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1.
Discussion about the validity of sharp‐interface models to deal with seawater intrusion in coastal aquifers 
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下载免费PDF全文 Analytical models have been exhaustively used to study simple seawater intrusion problems and the sustainable management of groundwater resources in coastal aquifers because of its simplicity, easy implementation, and low computational cost. Most of these models are based on the sharp‐interface approximation and the Ghyben–Herzberg relation, and their governing equations are expressed in terms of a single potential theory to calculate critical pumping rates in a coastal pumping scenario. The Ghyben–Herzberg approach neglects mixing of fresh water and seawater and implicitly assumes that salt water remains static. Therefore, the results of the analytical solutions may be inaccurate and unacceptable for some real‐complex case studies. This paper provides insight into the validity of sharp‐interface models to deal with seawater intrusion in coastal aquifers, i.e. when they can be applied to obtain accurate enough results. For that purpose, this work compares sharp‐interface solutions, based on the Ghyben–Herzberg approach, with numerical three‐dimensional variable‐density flow simulations for a set of heterogeneous groundwater flow and mass transport parameters, and different scenarios of spatially distributed recharge values and spatial wells placement. The numerical experiment has been carried out in a 3D unconfined synthetic aquifer using the finite difference numerical code SEAWAT for solving the coupled partial differential equations of flow and density‐dependent transport. This paper finds under which situations the sharp‐interface solution gives good predictions in terms of seawater penetration, transition zone width and critical pumping rates. Additionally, the simulation runs indicate to which parameters and scenarios the results are more sensitive. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
2.
Prestack image volumes may be decomposed into specular and non‐specular parts by filters defined in the dip‐angle domain. For space‐shift extended image volumes, the dip‐angle decomposition is derived via local Radon transform in depth and midpoint coordinates, followed by an averaging over space‐shifts. We propose to employ prestack space‐shift extended reverse‐time migration and dip‐angle decomposition for imaging small‐scale structural elements, considered as seismic diffractors, in models with arbitrary complexity. A suitable design of a specularity filter in the dip‐angle domain rejects the dominant reflectors and enhances diffractors and other non‐specular image content. The filter exploits a clear discrimination in dip between specular reflections and diffractions. The former are stationary at the specular dip, whereas the latter are non‐stationary without a preferred dip direction. While the filtered image volume features other than the diffractor images (for example, noise and truncation artefacts are also present), synthetic and field data examples suggest that diffractors tend to dominate and are readily recognisable. Averaging over space‐shifts in the filter construction makes the reflectors? rejection robust against migration velocity errors. Another consequence of the space‐shift extension and its angle‐domain transforms is the possibility of exploring the image in a multiple set of common‐image gathers. The filtered diffractions may be analysed simultaneously in space‐shift, scattering‐angle, and dip‐angle image gathers by means of a single migration job. The deliverables of our method obviously enrich the processed material on the interpreter's desk. We expect them to further supplement our understanding of the Earth's interior. 相似文献
3.
An exact, closed‐form analytical solution is derived for one‐dimensional (1D), coupled, steady‐state advection‐dispersion equations with sequential first‐order degradation of three dissolved species in groundwater. Dimensionless and mathematical analyses are used to examine the sensitivity of longitudinal dispersivity in the parent and daughter analytical solutions. The results indicate that the relative error decreases to less than 15% for the 1D advection‐dominated and advection‐dispersion analytical solutions of the parent and daughter when the Damköhler number of the parent decreases to less than 1 (slow degradation rate) and the Peclet number increases to greater than 6 (advection‐dominated). To estimate first‐order daughter product rate constants in advection‐dominated zones, 1D, two‐dimensional (2D), and three‐dimensional (3D) steady‐state analytical solutions with zero longitudinal dispersivity are also derived for three first‐order sequentially degrading compounds. The closed form of these exact analytical solutions has the advantage of having (1) no numerical integration or evaluation of complex‐valued error function arguments, (2) computational efficiency compared to problems with long times to reach steady state, and (3) minimal effort for incorporation into spreadsheets. These multispecies analytical solutions indicate that BIOCHLOR produces accurate results for 1D steady‐state, applications with longitudinal dispersion. Although BIOCHLOR is inaccurate in multidimensional applications with longitudinal dispersion, these multidimensional multispecies analytical solutions indicate that BIOCHLOR produces accurate steady‐state results when the longitudinal dispersion is zero. As an application, the 1D advection‐dominated analytical solution is applied to estimate field‐scale rate constants of 0.81, 0.74, and 0.69/year for trichloroethene, cis‐1,2‐dichloroethene, and vinyl chloride, respectively, at the Harris Palm Bay, FL, CERCLA site. 相似文献
4.
