Sinusoidal oscillations radiating from a cylindrical source in thermal conduction or groundwater flow: Closed‐form solutions

The diffusion equation governs thermal conduction and groundwater flow phenomena. In this paper, we study the two‐dimensional radial propagation of a sinusoidal perturbation radiating from a cylindrical source within an infinite slab of homogeneous material. The solution of this problem has several applications. For instance, it can be used to determine the hydraulic diffusivity of the subsurface based on measurements of the hydraulic head around a vertical well during its development. For thermal problems, it can be used to determine the thermal diffusivity based on measurements of the temperature distribution around a cylindrical heat source generating a sinusoidal power per unit length. In this paper, we present a comprehensive analytical solution of this problem and we compare these solutions with numerical solutions. Two approximate analytical solutions, which can be relevant in practice, are also presented. Finally, we give an upper bound for the survival time of the transient part of the solution and we provide an estimate of the radius of influence of the sinusoidal solicitation. Copyright © 2010 John Wiley & Sons, Ltd.     

The loess sequence of Dolní Věstonice,Czech Republic: A new OSL‐based chronology of the Last Climatic Cycle

The Dolní Věstonice loess section in the Czech Republic is well known for its high‐resolution loess–palaeosol sequence of the last interglacial–glacial climatic cycle (Upper Pleistocene). The loess section is situated in a climatic transition zone between oceanic and continental climates and is therefore of great value in reconstructing past regional climate conditions and their interaction with climate systems, in particular that of the North Atlantic. Based on a combination of optically stimulated luminescence (OSL) ages, stratigraphic field observations and magnetic susceptibility measurements, a chrono‐climatic interpretation of the Dolní Věstonice loess section is presented. To establish a reliable Upper Pleistocene chronology, a quartz OSL approach was applied for equivalent dose (D_e) determination. Monomineralic quartz extracts of three distinct grain sizes, fine (4–11 μm), middle (38–63 μm) and coarse (90–200 μm), were used and compared. Within error limits, the calculated OSL ages are the same for the different grain sizes, and the OSL ages are in stratigraphic order. The established OSL chronology is in agreement with a Weichselian litho‐ and pedostratigraphy. The Dolní Věstonice loess section is characterized by four pedosedimentary subsequences. At the base of the profile, subsequence I is characterized by a distinct Early Glacial soil complex, OSL‐dated to c. 110 to 70 ka, representing one of the most complete records of environmental change in the European loess belt. Subsequence II is allocated to the Lower Pleniglacial and is characterized by laminated sandy loess. Middle Pleniglacial subsequence III is represented by a brown soil complex, and is followed by the uppermost subsequence IV, characterized by a thick body of laminated sandy loess, indicating strong wind activity and a high sedimentation rate of more than ～1 mm a^?1 during the Upper Pleniglacial. According to the OSL chronology, as well as to the sedimentological and palaeopedological investigations, it is likely that the sequence at Dolní Věstonice has recorded most of the climatic events expressed in the NGRIP δ¹⁸O reference record between 110 and 70 ka.     

Fluid flow through the sedimentary cover in northern Switzerland recorded by calcite–celestite veins (Oftringen borehole,Olten)

Abundant veins filled by calcite, celestite and pyrite were found in the core of a 719 m deep borehole drilled in Oftringen near Olten, located in the north-western Molasse basin, close to the thrust of the Folded Jura. Host rocks are calcareous marl, argillaceous limestone and limestone of the Dogger and Malm. The δ¹⁸O values of vein calcite are lower than in host rock carbonate and, together with microthermometric data from fluid inclusions in vein calcite, indicate precipitation from a seawater-dominated fluid at average temperatures of 56–68°C. Such temperatures were reached at the time of maximum burial of the sedimentary pile in the late Miocene. The depth profile of δ¹³C and ⁸⁷Sr/⁸⁶Sr values and Sr content of both whole-rock carbonate and vein calcite show marked trends towards negative δ¹³C, high ⁸⁷Sr/⁸⁶Sr, and low Sr content in the uppermost 50–150 m of the Jurassic profile (upper Oxfordian). The ⁸⁷Sr/⁸⁶Sr of vein minerals is generally higher than that of host rock carbonate, up to very high values corresponding to Burdigalian seawater (Upper Marine Molasse, Miocene), which represents the last marine incursion in the region. No evidence for internally derived radiogenic Sr (clay minerals) has been found and so an external source is required. S and O isotope composition of vein celestite and pyrite can be explained by bacterial reduction of Miocene seawater sulphate. The available data set suggests the vein mineralization precipitated from descending Burdigalian seawater and not from a fluid originating in the underlying Triassic evaporites.     

