makes simultaneous use of the Kirchoff and Generalized Integral Transforms, providing thereby analytical solutions in 2D and 3D geometry. The results point to temperature variations of up to 300°C at the Moho depth, between the northern Salvador and southern São Francisco cratons. There are indications that differences in rheological properties, related to thermal field, are responsible for the contrasting styles of deformation patterns in the adjacent metamorphic fold belts.