Tidal synchronization of an anelastic multi-layered body: Titan’s synchronous rotation

Tidal torque drives the rotational and orbital evolution of planet–satellite and star–exoplanet systems. This paper presents one analytical tidal theory for a viscoelastic multi-layered body with an arbitrary number of homogeneous layers. Starting with the static equilibrium figure, modified to include tide and differential rotation, and using the Newtonian creep approach, we find the dynamical equilibrium figure of the deformed body, which allows us to calculate the tidal potential and the forces acting on the tide generating body, as well as the rotation and orbital elements variations. In the particular case of the two-layer model, we study the tidal synchronization when the gravitational coupling and the friction in the interface between the layers is added. For high relaxation factors (low viscosity), the stationary solution of each layer is synchronous with the orbital mean motion (n) when the orbit is circular, but the rotational frequencies increase if the orbital eccentricity increases. This behavior is characteristic in the classical Darwinian theories and in the homogeneous case of the creep tide theory. For low relaxation factors (high viscosity), as in planetary satellites, if friction remains low, each layer can be trapped in different spin-orbit resonances with frequencies \(n/2,n,3n/2,2n,\ldots \). When the friction increases, attractors with differential rotations are destroyed, surviving only commensurabilities in which core and shell have the same velocity of rotation. We apply the theory to Titan. The main results are: (i) the rotational constraint does not allow us to confirm or reject the existence of a subsurface ocean in Titan; and (ii) the crust-atmosphere exchange of angular momentum can be neglected. Using the rotation estimate based on Cassini’s observation (Meriggiola et al. in Icarus 275:183–192, 2016), we limit the possible value of the shell relaxation factor, when a deep subsurface ocean is assumed, to \(\gamma _s\lesssim 10^{-9}\,\hbox {s}^{-1}\), which corresponds to a shell’s viscosity \(\eta _s\gtrsim 10^{18}\,\hbox {Pa}\,\hbox {s}\), depending on the ocean’s thickness and viscosity values. In the case in which a subsurface ocean does not exist, the maximum shell relaxation factor is one order of magnitude smaller and the corresponding minimum shell’s viscosity is one order higher.     

The effect of the earth's rotation on ground water motion

The average pore velocity of ground water according to Darcy's law is a function of the fluid pressure gradient and the gravitational force (per unit volume of ground water) and of aquifer properties. There is also an acceleration exerted on ground water that arises from the Earth's rotation. The magnitude and direction of this rotation-induced force are determined in exact mathematical form in this article. It is calculated that the gravitational force is at least 300 times larger than the largest rotation-induced force anywhere on Earth, the latter force being maximal along the equator and approximately equal to 34 N/m(3) there. This compares with a gravitational force of approximately 10(4) N/m(3).     

横向非均匀地球负荷问题的CLFE有限元算法的有效性

本文设计了三个数值算例分别模拟径向分层黏弹地球对二阶球谐负荷、均厚圆盘负荷和全球末次冰期真实冰负荷的响应.利用耦合位扰动Laplace方程的三维有限元法(CLFE),计算出地球表面的位移、大地水准面的变化、冰后海平面变化和这些量的现今变化速率,并将其结果与传统谱方法的结果进行对比.结果表明,两种方法的结果总体上表现出良好的一致性,因此,CLFE方法被证实是正确的、有效的、能被用于研究地幔横向非均匀性的影响.值得注意的是,新的方法完全没有横向非均匀小扰动假设的限制.     

A 40 ka record of temperature and permafrost conditions in northwestern Europe from noble gases in the Ledo‐Paniselian Aquifer (Belgium)

The Ledo‐Paniselian Aquifer in Belgium offers unique opportunities to study periglacial groundwater recharge during the Last Glacial Maximum (LGM), as it was located close to the southern boundary of the ice sheets at that time. Groundwater residence times determined by ¹⁴C and ⁴He reveal a sequence of Holocene and Pleistocene groundwaters and a gap between about 14 and 21 ka, indicating permafrost conditions which inhibited groundwater recharge. In this paper, a dataset of noble gas measurements is used to study the climatic evolution of the region. The derived recharge temperatures indicate that soil temperatures in the periods just before and after the recharge gap were only slightly above freezing, supporting the hypothesis that permafrost caused the recharge gap. The inferred glacial cooling of 9.5°C is the largest found so far by the noble gas method. Yet, compared to other palaeoclimate reconstructions for the region, recharge temperatures deduced from noble gases for the cold periods tend to be rather high. Most likely, this is due to soil temperatures being several degrees higher than air temperatures during periods with extended snow cover. Thus the noble‐gas‐derived glacial cooling of 9.5°C is only a lower limit of the maximum cooling during the LGM. Some samples younger than the recharge gap are affected by degassing, possibly related to gas production during recharge in part of the recharge area, especially during times of melting permafrost. The findings of this study, such as the occurrence of a recharge gap and degassing related to permafrost and its melting, are significant for groundwater dynamics and geochemistry in periglacial areas. Copyright © 2010 John Wiley & Sons, Ltd.     

