semi analytical solution for flow in a leaky unconfined aquifer toward a partially penetrating pumping well summary a semi analytical solution is presented for the problem of flow in a system consisting of unconfined and confined aquifers separated by an aquitard the unconfined aquifer is pumped continuously at a constant rate from a well of infinitesimal radius that partially penetrates its saturated thickness the solution is termed semi analytical because the exact solution obtained in double laplace hankel transform space is inverted numerically the solution presented here is more general than similar solutions obtained for confined aquifer flow as we do not adopt the assumption of unidirectional flow in the confined aquifer typically assumed to be horizontal and the aquitard typically assumed to be vertical model predicted results show significant departure from the solution that does not take into account the effect of leakage even for cases where aquitard hydraulic conductivities are two orders of magnitude smaller than those of the aquifers the results show low sensitivity to changes in radial hydraulic conductivities for aquitards that are two or more orders of magnitude smaller than those of the aquifers in conformity to findings of earlier workers that radial flow in aquitards may be neglected under such conditions hence for cases were aquitard hydraulic conductivities are two or more orders of magnitude smaller than aquifer conductivities the simpler models that restrict flow to the radial direction in aquifers and to the vertical direction in aquitards may be sufficient however the model developed here can be used to model flow in aquifer aquitard systems where radial flow is significant in aquitards a 2008 elsevier b v all rights reserved

near 5 day nonisostatic response to atmospheric surface pressure and coastal trapped waves observed in the northern south china sea abstractoceanic nonisostatic responses to near 5 day rossby haurwitz atmospheric pressure waves have been observed in open oceans however such responses based on observations in marginal seas such as the south china sea have not been reported owing to the limited ocean bottom pressure pbot records the pbot measurements from pressure recording inverted echo sounders piess at sites in the northern south china sea revealed a nonisostatic like response near 5 days although the coastal trapped waves ctws appeared to obscure it because their broadband periods include the near 5 day band cross spectral analysis revealed that the pies pbot records and the sea level sl records of hong kong all correlate strongly with the atmospheric pressure and winds over the east china sea this is indicative of remotely forced ctws the pies pbot records showed higher coherence near 5 days with the zonal low pass wavelength filters applied to the atmospheric pressure and the phase analysis results strongly suggest

nature and origin of proterozoic a type granitic magmatism in the southwestern united states of america the mountain ranges of arizona and adjacent california and nevada contain large areas underlain by proterozoic anorogenic granites comprising the southwesternmost portion of a transcontinental belt of 1 4 1 5 ga old anorogenic complexes that extends across north america northeast into labrador of these a two mica monazite bearing granitic suite resides in central and southeastern arizona as part of a peraluminous subprovince that is bordered on the south southern arizona to sonora and west western arizona and adjacent portions of california and nevada by marginally metaluminous granites bearing biotite sphene hornblende and fluorite all of these 1 4 ga granites are distinctly more potassic iron enriched relative to mg and depleted in ca mg and sr in contrast to typical orogenic granitoids in general the large ion lithophile element enriched composition is a consequence of limited melting of a water deficient crustal source at depths greater than 25 37 km for the peraluminous granites this contrast is less extreme perhaps resulting from a larger degree of melting as a consequence of a greater metasedimentary component and water in its crustal source the anorogenic granitic magmas intruded into the upper crust at depths of 8 17 km or shallower at temperatures up to 790 c the most dramatic variation in the crystallization intensive parameters resides in the oxygen fugacity which spans three orders of magnitude relative to other anorogenic suites all of the magmas crystallized at elevated levels of o2 as reflected in their assignment to the anorogenic magnetite series yet a regionally significant rise in primary o2 levels unmatched elsewhere in the transcontinental belt occurs for plutons in western arizona including the holy moses and hualapai granites the most extreme case is the hualapai granite whose biotite fe fe mg ratios drop due to high o2 to a low of 0 27 down from more typical levels of 0 54 to 0 75 such extreme variations in primary levels of oxygen fugacity must be an indirect imprint of regional changes of the level of oxidation of the lower crust the high fo2 holy moses and hualapai plutons have intruded near the regional boundary between the metaluminous and peraluminous granites and appear to be imaging a major change in the level of oxidation of the lower crust this boundary is also approximately equivalent to significant changes in the nd and pb isotopic compositions of these granites and the metamorphic and magmatic character of the older orogenic terrane on a global scale the crust forming orogenies ended by 1 6 ga ago and the continents entered a long lived era dominated by localized extension and transcontinental intrusion of anorogenic potassic rapakivi granite mafic dike swarms charnockite and anorthosite the absence of orogenic deformation implies that plate consumption became intraoceanic during this time the profuse and widespread nature of the igneous activity has no phanerozoic analogue and is considered to be unique to the proterozoic a crustal overturn model ties the magmatism to heating within a largely undepleted subcontinental mantle the eventual rise of mantle plumes and the transfer of heat into the youthful undifferentiated proterozoic crust subsequent melting and rise of potassic granitic magmas from the lower crust leads to considerable crustal reorganization a process that would continue until both the mantle and crust reached a stable configuration