The analysis of infiltration of 2D trickle irrigation under multiple‐line sources, governed by the celebrated Richards equation, is performed, aiming at determining the efficiency of trickle irrigation so as to reduce the water demand. A closed‐form solution is explicitly obtained by utilizing the Fourier integral transformation, and this serves as a means to compute the distribution of volumetric water content during trickle irrigation. Results for the infiltration of 2D trickle irrigation under single line and multiple‐line sources are presented, which illustrate the distribution of infiltration water that diffuses into the soil, and make it possible to calculate the period of time required for trickle irrigation for different plants. The results can be applied to verify complicated solutions from other numerical models. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
5.
Antoine Guitton 《Geophysical Prospecting》2006,54(2):135-152
Surface‐related multiples are attenuated for one sail line and one streamer of a 3D data set (courtesy of Compagnie Générale de Géophysique). The survey was carried out in the Gulf of Mexico in the Green Canyon area where salt intrusions close to the water‐bottom are present. Because of the complexity of the subsurface, a wavefield method incorporating the full 3D volume of the data for multiple removal is necessary. This method comprises modelling of the multiples, where the data are used as a prediction operator, and a subtraction step, where the model of the multiples is adaptively removed from the data with matching filters. The accuracy of the multiple model depends on the source/receiver coverage at the surface. When this coverage is not dense enough, the multiple model contains errors that make successful subtraction more difficult. In these circumstances, one can either (1) improve the modelling step by interpolating the missing traces, (2) improve the subtraction step by designing methods that are less sensitive to modelling errors, or (3) both. For this data set, the second option is investigated by predicting the multiples in a 2D sense (as opposed to 3D) and performing the subtraction with a pattern‐based approach. Because some traces and shots are missing for the 2D prediction, the data are interpolated in the in‐line direction using a hyperbolic Radon transform with and without sparseness constraints. The interpolation with a sparseness constraint yields the best multiple model. For the subtraction, the pattern‐based technique is compared with a more standard, adaptive‐subtraction scheme. The pattern‐based approach is based on the estimation of 3D prediction‐error filters for the primaries and the multiples, followed by a least‐squares estimation of the primaries. Both methods are compared before and after prestack depth migration. These results suggest that, when the multiple model is not accurate, the pattern‐based method is more effective than adaptive subtraction at removing surface‐related multiples while preserving the primaries. 相似文献
6.
Linearized inversion methods such as Gauss‐Newton and multiple re‐weighted least‐squares are iterative processes in which an update in the current model is computed as a function of data misfit and the gradient of data with respect to model parameters. The main advantage of those methods is their ability to refine the model parameters although they have a high computational cost for seismic inversion. In the Gauss‐Newton method a system of equations, corresponding to the sensitivity matrix, is solved in the least‐squares sense at each iteration, while in the multiple re‐weighted least‐squares method many systems are solved using the same sensitivity matrix. The sensitivity matrix arising from these methods is usually not sparse, thus limiting the use of standard preconditioners in the solution of the linearized systems. For reduction of the computational cost of the linearized inversion methods, we propose the use of preconditioners based on a partial orthogonalization of the columns of the sensitivity matrix. The new approach collapses a band of co‐diagonals of the normal equations matrix into the main diagonal, being equivalent to computing the least‐squares solution starting from a partial solution of the linear system. The preconditioning is driven by a bandwidth L which can be interpreted as the distance for which the correlation between model parameters is relevant. To illustrate the benefit of the proposed approach to the reduction of the computational cost of the inversion we apply the multiple re‐weighted least‐squares method to the 2D acoustic seismic waveform inversion problem. We verify the reduction in the number of iterations in the conjugate'gradient algorithm as the bandwidth of the preconditioners increases. This effect reduces the total computational cost of inversion as well. 相似文献
7.
Sepúlveda N 《Ground water》2008,46(1):144-155
An analytical solution for three-dimensional (3D) flow in the storative semiconfining layers of a leaky aquifer fully penetrated by a production well is developed in this article to provide a method from which accurate hydraulic parameters in the semiconfining layers can be derived from aquifer test data. The analysis of synthetic aquifer test data with the 3D analytical solution in the semiconfining layers provided more accurate optimal hydraulic parameters than those derived using the available quasi-two-dimensional (2D) solution. Differences between the 3D and 2D flow solutions in the semiconfining layers become larger when a no flow boundary condition is imposed at either at the top of the upper semiconfining layer or at the bottom of the lower semiconfining layer or when the hydraulic conductivity ratio of the semiconfining layer to the aquifer is larger than 0.001. In addition, differences between the 3D and 2D flow solutions in the semiconfining layers are illustrated when the thickness ratio of the semiconfining layer to the aquifer is changed. Analysis of water level data from two hypothetical and one real aquifer test showed that the 3D solution in the semiconfining layers provides lower correlation coefficients among hydraulic parameters than the 2D solution. 相似文献
8.