Paleomagnetic evidence for large en-bloc rotations in the Eastern Alps during Neogene orogeny

We present new paleomagnetic data from the Northern Calcareous Alps and the Central Alps of Austria. All new data are overprint magnetizations and can be subdivided into two groups: In rocks older than earliest Rupelian, two remagnetizations reflecting both clockwise and counter-clockwise rotation were detected. In rocks of late Rupelian and younger ages, only a counter-clockwise rotated remagnetization was found. Our results together with results from previous paleomagnetic studies from the Eastern and Southern Alps suggest two main phases of vertical axis rotation. The first, clockwise rotation affecting the Northern Calcareous Alps was active between earliest to Late Rupelian. We propose a model where the Northern Calcareous Alps are segmented into individual blocks. Within a dextral shear corridor these blocks rotated clockwise due to the counter-clockwise rotation of the Southern Alps and Central Alps. The second, counter-clockwise rotation occurred in the Late Oligocene to Middle Miocene, affecting Eastern and Southern Alps. In this stage of orogeny, the internal massifs of the Western Alps were already accreted to the upper plate and therefore included in counter-clockwise rotation. This rotation is contemporaneous with counter-clockwise rotation in the Apennines and opening of the Balearic basin, and a genetic relationship is suggested. A second step of counter-clockwise rotation, reconstructed from published data, is observed in the sedimentary basins at the southeastern margin of the Eastern Alps, where counter-clockwise rotated Miocene and Pliocene sedimentary rocks are present. This rotation is seen in connection to a young counter-clockwise rotation of the Adriatic plate.     

Surface water quality in a sulfide mineral‐rich arid zone in North‐Central Chile: Learning from a complex past,addressing an uncertain future

This study presents an analysis of up to 30 years of hydrological variables and selected water quality parameters (pH, SO₄, Fe, Cu, and As) in the upper area of the Elqui River basin in North‐Central Chile. A correlation analysis determined statistically significant positive relationship for SO₄‐Cu, Fe‐As, and Fe‐Cu. In terms of historical behaviour, no statistically significant trends were detected for precipitation or temperature. In contrast, for flow, there is an overall decreasing pattern for the entire area of study, although only in one case this trend was statistically significant. Along with the aforementioned analysis, a characterization of the flow‐water quality relationships is considered for the time period analyzed. Although erratic behaviours were confirmed, a negative (i.e., inverse) flow‐concentration relationship was identified for SO₄, a positive (i.e., direct) relationship for Fe, and undefined relationships for As and Cu were obtained. From these analyses and based on previous studies on projections regarding climate change for the Andean region, and in particular for the upper Elqui zone, an estimation of the possible effects of the change in water regimes on water quality in the area of study is developed. It is likely that a decrease in surface flow, as a consequence of climate change could translate into improvements in water quality in terms of Fe and eventually As and Cu, but into an impairment in the case of SO₄. In any case, this is a complex situation that demands special attention in the face of industrial activities that could be developed in tributaries like the Claro River, which currently play an important role in depurating or diluting contaminants in the waters of the Elqui River. Finally, it should be noted that this study addresses an issue that goes beyond the local interest and could be used as a reference to compare other transitional environments containing sulphide ores or areas of hydrothermal alterations, which are considered to be highly vulnerable to climate change and variability.     

Sedimentological analysis of the tephra from the 12–15 August 1991 eruption of Hudson volcano

The tephra fallout from the 12–15 August 1991 explosive eruption of Hudson volcano (Cordillera de los Andes, 45°54 S-72°58 W; Chile) was dispersed on a narrow, elongated ESE sector of Patagonia, covering an area (on land) of more than 100 000 km². The elongated shape of the deposit, together with the relatively coarse mean and median values of the particles at a considerable distance from the vent, were the result of strong winds blowing to the southeast during the eruption. The thickness of the fall deposit decreases up to 250 km ESE from Hudson volcano, where it begins to thicken again. Secondary maxima are well developed at approximately 500 km from the vent. Secondary maxima, together with grainsize bimodality in individual layers and in the bulk deposit suggest that particle aggregation played an important role in tephra sedimentation. The fallout deposit is well stratified, with alternating fine-grained and coarsegrained layers, which is probably a result of strong eruptive pulses followed by relatively calm periods and/or changes in the eruptive style from plinian to phreatoplinian. The tephra is mostly composed of juvenile material: the coarse mode (mostly pumice) shifts to finer sizes with distance from the volcano; the fine mode (mostly glass shards) is always about 5/6 phi. Glass shards and pumice are mostly light gray to colorless. However, considerable amounts of dark, poorly vesiculated, blocky shards, suggest a hydromagmatic component in the eruption. A land-based tephra volume of 4.35 km³ was estimated, and a total volume of 7.6 km³ arose from an extrapolation, which took into account the probable volume sedimented in the sea. Bulk density ranges from 0.9 to 1.10 gr/cm³ (beyond 110 km from the vent). Rather uniform density values measured in crushed samples (2.45–2.50 gr/cm³ at all distances from the vent) reveal a relatively homogeneous composition. Mean and median sizes decrease rapidly up to 270 km from the vent; beyond that point they are more or less constant, whereas the maximum size (1 phi) shows a steady decrease up to 550 km. A concomitant improvement in sorting is observed. This is attributed to sorting due to wind transport combined with particle aggregation at different times and distances from the vent. The Hudson tephra fallout shares some strikingly similar features with the Mount St. Helens (18 May 1980) and Quizapu (1932) eruptions.     

