Steady flows driven by sources of random strength in heterogeneous aquifers with application to partially penetrating wells

Average steady source flow in heterogeneous porous formations is modelled by regarding the hydraulic conductivity K(x) as a stationary random space function (RSF). As a consequence, the flow variables become RSFs as well, and we are interested into calculating their moments. This problem has been intensively studied in the case of a Neumann type boundary condition at the source. However, there are many applications (such as well-type flows) for which the required boundary condition is that of Dirichlet. In order to fulfill such a requirement the strength of the source must be proportional to K(x), and therefore the source itself results a RSF. To solve flows driven by sources whose strength is spatially variable, we have used a perturbation procedure similar to that developed by Indelman and Abramovich (Water Resour Res 30:3385–3393, 1994) to analyze flows generated by sources of deterministic strength. Due to the linearity of the mathematical problem, we have focused on the explicit derivation of the mean head distribution G _d (x) generated by a unit pulse. Such a distribution represents the fundamental solution to the average flow equations, and it is termed as mean Green function. The function G _d (x) is derived here at the second order of approximation in the variance σ² of the fluctuation (where K _A is the mean value of K(x)), for arbitrary correlation function ρ(x), and any dimensionality d of the flow domain. We represent G _d (x) as product between the homogeneous Green function G _d ⁽⁰⁾(x) valid in a domain with constant K _A , and a distortion term Ψ _d (x) = 1 + σ²ψ _d (x) which modifies G _d ⁽⁰⁾(x) to account for the medium heterogeneity. In the case of isotropic formations ψ _d (x) is expressed via one quadrature. This quadrature can be analytically calculated after adopting specific (e.g.. exponential and Gaussian) shape for ρ(x). These general results are subsequently used to investigate flow toward a partially-penetrating well in a semi-infinite domain. Indeed, we construct a σ²-order approximation to the mean as well as variance of the head by replacing the well with a singular segment. It is shown how the well-length combined with the medium heterogeneity affects the head distribution. We have introduced the concept of equivalent conductivity K ^eq(r,z). The main result is the relationship where the characteristic function ψ^(w)(r,z) adjusts the homogeneous conductivity K _A to account for the impact of the heterogeneity. In this way, a procedure can be developed to identify the aquifer hydraulic properties by means of field-scale head measurements. Finally, in the case of a fully penetrating well we have expressed the equivalent conductivity in analytical form, and we have shown that (being the effective conductivity for mean uniform flow), in agreement with the numerical simulations of Firmani et al. (Water Resour Res 42:W03422, 2006).     

Some Statistics of the Temperature Structure Parameter in the Convective Boundary Layer Observed by Sodar

The characteristics of the temporal and height variations of the temperature structure parameter $C_\mathrm{T}^{2}$ in strongly convective situations derived from the sodar echo-signal intensity measurements were analyzed for the first 100 m. It was corroborated that the probability density function (pdf) of the logarithm of $C_\mathrm{T}^{2}$ in the lower convective boundary layer is markedly non-Gaussian, whereas turbulence theory predicts it to be normal. It was also corroborated that the sum of two weighted Gaussians, which characterize the statistics of $C_\mathrm{T}^{2}$ within convective plumes and in their environment and the probability of plume occurrence, well approximates the observed pdfs. It was shown that the height behaviour of the arithmetic mean of $ C_\mathrm{T}^{2}$ (both total and within plumes) follows well a power law $C_\mathrm{T}^{2} (z) \sim z^{-q}$ with the exponent $q$ close to the theoretically predicted value of 4/3. But for the geometrical means of $C_\mathrm{T}^{2}$ (both total and within the plumes), $q$ is close to 1. The difference between arithmetically and geometrically averaged $C_\mathrm{T}^{2}$ profiles was analyzed. The vertical profiles of the standard deviation, skewness and kurtosis of $\hbox {ln}C_\mathrm{T}^{2}$ pdfs were analyzed to show their steady behaviour with height. The standard deviations of the logarithm of $C_\mathrm{T}^{2}$ within the plumes and between them are similar and are 1.5 times less than the total standard deviation. The estimate of the variability index $F_\mathrm{T}$ and its height behaviour were obtained, which can be useful to validate some theoretical and modelling predictions. The vertical profiles of the skewness and kurtosis show the negative asymmetry of pdfs and their flatness, respectively. The spectra of variations in $\hbox {ln}C_\mathrm{T}^{2}$ are shown to be satisfactorily fitted by the power law $f^{-\gamma } $ in the frequency range 0.02 and 0.2 Hz, with the average exponent $\approx $ 1.27  $\pm $  0.22.     