There are two forms of systematic error in conventional deconvolution as applied to the problem of suppressing multiples with periodicities longer than a hundred milliseconds. One of these is the windowing effect due to the assumption that a true autocorrelation function can be computed from a finite portion of data. The second form of error concerns the assumption of periodicity, which is strictly true only at zero offset for a 1D medium. The seriousness of these errors increased with the lengthening of the multiple period. This paper describes and illustrates a rigorous 2D solution to the predictive deconvolution equations that overcomes both of the systematic errors of conventional 1D approaches. This method is applicable to both the simple or trapped system and to the complex or peg-leg system of multiples. It does not require that the design window be six to ten times larger compared to the operator dimensions and it is accurate over a wide range of propagation angles. The formulation is kept strictly in the sense of the classical theory of prediction. The solution of normal equations are obtained by a modified conjugate gradient method of solution developed by Koehler. In this algorithm, the normal equations are not modified by the autocorrelation approximation. As with all linear methods, approximate stationary attitude in the multiple generating process is assumed. This method has not been tested in areas where large changes in the characteristic of the multiple-generating mechanism occur within a seismic spread length. 相似文献
9.
An extension of the Grey Fuzzy Waste Load Allocation Model (GFWLAM) developed in an earlier work is presented here to address the problem of multiple solutions. Formulation of GFWLAM is based on the approach for solving fuzzy multiple objective optimization problems with max–min as the operator, which usually may not result in a unique solution. The multiple solutions of fuzzy multiobjective optimization model should be obtained as parametric equations or equations that represent a subspace. A two-phase optimization technique, two-phase GFWLAM, is developed to capture all alternative or multiple solutions of GFWLAM. The optimization model in Phase 1 is exactly same as the optimization model described in GFWLAM. The optimization model in Phase 2 maximizes the upper bounds of fractional removal levels of pollutants and minimizes the lower bounds of fractional removal levels of pollutants keeping the value of goal fulfillment level same as obtained from Phase 1. The widths of the interval-valued fractional removal levels play an important role in decision-making as these can be adjusted within their intervals by the decision-maker considering technical and economic feasibility in the final decision scheme. Two-phase GFWLAM widens the widths of interval-valued removal levels of pollutants, thus enhancing the flexibility in decision-making. The methodology is demonstrated with a case study of the Tunga-Bhadra river system in India. 相似文献
10.
11.
Jacob Zaidel 《Ground water》2013,51(6):952-959
Known analytical solutions of groundwater flow equations are routinely used for verification of computer codes. However, these analytical solutions (e.g., the Dupuit solution for the steady‐state unconfined unidirectional flow in a uniform aquifer with a flat bottom) represent smooth and continuous water table configurations, simulating which does not pose any significant problems for the numerical groundwater flow models, like MODFLOW. One of the most challenging numerical cases for MODFLOW arises from drying‐rewetting problems often associated with abrupt changes in the elevations of impervious base of a thin unconfined aquifer. Numerical solutions of groundwater flow equations cannot be rigorously verified for such cases due to the lack of corresponding exact analytical solutions. Analytical solutions of the steady‐state Boussinesq equation, associated with the discontinuous water table configurations over a stairway impervious base, are presented in this article. Conditions resulting in such configurations are analyzed and discussed. These solutions appear to be well suited for testing and verification of computer codes. Numerical solutions, obtained by the latest versions of MODFLOW (MODFLOW‐2005 and MODFLOW‐NWT), are compared with the presented discontinuous analytical solutions. It is shown that standard MODFLOW‐2005 code (as well as MODFLOW‐2000 and older versions) has significant convergence problems simulating such cases. The problems manifest themselves either in a total convergence failure or erroneous results. Alternatively, MODFLOW‐NWT, providing a good match to the presented discontinuous analytical solutions, appears to be a more reliable and appropriate code for simulating abrupt changes in water table elevations. 相似文献
12.