Aquifer storage capacity and maximum annual yield from long-term aquifer fluxes

Long-term time series data of aquifer recharge, groundwater extraction, and discharge are used to estimate aquifer storage capacity and maximum annual yield. Aquifer storage capacity is defined as the maximum volume of water that can be stored in an aquifer. It is estimated using a transient water-balance approach. The maximum annual yield is defined as the maximum combined groundwater extraction plus discharge that can be sustained in an aquifer judged by the historical record of recharge. It is determined according to a graphical mass-curve method. These two quantities are useful in aquifer characterization and groundwater management, the apportionment of groundwater rights and aquifer storage and recovery operations being two frequent applications. Time series data from the Edwards Aquifer, Texas, USA, illustrate the application of the methods presented.

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Résumé Des données sur le long terme de la recharge d’aquifère, de l’exploitation de l’eau souterraine et de la vidange sont utilisées pour estimer la capacité d’emmagasinement de l’aquifère et la capacité annuelle maximum. La capacité d’emmagasinement de l’aquifère est définit comme le volume maximum de l’eau qui peut être emmagasinée dans le réservoir. Elle est estimée en utilisant une approche par bilan hydrologique en transitoire. La capacité annuelle maximum est définit comme la combinaison de l’extraction de l’eau souterraine et de la vidange, combinaison qui peut être jugée durable ou non au regard de l’examen des valeurs de recharge. Elle est déterminée au moyen d’une méthode de courbe des valeurs cumulées. Ces deux quantités sont très utiles pour caractériser les aquifères et pour gérer les eaux souterraines, l’imputation des droits aux eaux souterraines, et du fait que les opérations de recharge des aquifères et de récupération sont très fréquentes. Les données temporelles provenant de l’aquifère Edwards, Texas, USA, illustrent l’application de la méthode présentée.

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Resumen Para estimar la capacidad de almacenamiento de un acuífero y su rendimiento máximo anual, se han utilizado series temporales largas de datos de recarga al acuífero, de extracciones de agua subterránea y de descarga. La capacidad de almacenamiento de un acuífero se define como el volumen máximo de agua que puede ser almacenado en el mismo. Se estima utilizando una aproximación con un balance de agua en régimen transitorio. El rendimiento máximo anual se define como el máximo resultante de la combinación de la extracción de aguas subterráneas y la descarga que puede ser sostenido por un acuífero según los registros históricos de recarga y se define según un método gráfico masa-curva. Estos dos valores son útiles en la caracterización de los acuíferos y en la gestión de las aguas subterráneas, el reparto de los derechos sobre las aguas subterráneas y las operaciones de almacenaje y recuperación de los acuíferos, que son dos aplicaciones frecuentes. Las series de tiempo para el Acuífero Edwards, Texas, USA, ilustra la aplicación de los métodos presentados.

     

Evidence for recent warming from perturbed geothermal gradients: examples from eastern Canada

Recent variations of the surface temperature of the Earth can be inferred from borehole temperature measurements. Generalized inversion is used to extract the information from the data; the potential of the method is evaluated. Tests were performed with synthetic data to demonstrate the effectiveness of the inversion to recover the gross features of the surface temperature history even when the data are affected by noise and errors. The tests show that it is possible to reconstruct the long term changes in ground temperature during the past 300 years; the resolution decreases with time, in particular if noise and errors must be filtered. Temperature logs, obtained in eastern Canada, and not suspected of being affected by non-climatic factors, have been inverted. The analysis confirms that eastern Canada has experienced warming by 1 to 2°C over the past 100–200 years. The relationship between air and ground temperatures has been examined. In eastern Canada ground temperature follows air temperature closely in summer but stays well above air temperature in winter. The number of days with snow on the ground correlates with the difference between annual mean ground and air temperature.Contribution to Clima Locarno — Past and Present Climate Dynamics; Conference September 1990, Swiss Academy of Sciences — National Climate-Program