Geostatistical approach for the assessment of the water reservoir capacity in arid regions: a case study of the Akdarya reservoir,Uzbekistan

The paper presents the results of a new geostatistical approach to generate bathymetric surface models from point measurement converted into continuous contour surfaces of reservoir bottoms in Uzbekistan. Sedimentation of reservoirs raises engineering, environmental and economical issues for the communities around the world in areas affected by a strong water deficit. Because of Uzbekistan’s arid climatic conditions, and uneven spatial and temporal water resources distribution, responsive and innovative water availability assessment surveys of all major water reservoirs are required. Bathymetric surveying is a traditional method that is carried out for the estimation of reservoir volumes and surface areas of the corresponding reservoir stages in order to assess the water availability. Volume and surface area differences derived from multiple surveys of a reservoir provide storage loss estimates over time due to sedimentation. However, two main factors, such as intensive field data measurement and post data-processing, often limit the frequency of these surveys. Alternatively, innovative depth measurement technologies coupled with contouring and surface mapping programs provide automated reservoir volume and surface area calculations. This significantly reduces time, workload and financial burdens for reservoir sedimentation projects. This research proposes the use of geostatistical approach to assess the reservoir sedimentation in the Akdarya reservoir of Uzbekistan. The geostatistical approach includes (semi-) variogram analysis and interpolation (kriging and simulations—turning bands) techniques predicting values at unsampled locations for generating digital bathymetric surface models of reservoir bottom conditions in order to calculate the volume and surface area at a given water elevation. The simulation enables to have range of reservoir volumes and surface areas with the same probability, in comparison to the kriging and traditional methods. This gives a real estimation of the resource availability for water operators to manage natural resources and hydraulic infrastructure in a sustainable manner.     

Analysis and Estimation of Multi-unit Deposits: Application to a Porphyry Copper Deposit

This work concerns mineral deposits consisting of geological bodies whose metal grades have different characteristics in terms of distribution and variogram, which means that estimating grades by ordinary kriging may produce unrealistic spatial continuity. This paper proposes a method based on the indicators of the geological objects (hereafter called units) and their product with the metal grade. This is illustrated by an application to a porphyry copper deposit. The aim of this paper is essentially to promote the use of variogram ratios to analyze and characterize deposits.     

A Leaky Aquifer below Champlain Sea Clay: Closed‐Form Solutions for Natural Seepage

Closed‐form solutions are proposed for natural seepage in semiconfined (leaky) aquifers such as those existing below the massive Champlain Sea clay layers in the Saint‐Lawrence River Valley. The solutions are for an ideal horizontal leaky aquifer below an ideal aquitard that may have either a constant thickness and a constant hydraulic head at its surface, or a variable thickness and a variable hydraulic head at its surface. A few simplifying assumptions were needed to obtain the closed‐form solutions. These have been verified using a finite element method, which did not make any of the assumptions but gave an excellent agreement for hydraulic heads and groundwater velocities. For example, the difference between the two solutions was smaller than 1 mm for variations in the 5 to 8 m range for the hydraulic head in the semiconfined aquifer. Note that fitting the hydraulic head data of monitoring wells to the theoretical solutions gives only the ratio of the aquifer and aquitard hydraulic conductivities, a clear case of multiple solutions for an inverse problem. Consequently, field permeability tests in the aquitard and the aquifer, and pumping tests in the aquifer, are still needed to determine the hydraulic conductivity values.     

Climatic variations in MIS 11 recorded by stable isotopes and trace elements in a French tufa (La Celle,Seine Valley)

Marine Isotope Stage (MIS) 11 palaeoclimate has so far been documented in marine and ice sheet isotopic records. However, excepting some lacustrine pollen records, very little is known about palaeoclimatic conditions in continental areas. This study uses geochemical records in calcareous tufa deposits from rivers as a basis for reconstructing temperate palaeoclimatic conditions. Tufa deposits are now proven to record high‐quality palaeoclimatic information in recent to Holocene deposits. Work on older interglacial tufas is just starting and in this paper we present the first comprehensive results from a MIS 11 tufa. The tufa comes from the Seine Valley (La Celle, northern France). Geochemical data in the tufa calcite are interpreted to record primarily air temperature (δ¹⁸O) and humidity (δ¹³C and Mg/Ca and Sr/Ca). The combined data identify a warm and wet climatic optimum followed by two temperature decreases associated with oscillations in humidity. These marked climatic variations recorded through the La Celle profile are strongly coherent with the palaeoenvironmental reconstructions from malacological data. The abrupt climatic and environmental events recorded could be related to short‐term degradation of vegetation cover in Europe, which is itself controlled by global palaeoclimatic events. Copyright © 2012 John Wiley & Sons, Ltd.     