Relationships between ultrapotassic and carbonate-rich volcanic rocks in central Italy: petrogenetic and geodynamic implications

The Pleistocene intra-Apennine volcanic (IAV) centres occurring east of the potassium-rich Roman comagmatic province show variable petrological and geochemical composition. Some rocks have a strongly undersaturated ultrapotassic kamafugitic affinity with K₂O/Na₂O=8–20, whereas the rocks from the southern center of Mt. Vulture are still strongly undersaturated in silica but are enriched in both Na₂O and K₂O with K/Na around unity. Carbonate-rich pyroclastic rocks, believed to represent carbonatitic magmas, are found in the IAV centers. Kamafugites have high abundances of LILE and high LILE/HFSE ratios, and their incompatible element patterns resemble closely those of ultrapotassic rocks from the adjoining Roman province. The Vulture volcanics also display high contents of LILE, but their LILE/HFSE ratios are intermediate between intraplate alkaline rocks and kamafugites. The carbonate-rich rocks exhibit an exotic mineralogy and high enrichments in LILE, which speaks for a carbonatitic affinity. However, they have similar incompatible element patterns but consistently lower abundances of almost all the elements than the associated silicate volcanics. These data favour the hypothesis that the IAV carbonate rocks may represent mixtures of silicate magmas and geochemically depleted carbonate material. The sedimentary carbonates that crop out extensively along the Apennine chain may be the source of barren carbonate material. Overall, geochemical data of IAV centres and of the rocks from the Roman province display strong geochemical and isotopic evidence of being generated in an upper mantle that was modified by addition of upper crustal material brought down by subduction processes. A possible exception is represented by Mt. Vulture which, however, occurs east of the main axis of the Apennines, on the western margin of the foreland Adria plate. The occurrence of strongly undersaturated alkaline rocks requires magma generation at high pressures and . This is in agreement with the hypothesis that subduction processes under the Apennines occurred by consumption of poorly hydrated thinned or delaminated continental crust.     

On the shape and orientation of the tail of Comet Kohoutek (1973f)

Twenty-two photographs of Comet Kohoutek (1973f) have been projected onto the comet's orbital plane under the assumption of a flat tail confined in that plane. The comet has a mixed-type tail; therefore the results concerning Type I and Type II components of the tail are presented separately. The axis of the Type I tail appears to sweep back and forth with respect to the prolonged radius vector in a rather periodical way. Interpretations advanced by some authors for the analogous case of Comet Burnham (1959k) are mentioned briefly. For the Type II tail, a comparison with a theoretical tail model by Sekanina has allowed us to establish when the onset of appreciable dust production occurred. Finally, mention is made of the fact that some peculiarities of the dust tail might be also explained by assuming a three-dimensional model.     

Nature, distribution and origin of polycyclic aromatic hydrocarbons (PAHs) in the sediments of Olbia harbor (Northern Sardinia, Italy)

The nature, origin and distribution of US EPA polycyclic aromatic hydrocarbons (PAHs) in the sediments of Olbia harbor (North Sardinia, Italy) were investigated by gas-chromatography/mass spectrometry (GCMS). PAH concentrations in the sediments (SigmaPAHs) ranged from 0.16 to 0.77 microg g(-1), indicating a homogeneously low level of pollution. A rather exceptional prevalence of low molecular weight PAHs was substantiated: nearly 80% of SigmaPAHs include naphthalene (15.19%) and phenanthrene (64.47%). Carcinogenic compounds were present in very low (BaP, BkF, BaA and DBA) or negligible (BbF and Inp) concentrations. As indicated by the Phen/Ant molar ratio, the main source of PAHs is petrogenic, probably due to oil spills from shipping. The low/high molecular weight ratio (ranging between 1.2 and 26) distinguishes the sediments of the tourist harbor from those of the commercial/industrial harbor. Moreover, a slight but meaningful pyrolytic contribution to pollution was found in the tourist harbor, which has the most polluted sediments in the whole harbor. Finally, good linear correlations were found between a selected PAH (Phen and Naph) and selected sums of PAHs (i.e. the total amount of the other 15 US EPA and the sum of low molecular weight PAHs).     

