Fast computation of Hankel Transform using orthonormal exponential approximation of complex kernel function

The computation of electromagnetic (EM) fields, for 1-D layered earth model, requires evaluation of Hankel Transform (HT) of the EM kernel function. The digital filtering is the most widely used technique to evaluate HT integrals. However, it has some obvious shortcomings. We present an alternative scheme, based on an orthonormal exponential approximation of the kernel function, for evaluating HT integrals. This approximation of the kernel function was chosen because the analytical solution of HT of an exponential function is readily available in literature. This expansion reduces the integral to a simple algebraic sum. The implementation of such a scheme requires that the weights and the exponents of the exponential function be estimated. The exponents were estimated through a guided search algorithm while the weights were obtained using Marquardt matrix inversion method. The algorithm was tested on analytical HT pairs available in literature. The results are compared with those obtained using the digital filtering technique with Anderson filters. The field curves for four types (A-, K-, H-and Q-type) of 3-layer earth models are generated using the present scheme and compared with the corresponding curves obtained using the Anderson sc heme. It is concluded that the present scheme is more accurate than the Anderson scheme     

Arsenic, antimony and other toxic elements in the drinking water of Eastern Thessaly in Greece and its possible effects on human health

Twenty-six groundwater samples were collected from the Eastern Thessaly region and analysed by ICP-ES for these elements: Al, As, P, Pb, Zn, Mn, Fe, Cr, Sb, Cu, Na, Br, Cl, Si, Mg, Ag, Be, Bi, Dy, Er, Eu, Au, Ge, Ho, In, Ir, Os, Pt, Re, Rh, Ru, Lu, Hf, Hg, Tm, Zr and Nb. The objectives of the study were to assess the level of water contamination with respect to the EC and the USEPA health-based drinking water criteria. The geology of the studied area includes schists, amphibolites, marbles of Palaeozoic age, ophiolites, limestones of Triassic and Cretaceous age, Neogene and Quaternary deposits. The element ranges for groundwater samples are: Al 7–56 μg l⁻¹, As 1–125 μg l⁻¹, Br 6–60 μg l⁻¹, Cl 500–25,000 μg l⁻¹, Cr 1–6 μg l⁻¹, Cu 1–15 μg l⁻¹, Fe 10–352 μg l⁻¹, Mg 2,940–40,100 μg l⁻¹, Mn 0–8 μg l⁻¹, Na 3,650–13,740 μg l⁻¹, P 20–48 μg l⁻¹, Pb 0–7 μg l⁻¹, Sb 0–21 μg l⁻¹, Si 3,310–13,240 μg l⁻¹ and Zn 7–994 μg l⁻¹. The results of groundwater analyses from the region of Eastern Thessaly showed elevated concentrations of As and Sb. Factor analysis explained 77.8% of the total variance of the data through five factors. Concentration of Br, Cl, Mg, Na and Si is directly related to the presence of saltwater in the aquifer, so grouping of these variables in factor 1 probably reflects the seawater intrusion. Al, As and Sb are known to form complexes in the environment, so grouping of these elements in factor 2 indicates their similar geochemical behaviour in the environment. The high negative loading of Mn in factor 2 indicates the presence of manganese oxides–hydroxides in the study area. Pb and Zn are associated together in sulphide mineralisation; so grouping of these elements in factor 3 reflects the sulphide mineralization paragenesis in the Melivoia area. P and Cu are associated together in phosphate fertilizers; so grouping of these variables in factor 4 could be related to agricultural practices. Cr, Fe, Mn and Mg are associated together in iron and manganese oxides–hydroxides and the weathering products of the olivine of the ultrabasic rocks; so grouping of these elements in factor 5 reflects the lithology of the area. There is a natural contamination of groundwaters with elevated concentrations of As and Sb due to the presence of the arsenopyrite and stibnite mineralisation in the Melivoia, Sotiritsa and Ano Polydendri areas. Contamination over the health-based drinking water guidelines given by EC and EPA has been investigated from nine sampling sites out of 26 of Eastern Thessaly region.     