An algorithm for interpolation in the pyramid domain‡

With the pyramid transform, 2D dip spectra can be characterized by 1D prediction‐error filters (pefs) and 3D dip spectra by 2D pefs. These filters, contrary to pefs estimated in the frequency‐space domain (ω, x) , are frequency independent. Therefore, one pef can be used to interpolate all frequencies. Similarly, one pef can be computed from all frequencies, thus yielding robust estimation of the filter in the presence of noise. This transform takes data from the frequency‐space domain (ω, x) to data in a frequency‐velocity domain (ω, u=ω·x) using a simple mapping procedure that leaves locations in the pyramid domain empty. Missing data in (ω, x) ‐space create even more empty bins in (ω, u) ‐space. We propose a multi‐stage least‐squares approach where both unknown pefs and missing data are estimated. This approach is tested on synthetic and field data examples where aliasing and irregular spacing are present.     

3D Reconstruction from SECCHI-EUVI Images Using an Optical-Flow Algorithm: Method Description and Observation of an Erupting Filament

SECCHI-EUVI telescopes provide the first EUV images enabling a 3D reconstruction of solar coronal structures. We present a stereoscopic reconstruction method based on the Velociraptor algorithm, a multiscale optical-flow method that estimates displacement maps in sequences of EUV images. Following earlier calibration on sequences of SOHO-EIT data, we apply the algorithm to retrieve depth information from the two STEREO viewpoints using the SECCHI-EUVI telescope. We first establish a simple reconstruction formula that gives the radial distance to the centre of the Sun of a point identified both in EUVI-A and EUVI-B from the separation angle and the displacement map. We select pairs of images taken in the 30.4 nm passband of EUVI-A and EUVI-B, and apply a rigid transform from the EUVI-B image in order to set both images in the same frame of reference. The optical flow computation provides displacement maps from which we reconstruct a dense map of depths using the stereoscopic reconstruction formula. Finally, we discuss the estimation of the height of an erupting filament.     

Imprint of North-Atlantic abrupt climate changes on western European loess deposits as viewed in a dust emission model

Western European loess sequences of the last glaciation (100,000–15,000 years BP) exhibit strong, cyclic variations of the sedimentation rate, which are coeval to the Greenland stadial/interstadial cycles and the Heinrich events. These North-Atlantic rapid climate changes appear, thus, as a potential cause for the sedimentation variations, via changes in dust intensity cycle. Here we make a first step in testing this hypothesis, by modelling the impact of the North-Atlantic abrupt climate variations on dust emission. Our dust emission calculations use meteorological fields generated by the LMDZ atmospheric general circulation model at a resolution down to 60 km over Western Europe. Three numerical experiments are run, representing a Greenland stadial, an interstadial and a Heinrich event. Orbital parameters and ice-sheet configuration correspond to conditions from Marine Isotope Stage 3 (60,000–25,000 years BP), a period characterized by strong millennial-scale climate variability. The only differences we impose in the boundary conditions regard the North-Atlantic surface temperature and sea-ice cover in the latitudinal band 30°–63°N. The changes in wind, precipitation, soil moisture and snow cover from one simulated state to another result in small differences in dust emission intensity. In contrast, when the inhibition of the aeolian erosion by vegetation is taken into account, the dust fluxes for the cold climate states (Greenland stadial and Heinrich event) become generally more than twice higher than those for the relatively warmer Greenland interstadial, in agreement with the loess data. These results support the hypothesis that the North-Atlantic millennial-scale variability is imprinted in Western European loess profiles, and point to vegetation changes as the main factor responsible for millennial-scale sedimentation variations. An analysis for the English Channel and southern North Sea areas, major potential dust sources, shows that the seasonality of dust emission is not controlled by the wind speed, as in modern large deserts, but by the surface conditions. Consequently, the dusty season lasts from late winter to early summer, with maximum activity in April–May, and is shifted towards summer when the climate is colder.