Time–space fractional governing equations of transient groundwater flow in confined aquifers: Numerical investigation

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.     

重力异常垂向一阶导数的一种简便算法

利用拉格朗日插值导出了重力异常垂向一阶导数的计算公式，给出了地面以及地面之上不同高度的求导系数。该公式可以计算地面上的重力垂向一阶导数，还可以直接计算地面之上任意高度上的垂向一阶导数。鉴于该公式除系数不同外，与上延公式完全相同，因此，程序设计尤为简单。使用本公式对模型数据和实际资料进行了处理，证明了本算法的实用性。     

重力斜导数方法在时间域中的理论模型与研究

Miller和Singh在1994年首次提出了斜导数(Tilt梯度)的定义,J.Derek Fairhead和Chris M.Green又于2004年在斜导数的基础上提出了Tilt梯度水平导数的概念。国内学者已对斜导数及斜导数水平导数展开研究,设定了多体模型、无限延伸倾斜脉模型、有限延伸倾斜台阶模型及埋深相同无限延伸垂直厚板及薄板模型,得出一些结论。针对一些地质体产状的判断,提出非绝对值斜导数水平导数的新概念,并应用于理论模型中验证,得出正确的结论。在上述理论模型基础上补充了断层模型和无限延伸倾斜台阶模型,应用非绝对值水平导数的理论解释地质体的产状,并对上述模型提出新的观点和看法。     

Structural damage detection using the optimal weights of the approximating artificial neural networks

This work presents a novel neural network‐based approach to detect structural damage. The proposed approach comprises two steps. The first step, system identification, involves using neural system identification networks (NSINs) to identify the undamaged and damaged states of a structural system. The partial derivatives of the outputs with respect to the inputs of the NSIN, which identifies the system in a certain undamaged or damaged state, have a negligible variation with different system errors. This loosely defined unique property enables these partial derivatives to quantitatively indicate system damage from the model parameters. The second step, structural damage detection, involves using the neural damage detection network (NDDN) to detect the location and extent of the structural damage. The input to the NDDN is taken as the aforementioned partial derivatives of NSIN, and the output of the NDDN identifies the damage level for each member in the structure. Moreover, SDOF and MDOF examples are presented to demonstrate the feasibility of using the proposed method for damage detection of linear structures. Copyright © 2001 John Wiley & Sons, Ltd.     

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

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.     

两等级网不使用导数的联合非线性最小二乘估计

针对不同等级测量控制网的联合平差，介绍一种不使用导数的解析方法，该方法一方面克服了传统平差中由于起算数据误差对低级网的精度影响，而使加密的精度逐次降低的缺点；另一方面，完全避免了导数的计算，大大减少了计算工作量。     

新疆阿拉尔花岗岩MFC过程的微量元素综合效应

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。     

三维溶质运移问题的分步广义迎风解法

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。     

Petrogenesis of Tertiary Continental Intra-plate Lavas from the Westerwald Region, Germany

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