Time–space fractional governing equations of transient groundwater flow in confined aquifers: Numerical investigation          下载免费PDF全文

Tongbi Tu  Ali Ercan  M. Levent Kavvas 《水文研究》2018,32(10):1406-1419

In order to model non‐Fickian transport behaviour in groundwater aquifers, various forms of the time–space fractional advection–dispersion equation have been developed and used by several researchers in the last decade. The solute transport in groundwater aquifers in fractional time–space takes place by means of an underlying groundwater flow field. However, the governing equations for such groundwater flow in fractional time–space are yet to be developed in a comprehensive framework. In this study, a finite difference numerical scheme based on Caputo fractional derivative is proposed to investigate the properties of a newly developed time–space fractional governing equations of transient groundwater flow in confined aquifers in terms of the time–space fractional mass conservation equation and the time–space fractional water flux equation. Here, we apply these time–space fractional governing equations numerically to transient groundwater flow in a confined aquifer for different boundary conditions to explore their behaviour in modelling groundwater flow in fractional time–space. The numerical results demonstrate that the proposed time–space fractional governing equation for groundwater flow in confined aquifers may provide a new perspective on modelling groundwater flow and on interpreting the dynamics of groundwater level fluctuations. Additionally, the numerical results may imply that the newly derived fractional groundwater governing equation may help explain the observed heavy‐tailed solute transport behaviour in groundwater flow by incorporating nonlocal or long‐range dependence of the underlying groundwater flow field.  相似文献   

大别山东部花岗岩类的稀土元素地球化学及其地质意义   总被引：1，自引：0，他引：1  

胡雄星  马东升 《矿产与地质》2002,16(6):321-326

在研究大别山东部主要花岗岩体的稀土元素地球化学特征、稀土元素配分型式的基础上 ,探讨了花岗岩体的物质来源、成岩模式及其构造意义。研究表明 :(1)大别山东部出露的主要花岗岩类岩体的物质来源基本相同 ,且源区具有古岛弧的特征 ;(2 )各岩体的成岩模式呈现以分离结晶作用为主的特征 ;(3)花岗质岩浆上侵的构造环境与中国东部燕山期构造转折的大背景有关。伸展拉张过程造成的地幔上涌不但是花岗岩类形成的构造条件 ,也对超高压变质岩的快速折返有重要影响。  相似文献   

The Role of Fractional Crystallization and Assimilationin the Evolution of the Zoned Mukhattata Pluton, Eastern Desert, Egypt     

Said A. El-Nisr  Mohamed M. El-Sayed 《Chemie der Erde / Geochemistry》2002,62(3):216-236

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Volcanological and petrological evolution of Marsili Seamount (southern Tyrrhenian Sea)     

Teresa Trua  Giancarlo Serri  Michael Marani  Alberto Renzulli  Fabiano Gamberi 《Journal of Volcanology and Geothermal Research》2002,114(3-4)

A swath bathymetric survey was conducted on Marsili Volcano, the biggest seamount in the Tyrrhenian Sea. It stands 3000 m above the surrounding oceanic crust of the 3500 m-deep Marsili back-arc basin and is axially located within the basin. The seamount has an elongated shape and presents distinctive morphology, with narrow (<1000 m) ridges, made up of several elongated cones, on the summit zone and extensive cone fields on its lower flanks. A dredging campaign carried out at water depths varying between 3400 and 600 m indicates that most of Marsili Seamount is composed of medium-K calc-alkaline basalts. Evolved high-K andesites were only recovered from the small cones on the summit axis zone. Petrological and geochemical characteristics of the least differentiated basalts reveal that at least two varieties of magmas have been erupted on the Marsili Volcano. Group 1 basalts have plagioclase and olivine as dominant phases and show lower Al, Ca, K, Ba, Rb and Sr, and higher Fe, Na, Ti and Zr with respect to a second type of basaltic magma. Group 2 basalts reveal the presence of clinopyroxene as an additional phenocryst phase. In addition, the two basaltic magmas have different original pre-eruptive H₂O content (group 1, H₂O-poor and group 2, H₂O-rich). Moreover, comparison of the compositional trends and mineralogical compositions obtained from MELTS [Ghiorso, M.S., Sack, R.O., Contrib. Mineral. Petrol. 119 (1995) 197–212] fractional crystallization calculations reveal that the evolved andesites can only exclusively be derived from a low-pressure (0.3 kbar) fractionation of magmas compositionally similar to the least evolved group 2 basalts. Finally, we suggest that the high vesicularity of the basalts sampled at relatively great depths (>2400 m) on the edifice is governed by H₂O and, probably, CO₂ exsolution and is not a feature indicative of shallow water depth eruption.  相似文献   