semi analytical solution of flow to a well in an unconfined fractured aquifer system separated by an aquitard abstract semi analytical solutions are presented for flow to a well in an extensive homogeneous and anisotropic unconfined fractured aquifer system separated by an aquitard the pumping well is of infinitesimal radius and screened in either the overlying unconfined aquifer or the underlying fractured aquifer an existing linearization method was used to determine the watertable drainage the solution was obtained via laplace and hankel transforms with results calculated by numerical inversion the main findings are presented in the form of non dimensional drawdown time curves as well as scaled sensitivity dimensionless time curves the new solution permits determination of the influence of fractures matrix blocks and watertable drainage parameters on the aquifer drawdown the effect of the aquitard on the drawdown response of the overlying unconfined aquifer and the underlying fractured aquifer was also explored the results permit estimation of the unconfined and fractured aquifer hydraulic parameters via type curve matching or coupling of the solution with a parameter estimation code the solution can also be used to determine aquifer hydraulic properties from an optimal pumping test set up and duration

inter annual and decadal sea level variations in the north western pacific marginal seas abstract long term sea level changes in the okhotsk japan east east china and yellow seas have been explored based on mean monthly values of sea level from tide gauge and altimetry measurements the analysis of low frequency sea level variability reveals clearly differentiated areas the okhotsk sea and the northern sector of the japan east sea display lower sea level variances and no sea level rise the southern japan east sea presents larger sea level variability associated with the circulation regime of the warm current entering through the tsushima strait and inter annual sea level variations that are driven by steric and atmospheric changes the largest sea level variances are found in the yellow sea due to the effect of atmospheric forcing over the continental shelf inter annual variability is spatially varying within the yellow sea and the east china sea and is mainly related to the steric sea level changes regional mean sea level indices have been synthesized for each area using the longest tide gauge records and have revealed correlations between the southern japan east and yellow seas with pdo and np climatic indices linear trends at coastal sites in the japan east east china and yellow seas show a rather heterogeneous pattern with values between 1 5 and 5 5 mm yr for the period 1960 2000 during the period 1993 2008 linear trends derived from coastal tide gauges and from altimetry observations are coherent and reveal a southwards increasing pattern with maximum averaged values reached at the yellow sea 4 9 1 9 mm yr followed by the japan east sea 3 8 0 9 mm yr decadal rates of sea level change show distinct behaviour among basins as well as with the global average the southern japan east sea the east china sea and the yellow sea display decadal variability which is out of phase with respect to the global values

unsteady flow to a partially penetrating pumping well with wellbore storage in a dual permeability confined aquifer abstract in this article a new model is presented for imparting unsteady flow to a partially penetrating pumping well with wellbore storage placed in double permeability confined aquifers to investigate the wellbore drawdown transient behavior in this model both the fracture and matrix systems are connected directly with the wellbore as flow pathways while comprehensively considering the crossflow between the matrix and the fractures the top and bottom boundaries are assumed to be impermeable and the outer side boundaries could be infinite subsequently laplace transformation and finite fourier cosine transformation are employed to obtain analytical solutions of the dual permeability flow model in the laplace domain the derived analytical solution is general and can be reduced to several other previous results the numerical inversion algorithm of stehfest is used to solve the wellbore drawdown in the real time domain subsequently the model is validated by comparing it with previous results groundwater flow characteristics are analyzed in detail and divided into five flow stages wellbore storage flow early radial flow quasi spherical flow crossflow between the matrix and the fractures and quasi radial flow the different flow stages show some special values on the drawdown and its derivative log log plots there is a hump dip feature in the semi logarithmic curve of the drawdown derivative which are inherent characteristic for dual permeability flow behavior the effects of some important parameters of the aquifer or pumping wells on drawdown and its derivative such as wellbore storage coefficient penetration ratio crossflow coefficient storativity ratio transmissivity ratio dimensionless aquifer thickness of anisotropy and skin factor are analyzed and discussed in detail