Geochronological constraints on the Legs Lake shear zone with implications for regional exhumation of lower continental crust, western Churchill Province, Canadian Shield

The Legs Lake shear zone marks the southeastern boundary of an extensive region (>20,000 km²) of high-pressure (0.8–1.5+ GPa) granulite-facies rocks in the western Churchill Province, Canada. The shear zone is one of the largest exhumation-related structures in the Canadian Shield and coincides with the central segment of the ∼2,800 km long Snowbird tectonic zone. The movement history of this shear zone is critical for the development of models for the exhumation history of the high-pressure region. We used electron microprobe U–Th–Pb dating of monazite with supplemental ID-TIMS U–Pb geochronology to place constraints on the timing of shear zone activity. Combining these and other data, we suggest that regional exhumation occurred during at least three distinct phases over an ∼150 million year period. The first phase involved high temperature decompression from ∼1.0 to 0.8–0.7 GPa shortly following 1.9 Ga peak metamorphism, possibly under an extensional regime. The second phase involved rock uplift and decompression of the hanging wall to 0.5–0.4 GPa during east-vergent thrusting across the Legs Lake shear zone at ca. 1.85 Ga. This phase was likely driven by early collision-related convergence in the Trans-Hudson orogen. The final phase of regional exhumation, involving the removal of 15–20 km of overburden from both footwall and hanging wall, likely occurred after ∼1.78 Ga and may have been related to regional extensional faulting.Electronic Supplementary Material Supplementary material is available to authorised users in the online version of this article at .     

Decarbonation reaction of magnesite in subducting slabs at the lower mantle

High-pressure and temperature experiments (28–62 GPa, and 1,490–2,000 K, corresponding to approximately 770–1,500 km depth in the mantle) have been conducted on a MgCO₃ + SiO₂ mixture using a laser-heated diamond anvil cell combined with analytical transmission electron microscope observation of the product phases to constrain the fate of carbonates carried on the subducting basalt into the lower mantle. At these conditions, the decarbonation reaction MgCO₃ (magnesite) + SiO₂ (stishovite) → MgSiO₃ (perovskite) + CO₂ (solid) has been recognized. This indicates that above reaction takes place as a candidate for decarbonation of the carbonated subducting mid ocean ridge basalts in the Earth’s lower mantle.     

Paleoproterozoic accretion in the Northeast Siberian craton: Isotopic dating of the Anabar collision system

Geochronological database considered in the work and characterizing the Anabar collision system in the Northeast Siberian craton includes coordinated results of Sm-Nd and Rb-Sr dating of samples from crustal xenoliths in kimberlites, deep drill holes, and bedrock outcrops. As is inferred, collision developed in three stages dated at 2200–2100, 1940–1760, and 1710–1630 Ma. The age of 2000–1960 Ma is established for substratum of mafic rocks, which probably originated during the lower crust interaction with asthenosphere due to the local collapse of the collision prism. Comparison of Sm-Nd and Rb-Sr isochron dates shows that the system cooling from ≈700 to ≈300°C lasted approximately 300 m.y. with a substantial lag relative to collision metamorphism and granite formation. It is assumed that accretion of the Siberian craton resulted in formation of a giant collision mountainous structure of the Himalayan type that was eroded by 1.65 Ga ago, when accumulation of gently dipping Meso-to Neoproterozoic (Riphean) platform cover commenced.     

Reliability Based Assessment of Shallow Foundations Using Mathcad

A reliability based method was used to design and analyse shallow foundations using first-order Taylor series approximation. The computer program Mathcad was used to facilitate all mathematical and computional efforts. This method is an effective tool to assist the foundation designers and analyists to investigate how reliable their designs or analyses are in relation to the ultimate bearing capacity of the foundations. The approach presented in this paper provides a reliable alternative for design and analysis of shallow foundations, rather than the conventional design methods, which employs the assumptions of a specified saftey factor. Several examples were presented for design and analysis of strip footings embedded in sandy soil, and rectangular and square footings analysis embedded in clayey soils. The program input and output of each example are also presented and discussed.     

Determination of specific yield using a water balance approach – case study of Torla Odha watershed in the Deccan Trap province, Maharastra State, India

Specific yield is an essential parameter for any groundwater management plan. Volumetric analysis in the domain of groundwater budgeting for the non-monsoon months has been undertaken for a typical watershed of the Deccan basalt province. The Torla Odha watershed covers an area of over 22 km² on a third-order tributary of the westerly flowing Bhima River. The watershed receives a normal annual rainfall of 643 mm. The entire water demand is supplied by dug wells, which penetrate a shallow aquifer. The specific yield was estimated by comparing the monthly net volume of water removed from the aquifer, with the volume of aquifer de-saturated, based on monthly water level data. The estimated specific yield ranges from 0.0019 in May to 0.0173 in November with an average value of 0.0093. A correlation of the groundwater levels with the detailed geology suggests that the higher specific yield value (0.017) corresponds to dewatering of the weathered zone within the shallow aquifer. The specific yield of the massive basalt immediately below the weathered zone varies from 0.0089 to 0.0103. The underlying vesicular basalt, which is dissected by sheet joints, has a relatively higher specific yield (0.0121). The massive basalt, which forms the base of the shallow aquifer system, has a lower specific yield from 0.0019 to 0.0022.