新疆阿拉尔花岗岩MFC过程的微量元素综合效应     

刘伟 《地质论评》1997,43(5):465-475

新疆阿拉尔花岗岩的微量元素比相关图显示了线性样点列与幂函数曲线形式的样点列相 复杂图型。该图型用简单混合或者单一结果分异模型都不能解释。本文建立了混合－结晶分异复合过程的微量元素综合效应模型。模型１：从初始混合线引起害虫函数曲线束形式的结晶分异线。特殊情况有结晶分异线简化为通过原点的直线束形式或者与初始混合线重合。  相似文献   

三维溶质运移问题的分步广义迎风解法     

姚磊华 《吉林大学学报(地球科学版)》1997,(4)

对对流占优的三维溶质运移问题提出了分步广义迎风解法，首先利用Ｎ．Ｎ．Ｙａ－ｎｅｎｋｏ对水动力弥散方程分步求解的思想，将原来的一个定解问题分解为两个定解问题即对流定解问题和扩散定解问题，对对流定解问题采用广义迎风对偶单元均衡法求解，对扩散定解问题采用一般的Ｇａｌｅｒｋｉｎ有限元法求解，不仅避免了用一般有限元法和有限差分法求解对流占优的地下水水质数学模型时常出现数值弥散和过量问题，而且避免了求节点速度这一步，节省运算步骤，对井点的浓度变化给出了更合适的求解方法。  相似文献   

Geodynamic Information in Peridotite Petrology   总被引：12，自引：1，他引：12  

HERZBERG  CLAUDE 《Journal of Petrology》2004,45(12):2507-2530

Systematic differences are observed in the petrology and majorelement geochemistry of natural peridotite samples from thesea floor near oceanic ridges and subduction zones, the mantlesection of ophiolites, massif peridotites, and xenoliths ofcratonic mantle in kimberlite. Some of these differences reflectvariable temperature and pressure conditions of melt extraction,and these have been calibrated by a parameterization of experimentaldata on fertile mantle peridotite. Abyssal peridotites are examplesof cold residues produced at oceanic ridges. High-MgO peridotitesfrom the Ronda massif are examples of hot residues producedin a plume. Most peridotites from subduction zones and ophiolitesare too enriched in SiO₂ and too depleted in Al₂O₃ to be residues,and were produced by melt–rock reaction of a precursorprotolith. Peridotite xenoliths from the Japan, Cascades andChile–Patagonian back-arcs are possible examples of arcprecursors, and they have the characteristics of hot residues.Opx-rich cratonic mantle is similar to subduction zone peridotites,but there are important differences in FeO_T. Opx-poor xenolithsof cratonic mantle were hot residues of primary magmas with16–20% MgO, and they may have formed in either ancientplumes or hot ridges. Cratonic mantle was not produced as aresidue of Archean komatiites. KEY WORDS: peridotite; residues; fractional melting; abyssal; cratonic mantle; subduction zone; ophiolite; potential temperature; plumes; hot ridges  相似文献   

Petrogenesis of Tertiary Continental Intra-plate Lavas from the Westerwald Region, Germany   总被引：2，自引：2，他引：2  

HAASE  KARSTEN M.; GOLDSCHMIDT  BJORN; GARBE-SCHONBERG  C.-DIETER 《Journal of Petrology》2004,45(5):883-905