internal differentiation of rare element pegmatites effects of boron phosphorus and fluorine lithium rich rare element pegmatites are characterized by high concentrations of b p and f the interactions of these components with h2o and rare alkalis lower liquidas and solidus temperatures enhance silicate liquid h2o miscibility and control partitioning and concentration of group i elements and higher field strength cations boron f and perhaps p may form peralkaline na and li species that promote early saturation in mica quartz activities of f p and especially b are largely unbuffered throughout crystallization concentration of these components through fractional crystallization involving muscovite generates a peralkaline na aluminosilicate rich melt or vapor from which albitites rich in tourmaline phosphates f rich micas beryl zircon and nb ta sn oxides crystallize phase equilibrium experiments with peraluminous b p f rich rhyolite obsidian macusanite simulate many features of rare element pegmatites especially at h2o undersaturated conditions

groundwater flow to a general well configuration in an unconfined aquifer overlying a fractured bedrock abstract unconfined aquifers sometimes overlie fractured bedrocks consisting of unconfined fractured aquifer systems pumping induced hydrodynamics in such aquifer systems has not received much attention as in other types of aquifer systems this paper aims to obtain semi analytical solutions of flow to a general well configuration in such an unconfined fractured two layer aquifer system the examples of general well configuration specifically discussed here include 1 a horizontal well 2 a vertical well 3 a vertical well with one horizontal collector and 4 a vertical well with two horizontal collectors which are perpendicular with each other the methodology is general and can be extended to other types of wells with minor modifications of solutions developed in this study the point sink source solution is first obtained using double infinite fourier and laplace transformations where sink is for pumping and source is for injection the line sink source solution is then obtained via integrating the point sink source along the desired direction and following the principle of superposition the de hoog numerical inverse laplace transform and gaussian quadrature are used to obtain time domain dimensionless drawdown solutions the instantaneous drainage of water table and the inter porosity flow of the underlying fractured aquifer are taken into account the effects of the length of horizontal well on dimensionless drawdown and dimensionless drawdown derivative and scaled sensitivity of the hydraulic parameters of the underlying fractured aquifer are explored the dimensionless drawdowns and drawdown derivatives of a vertical pumping well a vertical well with a single horizontal collector and a vertical well with two perpendicular horizontal collectors are also compared the scaled sensitivity of dimensionless drawdown to the hydraulic parameters of the underlying fractured aquifer of these different pumping well structures is explored the results of this study can be used to evaluate the hydraulic parameters using the drawdown data collected during a pumping test performed in a general well configuration in a unconfined fractured two layer aquifer system furthermore the presented solutions can be utilized to design the pumping well to minimize drawdown in low permeability or thin aquifers by eliminating the inter porosity flow term from the underlying fractured aquifer the solutions are applicable to groundwater flow to a pumping well in leaky aquifers

semi analytical solution for flow in leaky unconfined aquifer aquitard systems this study presents a semi analytical solution for the problem of leakage in an unconfined aquifer bounded below by an aquitard of finite or semi infinite extent the homogeneous anisotropic unconfined aquifer of infinite radial extent is pumped continuously at a constant rate from a well of infinitesimal radius the aquitard is also homogeneous anisotropic and of infinite radial extent flow in both the aquifer and the aquitard is allowed to occur both vertically and horizontally exact solutions to the governing equations given in this work are developed in the double laplace hankel transform space for drawdown response in the unconfined aquifer and the underlying aquitard the inverse transforms of the solutions are obtained numerically the theoretical results show that leakage can cause significant departure at both early and late times from the solution with no leakage the solution presented here can be used in least squares routines for estimation of hydraulic parameters for two layered unconfined aquifer aquitard systems