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Résumé Le débit spécifique est un paramètre essentiel pour tout plan de gestion des eaux souterraines. Les analyses volumétriques, dans le cadre des bilans hydriques des eaux en dehors des mois de mousson, ont été entreprises pour un bassin-versant typique de la province basaltique du Deccan. Le bassin-versant du Torla Odha couvre une superficie de 22 km², et alimente l’affluent du troisième ordre de la rivière Bhima, qui coule vers l’Ouest. La pluviométrie annuelle atteint 643 mm. Toute la demande en eau es assurée par des puits foncés pénétrant dans l’aquifère phréatique. Le débit spécifique a été estimé en comparant le volume net mensuel d’eau captée dans l’aquifère, avec le volume de l’aquifère dé-saturé, basé sur les données des niveaux piézométriques mensuels. Le débit spécifique estimé s’étend entre 0,0019 en Mai et 0.173 en Novembre; la moyenne se situe à 0,0093. Une corrélation entre les niveaux des eaux souterraines et la géologie, suggère que les débits spécifiques les plus importants (0,017) correspondent aux zones altérées de l’aquifère phréatique. Le débit spécifique du massif basaltique, immédiatement sous la zone altérée, varie entre 0,0089 et 0,0103. Le basalte vésiculaire, situé juste en dessous et traversé par des diaclases parallèles, possède un débit spécifique sensiblement plus élevé (0,0121). Le basalte massif, qui forme la base de l’aquifère phréatique, possède un débit spécifique moins important, compris entre 0,0019 et 0,0022.

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Resumen El rendimiento específico es un parámetro esencial para cualquier plan de manejo de aguas subterráneas. Se ha llevado a cabo el análisis volumétrico, en el entorno de balance de aguas subterráneas, para los meses sin monzón de una cuenca típica de la provincia de basaltos Deccan. La cuenca Rorla Odha cubre un área de 22 km² en un tributario de tercer orden del Río Bhima que fluye al oeste. La cuenca capta una lluvia anual normal de 643 mm. La totalidad de la demanda de agua es abastecida por pozos manuales que penetran un acuífero somero. Se estimó el rendimiento específico al comparar el volumen neto mensual de agua removido del acuífero con el volumen de agua de-saturado estimado a partir de datos de niveles de agua mensuales. Los valores estimados de rendimiento específico varían de 0.0019 en mayo a 0.0173 en noviembre con un valor promedio de 0.0093. La correlación de niveles de agua subterránea con la geología de detalle sugieren que el valor más alto (0.017) de rendimiento específico corresponden con el desaguado de la zona de intemperismo dentro del acuífero somero. El rendimiento específico del basalto masivo que se encuentra inmediatamente debajo de la zona de intemperismo varía de 0.0089 a 0.0103. El basalto vesicular subyacente, el cual está disectado por fracturas laminares, tiene un rendimiento específico relativamente más alto (0.0121). El basalto masivo, que forma la base del sistema de acuífero somero, tiene un rendimiento específico más bajo el cual varía de 0.0019 a 0.0022. Palabras clave: basalto Deccan. India. Rendimiento específico. Recarga de agua subterránea. Balance hídrico.

     

World-wide synthetic tide parameters for gravity and vertical and horizontal displacements

The response of the Earth’s crust to the direct effect of lunisolar gravitational forcing is known as the body tide. The body tide is superimposed by surface-loading forces due to the pressure of the periodically varying ocean tide acting on the Earth, called ocean tide loading (OTL). Both body tide and OTL can be decomposed into components of the same frequency known as tidal parameters. However, OTL is more complicated than body tides because of the dynamic effects of the ocean. Estimating OTL requires a model of the ocean tides and knowledge of the elastic properties of the solid Earth. Thus, synthetic tide parameters (amplitude factors and phase leads) have been developed here on a world-wide grid for gravity and positional displacements. The body tide contributions were added to the oceanic contribution to provide the Earth tide response. The accuracy and reliability of the synthetic tidal parameters have been estimated by comparing observed gravity and vertical-displacement tide parameters with those interpolated from our synthetic model, which shows good agreement. Tests also indicate that the synthetic tide parameters provide realistic gravimetric and displacements for practical use in tidal prediction.