The occurrence and significance of Pleistocene and Upper Pliocene sapropels in the Tyrrhenian Sea

Numerous sapropels and sapropelic strata from Upper Pliocene and Pleistocene hemipelagic sediments of the Tyrrhenian Sea show that intermittent anoxia, possibly related to strongly increased biological productivity, was not restricted to the eastern Mediterranean basins and may be a basin-wide result of Late Pliocene-Pleistocene climatic variability. Even though the sapropel assemblage of the Tyrrhenian Sea clearly originates from multiple processes such as deposition under anoxic conditions or during spikes in surface water productivity and lateral transport of organic-rich suspensates, many “pelagic sapropels” have been recognized. Stratigraphic ages calculated for the organic-rich strata recovered during ODP Leg 107 indicate that the frequency of sapropel formation increased from the lowermost Pleistocene to the base of the Jaramillo magnetic event, coinciding with a period when stable isotope records of planktonic foraminifera indicate the onset of climatic cooling in the Mediterranean. A second, very pronounced peak in sapropel formation occurred in the Middle to Late Pleistocene (0.73-0.26 Ma). Formainifers studied in three high-resolution sample sets suggest that changes in surface-water temperature may have been responsible for establishing anoxic conditions, while salinity differences were not noted in the faunal assemblage. However, comparison of sapropel occurrence at Site 653 with the oxygen isotopic record of planktonic foraminifers established by Thunell et al. (Proc. ODP, Sci. Results 107, 1990) indicates that sapropel occurrences coincide with negative δ¹⁸O excursions in planktonic foraminifers in thirteen of eighteen sapropels recognized in Hole 653A. A variant of the meltwater hypothesis accepted for sapropel formation in the Late Pleistocene eastern Mediterranean may thus be the cause of several “anoxic events” in the Tyrrhenian as well. Model calculations indicate that the amount of oxygen advection from Western Mediterranean Deep Water exerts the dominant control on the oxygen content in deep water of the Tyrrhenian Sea. Inhibition of deep-water formation in the northern Adriatic and the Balearic Basin by increased meltwater discharge and changing storm patterns during climatic amelioration may thus be responsible for sapropel formation in the Tyrrhenian Sea.     

Contamination risk of the Alburni Karst System (Southern Italy)

The Alburni massif (1742m a.s.l.) stretches NW–SE, about 23km long and 9–10km wide, covering 246km² with an average elevation of about 940m a.s.l. This massif, with more than 500 caves, is the most important karst area in southern Italy. The karst channel network is hierarchically organized: some channels feed a major spring (1m³/s) with a very short transit time while others communicate directly with the basal water table related to other springs (Q > 3m³/s).There are several dolines and swallow holes just above the basal water table and in the urbanized areas; for years a swallow hole directly transferred pollutants into the aquifer. The contamination vulnerability map shows that the prevalent vulnerability degree ranges from high to very high, due to the widespread karstification of the area and to the presence, on the plateau, of large vegetated areas with gentle slopes favouring fast infiltration.Hence it is important to ascertain the human impact on the area and the consequent contamination risk of the aquifer of the Alburni karst area. Three main layers were created to assess groundwater contamination risk: the vulnerability map, the hazard map, and the value map.The groundwater contamination risk map stresses the importance in a park area of aquifer vulnerability, which strongly influences the risk: indeed, the prevalent moderate degree of risk in the final map depends on the high vulnerability and the low hazard degree. However, in the future it is crucial to take into account the nature of the agricultural land use allowed in the park, which could increase the hazard degree and consequently the risk degree.     

Trace-element and Sr–Nd isotopic evidence for the origin of the Sardinian fluorite mineralization (Italy)

The fluorite-bearing hydrothermal mineralization in Sardinia mainly occurs within Paleozoic volcanic and metasedimentary rocks. Only 3 occurrences are located in volcanic and siliciclastic Cenozoic rocks. Most Sardinian fluorites exhibit relatively high rare earth and Y (REY) contents, strong positive Y anomalies, slightly negative Ce and generally positive Eu anomalies. These features indicate that the REY were mobilized mainly from non-carbonate rocks. Neither Sr nor Nd isotopes can be used to date radiometrically the Sardinian fluorites. However, the measured Sr-isotope ratios of the fluorites hosted by Paleozoic rocks fit mixing lines in the 1000/Sr versus ⁸⁷Sr/⁸⁶Sr plot once recalculated at 280 Ma, suggesting that the age inferred for the correction probably represents that of the formation of the fluorite mineralization. Mixing likely occurred between diluted surficial waters and brines circulating mainly through the Lower Paleozoic metasedimentary basement. The Cenozoic fluorites exhibit chemical and isotopic features similar to those of the Paleozoic fluorites, except the Nuraghe Onigu fluorite displaying a possible contribution of Sr from Cenozoic magmatic rocks. The initial ε_Nd values of the Paleozoic fluorites fit the age proposed for the formation of the deposits. Moreover, the values suggest that radiogenic Nd was provided to the fluids from the Ordovician siliciclastic basement, except for 3 deposits where the potential source rocks of Nd were mainly Ordovician acidic magmatic rocks. The initial ε_Nd values of the Cenozoic fluorites suggest a provenance of Nd essentially from the leaching of Variscan granitoids.