constant head test at a partially penetrating well in an aquifer aquitard system abstract an analytical model for describing pumping induced drawdown by constant head test at a partially penetrating well in a leaky confined aquifer is developed by treating the leakage of aquitard storage as an interface phenomenon rather than an volumetric effect which is the novel and never developed so far three different cases of remote lateral boundaries are considered in the model the new drawdown solution in laplace space is obtained and inverted into time domain solution utilizing the stehfest method the semi analytical solutions for well discharge are then obtained under three different cases analytical solutions in laplace and time domains are developed for calculating the total leakage rate and volume across the aquitard aquifer interface due to constant head test at a partially penetrating well in a leaky confined aquifer and such solutions are of great use for groundwater resource management based on the newly developed solutions the distribution of wellbore flowrate and aquitard leakage are explored and the sensitivity analysis is conducted to identify the most important controlling factor the sensitivity analysis shows that the wellbore flowrate and the drawdown in infinite case 1 finite case 2 and closed case 3 leaky confined aquifer systems are both sensitive to the variation of well partial penetration well radius and aquifer anisotropic ratio during the whole pumping period and they are most sensitive to the change of outer boundary distance at late time for case 3 the effect of the outer boundary on the drawdown or wellbore flowrate is more significant for a shorter outer boundary distance

flow to a well in an unconfined fractured and leaky wedge shaped aquifer system abstract wedge shaped aquifers are usually formed where two linear boundaries intersect these types of aquifers are commonly seen in river basins and alluvial fans but have received much less attention in the hydrological sciences community fundamental understanding of the effects of lateral boundaries on the hydrodynamic process in such aquifers is quite poor particularly for unconfined fractured and leaky wedge shaped aquifer systems which will be the concern of this study solutions of flow to a well in an unconfined fractured wedge shaped two aquifer system are obtained using laplace hankel and fourier transforms an infinitesimal radius pumping well partially penetrates the overlying unconfined aquifer both aquifer layers are homogeneous and anisotropic bounded by two intersecting linear lateral boundaries of constant head or barrier types and the aquifer system is semi infinite in radial direction the time domain drawdowns are obtained via the stehfest algorithm and gaussian quadrature the inter porosity flow in the underlying fracture aquifer the instantaneous water table drainage the horizontal and vertical hydraulic conductivity anisotropy and the wedge angle are taken into account eliminating the inter porosity flow in the underlying fractured aquifer the presented solution reduces to a leaky wedge shaped aquifer case the influences of the underlying fractured aquifer hydraulic parameters on the overlying unconfined aquifer for different wedge angles and linear lateral boundaries types are explored using dimensionless drawdown and scaled sensitivity curves the results of this study can be utilized to obtain hydraulic parameters of an alluvial and river basin unconfined fractured wedge shaped aquifer systems the presented solution can also be used for water budget assessment of river basin aquifers

phase equilibria of phlogopite lamprophyres from western mexico biotite liquid equilibria and p t estimates for biotite bearing igneous rocks olivine and augite minette powders have been equilibrated from one bar to nearly 2 0 kbar water saturated and from 900 to 1300 c and then quenched rapidly at oxygen fugacities controlled between the nickel nickel oxide nno and hematite magnetite hm oxygen buffers the liquidus of both samples is suppressed 100 c at water saturated conditions and 1500 bar both lavas contained between 3 and 4 wt water at the stage of phenocryst precipitation the partitioning of ferric and ferrous iron between phlogopite and liquid has been determined on eight samples across 3 log f o2 units when these determinations are combined with previous studies fe2o3 feo total of mg rich biotite can be calculated knowing log fo2 t and xfe thermodynamic modelling of biotite liquid equilibria results in two expressions for calculating activity coefficients for annite and phlogopite in natural biotites based on the partitioning of bao and tio2 between biotite and liquid we have formulated a thermometer and barometer over the range of 400 c tio2 partitioning between phlogopite and liquid is a function of temperature 50 c and is insensitive to pressure and h2o and o2 activities bao partitioning between phlogopite and liquid is a function of both temperature and pressure 4 kbar the latter being most important applying the tio2 and bao partitioning expressions to lamprophyre and lamproite suites shows that mexican minettes equilibrated at low pressures 5 to 15 kbar 4 kbar and temperatures 1090 to 1160 c 50 c while australian lamproites equilibrated at higher p up to 30 kbar 4 kbar and t 1125 to 1400 c 50 c experimental glass compositions and phenocryst fractionation calculations together with the bao and tio2 based pressure calculations indicate that felsic minettes from the mexican suite of lavas can be generated by simple fractionation of a more mafic parent minette at mid to lower crustal pressures