Tertiary volcanic rocks from the Westerwald region range frombasanites and alkali basalts to trachytes, whereas lavas fromthe margin of the Vogelsberg volcanic field consist of morealkaline basanites and alkali basalts. Heavy rare earth elementfractionation indicates that the primitive Westerwald magmasprobably represent melts of garnet peridotite. The Vogelsbergmelts formed in the spinel–garnet peridotite transitionregion with residual amphibole for some magmas suggesting meltingof relatively cold mantle. Assimilation of lower-crustal rocksand fractional crystallization altered the composition of lavasfrom the Westerwald and Vogelsberg region significantly. Thecontaminating lower crust beneath the Rhenish Massif has a differentisotopic composition from the lower continental crust beneaththe Hessian Depression and Vogelsberg, implying a compositionalboundary between the two crustal domains. The mantle sourceof the lavas from the Rhenish Massif has higher ²⁰⁶Pb/²⁰⁴Pband ⁸⁷Sr/⁸⁶Sr than the mantle source beneath the Vogelsbergand Hessian Depression. The 30–20 Ma volcanism of theWesterwald apparently had the same mantle source as the QuaternaryEifel lavas, suggesting that the magmas probably formed in apulsing mantle plume with a maximum excess temperature of 100°Cbeneath the Rhenish Massif. The relatively shallow melting ofamphibole-bearing peridotite beneath the Vogelsberg and HessianDepression may indicate an origin from a metasomatized portionof the thermal boundary layer. KEY WORDS: continental rift volcanism; basanites; trachytes; assimilation; fractional crystallization; partial melting  相似文献   

Numerical modelling method for wave propagation in a linear viscoelastic medium with singular memory   总被引：1，自引：0，他引：1  

Jian-Fei Lu  Andrzej Hanyga 《Geophysical Journal International》2004,159(2):688-702

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Assimilation and Fractional Crystallization Controlled by Transport Process of Crustal Melt: Implications from an Alkali Basalt-Dacite Suite from Rishiri Volcano, Japan   总被引：2，自引：0，他引：2  

KURITANI  TAKESHI; KITAGAWA  HIROSHI; NAKAMURA  EIZO 《Journal of Petrology》2005,46(7):1421-1442

Mechanisms of fractional crystallization with simultaneous crustalassimilation (AFC) are examined for the Kutsugata and Tanetomilavas, an alkali basalt–dacite suite erupted sequentiallyfrom Rishiri Volcano, northern Japan. The major element variationswithin the suite can be explained by boundary layer fractionation;that is, mixing of a magma in the main part of the magma bodywith a fractionated interstitial melt transported from the mushyboundary layer at the floor. Systematic variations in SiO₂ correlatewith variations in the Pb, Sr and Nd isotopic compositions ofthe lavas. The geochemical variations of the lavas are explainedby a constant and relatively low ratio of assimilated mass tocrystallized mass (‘r value’). In the magma chamberin which the Kutsugata and Tanetomi magmas evolved, a strongthermal gradient was present and it is suggested that the marginalpart of the reservoir was completely solidified. The assimilantwas transported by crack flow from the partially fused floorcrust to the partially crystallized floor mush zone throughfractures in the solidified margin, formed mainly by thermalstresses resulting from cooling of the solidified margin andheating of the crust. The crustal melt was then mixed with thefractionated interstitial melt in the mushy zone, and the mixedmelt was further transported by compositional convection tothe main magma, causing its geochemical evolution to be characteristicof AFC. The volume flux of the assimilant from the crust tothe magma chamber is suggested to have decreased progressivelywith time (proportional to t^–1/2), and was about 3 x 10^–2m/year at t = 10 years and 1 x 10^–2 m/year at t = 100years. It has been commonly considered that the heat balancebetween magmas and the surrounding crust controls the couplingof assimilation and fractional crystallization processes (i.e.absolute value of r). However, it is inferred from this studythat the ratio of assimilated mass to crystallized mass canbe controlled by the transport process of the assimilant fromthe crust to magma chambers. KEY WORDS: assimilation and fractional crystallization; mass balance model; magma chamber; melt transport; Pb isotope  相似文献