partitioning of fluorine and chlorine between biotite and granitic melt experimental calibration at 200 mpa h 2 o experiments from 640 to 680 c 200 mpa h2o at fo2 nno employing a natural f rich vitrophyric rhyolite from spor mountain utah assessed the effect of variable mg 100mg mg mn fe on the partitioning of fluorine and chlorine between biotite bt and melt over this temperature interval bt fluorite quartz is the sole liquidus phase partition coefficients for fluorine between biotite and glass dfbt melt show a strong dependence on the mg of bt dfbt melt varies from 1 5 to 7 2 over the range of mg from 21 to 76 a strong linear correlation between dfbt melt and mg has a slope of 9 4 and extrapolates through the origin i e dfbt melt 0 at mg 0 an annite siderophyllite solid solution in these experiments dclbt melt values 1 to 6 in the same experiments vary inversely with mg the al content of biotite does not vary with the aluminum saturation index asi molar al2o3 alkali and alkaline earth oxides of melt but two exchange mechanisms involving al appear to operate in these micas 1 alvi aliv siiv mgiv and mgiv 2aliv 2siiv iv the effects of other components such as li or other intensive parameters including fo2 have yet to be evaluated systematically at comparable mg of bt however the spor mountain rhyolite yields higher dfbt melt values than an li rich strongly peraluminous melt previously investigated the results indicate that the mg of bt exerts the principal control on halogen partitioning with asi and t as second order variables the experimental partition coefficients compare well with other experimental results but not with most volcanic rocks magmatic bt from most rhyolites records higher dfbt melt due to reequilibration with degassed h2o depleted magma and perhaps with f2o 1 exchange that may accompany oxidation fe3 o fe2 oh 1 this behavior is evident in magmatic biotite from a zoned peraluminous rhyolite complex near morococala bolivia bt is sharply zoned with f rich rims but bt core melt inclusion pairs fall on our experimental curve for dfbt melt these experimental data can be used in part to assess the preservation of magmatic volatile contents in plutonic or volcanic silicic rocks for plutonic rocks the actual f content of melt not a relative activity ratio involving hf species can be reasonably estimated if the mica has not undergone subsolidus reequilibration this information is potentially useful for some shallow level ca poor magmas that are thought to be rich in f e g a and s type granites but do not conserve f well as rocks

a method of calculating pumping induced leakage summary we have discussed pumping induced leakage in a leaky confined aquifer bounded by a relatively thin aquitard whose storage effect is neglected both constant rate and constant drawdown fully penetrating vertical pumping wells are considered we have derived closed form analytical solutions of the steady state leakage rates and volumes within any given radial distance from the well for both the constant rate and constant drawdown pumping wells for the constant rate well we have derived the closed form analytical solutions for the total leakage rate and volume over the entire aquitard aquifer boundary at a given time and the semi analytical solutions for calculating the leakage rate and volume within any radial distance from the pumping well at a given time for the constant drawdown well we have further provided the analytical solutions of the leakage rate and volume in the laplace domain those solutions are numerically inverted to yield results in the real time domain with the scale invariant relationship of butler jr j j tsou m s 2003 pumping induced leakage in a bounded aquifer an example of a scale invariant phenomenon water resour res 39 12 1344 doi 10 1029 2002wr001484 the solutions of the total leakage rates and volumes can be generalized to finite size aquifers with lateral impermeable boundaries these solutions are useful for managing multi layer aquifers in which pumping induced water transfer across the aquitards can occur

three dimensional saturated unsaturated flow with axial symmetry to a partially penetrating well in a compressible unconfined aquifer 1 a new analytical solution is presented for the delayed response process characterizing flow to a partially penetrating well in an unconfined aquifer the new solution generalizes that of neuman 1972 1974 by accounting for unsaturated flow above the water table three dimensional axially symmetric flow in the unsaturated zone is described by a linearized version of richards equation in which hydraulic conductivity and water content vary exponentially with incremental capillary pressure head relative to its air entry value defining the interface between the saturated and unsaturated zones unsaturated soil properties are characterized by an exponent having the dimension of inverse length or equivalently a dimensionless exponent d b where b is initial saturated thickness our treatment of the unsaturated zone is similar to that of kroszynski and dagan 1975 who however have ignored internal artesian aquifer storage according to kroszynski and dagan aquifers that are not excessively shallow have values of d their parameter a much greater than 10 we find that in such typical cases unsaturated flow has little impact on early and late dimensionless time drawdown a short distance below the water table unsaturated flow causes drawdown to increase slightly at intermediate dimensionless time values that represent transition from an early artesian dominated to a late water table dominated flow regime delayed drainage from the unsaturated zone becomes less and less important as d increases as d this effect dies out and drawdown is controlled entirely by delayed decline in the water table as in the model of neuman the unsaturated zone has a major impact on drawdown at intermediate time and a significant impact at early and late times in the atypical case of d 1 becoming the dominant factor as d approaches zero the soil water retention capacity becomes very large and or saturated thickness becomes insignificant our new solution was used to analyze field data from a pumping test conducted by moench et al 2001 in a glacial outwash deposit at cape cod massachusetts the solution was fitted individually and simultaneously to time drawdown data from 20 piezometers and observation wells and simultaneously to data from three piezometers in each of two clusters at various depths and distances from the pumping well with very good results our parameter estimates of hydraulic conductivities from the simultaneous fit are similar to those obtained previously by moench 2004 but our estimates of specific yield and storage are smaller and larger respectively while our estimate of is not comparable with his estimates of three empirical parameters

fundamental mode basin oscillations in the japan east sea 4 in the real jes energy dissipation exists four straits connect to the open ocean and bottom topography is highly variable so rikiishi s model may be expected to differ somewhat in period and structure from observations we find no published report of direct observations of basin oscillations in the jes in this paper we provide observational evidence that fundamental mode basin oscillations exist continually in the jes the observed results are compared with rikiishi s model and the forcing is investigated

waves along the equator in the atlantic abstract spectra of two hundred days of data from five inverted echo sounders deployed along the equator in 1983 84 and a thousand days of 30 crossings of the equator by the topex poseidon altimeter in 1993 95 are both found to have enhanced variance of sea surface displacement in two frequency bands centered nominally about 50 1 and 25 1 cycles day complex empirical orthogonal function analysis of the two bands finds much of the variance being accounted for by eastward and westward propagating waves respectively that are coherent across the basin the eastward propagating wave is identifiable as a first mode kelvin wave with a period of 54 49 days in the sounder altimeter dataset a basinwide wavelength and a speed of 2 1 1 8 m s 1 it is suggested that the westward propagating wave is a surface expression of the meridional oscillation of the equatorial undercurrent about the equator presumably induced by a tropical instability wave with a period of 24 28 days a wavelength of 600 580 km

partitioning of f between h2o and co2 fluids and topaz rhyolite melt implications for mineralizing magmatic hydrothermal fluids in f rich granitic systems fluid melt distribution coefficients for f have been determined in experiments conducted with peraluminous topaz rhyolite melts and fluids consisting of h2o and h2o co2 at pressures of 0 5 to 5 kbar temperatures of 775 1000 c and concentrations of f in the melt ranging from 0 5 to 6 9 wt the major element f and cl concentrations of the starting material and run product glasses were determined by electron microprobe and the concentration of f in the fluid was calculated by mass balance the h2o concentrations of some run product glasses were determined by ion microprobe sims the solubility of melt in the fluid phase increases with increasing f in the system the solubility of h2o in the melt is independent of the f concentration of the system with up to 6 3 wt f in the melt no evidence of immiscible silica and fluoriderich liquids was detected in the hydrous but water undersaturated starting material glasses 8 5 wt f in melt or in the water saturated run product glasses f concentrates in topaz rhyolite melts relative to coexisting fluids at most conditions studied however df wt f in fluid wt f in melt increases strongly with increasing f in the system maximum values of df in this study are significantly larger than those previously reported in the literature linear extrapolation of the data suggests that df is greater than one for water saturated peraluminous granitic melts containing 8 wt f at 800 c and 2 kbar df increases as temperature and as h2o h2o co2 of the fluid increase for topaz rhyolite melts containing 1 wt f and with h2o rich fluids df is independent of changes in pressure from 2 to 5 kbar at 800 c for melts containing 1 wt f and in equilibrium with co2 bearing fluids the concentrations of f in fluid increases with increasing pressure f and lithophile element enriched granites may evolve to compositions containing extreme concentrations of f during the final stages of crystallization if f in the melt exceeds 8 wt df is greater than one and the associated magmatic hydrothermal fluid contains 4 molal f such f enriched fluids may be important in the mass transport of ore constituents i e f mo w sn li be rb cs u th nb ta and b from the magma

aquitard effect on drawdown in water table aquifers 1 the effects of an aquitard on drawdown in an overlying unconfined aquifer can be represented by a drainage type term at the aquitard aquifer interface the functional form of this boundary condition is similar to the boulton neuman boundary condition used for water table aquifers except the kernel contains an inverse square root of time instead of a negative exponential type curves using the new boundary condition were obtained in semianalytical form examples for several representative conditions show that the effect of the underlying aquitard can contribute to the type curve at early and intermediate times but the effect becomes negligible at late times

genesis of the two main types of peraluminous granitoids two mica monzogranites to leucogranites and biotite rich cordierite bearing tonalites to monzogranites form two distinct groups of peraluminous granitoids they can be distinguished by mineral and rock associations and by the variation of their peraluminosity during differentiation except for the rare muscovite bearing granitoids produced by extreme fractionation or local contamination of metaluminous magmas the majority of peraluminous granitoids are produced by partial melting of crustal rocks production of either muscovite bearing granites or biotite rich cordierite bearing granitoids does not depend only on the nature of the sources but is also controlled by the physical parameters of partial melting and consequently by the way anatexis of a thickened crust is enhanced biotite rich cordierite bearing granitoids are generated where mantle derived magmas are injected into or have underplated crustal rocks two mica granites are generated where thickened crust is affected by major crustal shears or thrusts correlations between differentiation and peraluminosity indicate the dominant role of either restite unmixing or fractional crystallization in the production and evolution of the various types of peraluminous granitoids

flow to a partially penetrating well with variable discharge in an anisotropic two layer aquifer system abstract a general analytical model for the problem of variable discharge of groundwater from a well in an anisotropic two layered aquifer system is developed by taking account of the interface flow between the two layers the well of infinitesimal radius partially penetrates the lower layer and is pumped at a variable discharge the horizontal as well as vertical flows in both layers are included and importantly the effects of constant head case 1 and no flux case 2 boundaries at the top of the upper layer are considered laplace domain solutions for drawdown in dimensionless form are derived with the help of hankel transform and are inverted to the time domain numerically the drawdown characteristics induced by an exponentially decayed rate of pumping are discussed and sensitivity analysis is also performed to explore the influence of different parameters on drawdown characteristics the results show that the drawdown around a partially penetrating well in the lower pumped layer induced by an exponential decreasing pumping rate usually contains three stages the effect of anisotropy and well configuration have great influences on the drawdown distribution near the pumping well and the horizontal flow and storativity of the upper unpumped layer cannot be ignored in determining the upper aquifer drawdown the sensitivity analysis also illustrates that the dimensionless drawdown in the lower pumped layer is very sensitive to well configuration parameters all the time it is only sensitive to the hydraulic parameters of the lower aquifer for case 1 and to the hydraulic parameters of the lower layer and the specific storage of the upper layer at late times the dimensionless drawdown of the upper layer is not sensitive to the variable well discharge parameters over the whole pumping period and is not sensitive to the storage parameters of both layers for case 1 however the drawdown in the upper layer is sensitive to all the hydraulic parameters and well configuration parameters for case 2 at late times

three dimensional response to a partially penetration well pumping in a general anisotropic three layer aquifer system abstract three dimensional response to well pumping in a multilayer aquifer system with rigorous treatment of interfacial flow attracts great attention among the subsurface hydrologists because of its theoretical importance and practical merits in this study a general theory of three dimensional groundwater flow to a well of infinitesimal radius in an anisotropic three layer aquifer system is developed with a constant rate pumping in the lower layer and associated semi analytical solutions of drawdowns in individual layers are obtained this theory discards many previous assumptions for studying a multilayer aquifer system such as simplified flow configuration in the aquitard treatment of cross formation flow as a volumetric averaged term adding to the governing equations of aquifer flows and sometimes negligence of vertical flow components in the aquifers additionally this theory considers three types of commonly used top boundary conditions a water table with delayed gravity drainage boundary condition case 1 a constant head top boundary condition case 2 and a no flow top boundary condition case 3 the dimensionless drawdown solutions in laplace domain are obtained and inverted numerically to calculate the time domain solutions the solution encompasses existing solutions for a two layer or a single layer e g unconfined or confined aquifer system as subsets the developed solutions are tested extensively with a finite element numerical solution using comsol and other existing solutions and a sensitivity analysis is performed to prioritize the influences of different parameter groups the results of this study can be used to predict the pumping induced drawdown at any position with an observation well and to estimate the hydraulic parameters of the lower pumped layer and upper layer as well as the middle layer the developed theory provides a basis for other potential applications such as geotechnical engineering and groundwater management