A new method is presented for solving the 2D problem of diffraction of a plane wave by a wedge of arbitrary angle in a purely acoustic, constant-density medium with different constant compressional wave speeds inside and outside the wedge. The diffraction problem is formulated as integral equations, and a wavenumber–frequency representation of the scattered field is obtained. With the aid of the Cagniard–de Hoop method, exact analytical expressions in the space–time domain are obtained for the different wave constituents, i.e. geometric optical scattered waves and edge diffracted waves including head waves. These expressions can be computed to any degree of accuracy within reasonable computation times on a computer, and the semi-analytical method of solution presented thus constitutes a means of constructing reference solutions for wedge configurations. Such highly accurate reference solutions are of importance for verification of results that include diffraction phenomena modelled by general numerical approximate methods, e.g. finite differences, finite elements and spectral methods. Examples of such applications of the method of solution are given. 相似文献
13.
3D magnetotelluric modelling including surface topography 总被引：9，自引：0，他引：9
Myung Jin Nam Hee Joon Kim Yoonho Song Tae Jong Lee Jeong-Sul Son Jung Hee Suh 《Geophysical Prospecting》2007,55(2):277-287
An edge finite‐element method has been applied to compute magnetotelluric (MT) responses to three‐dimensional (3D) earth topography. The finite‐element algorithm uses a single edge shape function at each edge of hexahedral elements, guaranteeing the continuity of the tangential electric field while conserving the continuity of magnetic flux at boundaries. We solve the resulting system of equations using the biconjugate gradient method with a Jacobian preconditioner. The solution gives electric fields parallel to the slope of a surface relief that is often encountered in MT surveys. The algorithm is successfully verified by comparison with other numerical solutions for a 3D‐2 model for comparison of modelling methods for EM induction and a ridge model. We use a 3D trapezoidal‐hill model to investigate 3D topographic effects, which are caused mainly by galvanic effects, not only in the Zxy mode but also in the Zyx mode. If a 3D topography were approximated by a two‐dimensional topography therefore errors occurring in the transverse electric mode would be more serious than those in the transverse magnetic mode. 相似文献
14.
从麦克斯韦旋度方程出发可以直接导出瞬变电磁场扩散方程,然而扩散方程不含电场对时间的一阶导数,不能构成显式的时域有限差分方程,借鉴du Fort-Frankel有限差分离散方法引入虚拟位移电流项构建显式时域有限差分方程.对Wang和Hohmann的经典时域算法进行了两点改进:第一,通过将矩形回线源电流密度加入麦克斯韦方程组的安培环路定理方程,实现回线源瞬变电磁激发源加入;第二,在计算中考虑关断时间.第一点改进使时域有限差分方程考虑了一次场的计算,并且源的计算不再依赖均匀半空间模型响应作为初始条件,使算法能够适应表层电阻率不均匀时的三维复杂模型.由于实际观测中不可能出现阶跃电流的关断形式,第二点改进可以方便设置发射电流下降沿.采用改进的三维时域有限差分正演算法对均匀半空间模型、四类三层模型、均匀半空间中含有低阻块体模型进行了计算并分别与解析解、线性数字滤波解、积分方程解和Wang的三维时域有限差分解进行了对比验证.以H模型为例,采用建立的三维时域有限差分正演算法计算了不同关断时间的斜阶跃脉冲回线源瞬变电磁中心点感应电动势衰减曲线.以实际地质资料为基础,构建包含两层采空区的三维复杂模型,以1 μs的极短关断时间进行了复杂模型定回线源瞬变电磁响应计算,并计算了该复杂模型的视电阻率曲线. 相似文献
15.
Alberto Canestrelli Michael Dumbser Annunziato Siviglia Eleuterio F. Toro 《Advances in water resources》2010
In this paper, we study the numerical approximation of the two-dimensional morphodynamic model governed by the shallow water equations and bed-load transport following a coupled solution strategy. The resulting system of governing equations contains non-conservative products and it is solved simultaneously within each time step. The numerical solution is obtained using a new high-order accurate centered scheme of the finite volume type on unstructured meshes, which is an extension of the one-dimensional PRICE-C scheme recently proposed in Canestrelli et al. (2009) [5]. The resulting first-order accurate centered method is then extended to high order of accuracy in space via a high order WENO reconstruction technique and in time via a local continuous space–time Galerkin predictor method. The scheme is applied to the shallow water equations and the well-balanced properties of the method are investigated. Finally, we apply the new scheme to different test cases with both fixed and movable bed. An attractive future of the proposed method is that it is particularly suitable for engineering applications since it allows practitioners to adopt the most suitable sediment transport formula which better fits the field data. 相似文献
16.
The shallow water equations are used to model flows in rivers and coastal areas, and have wide applications in ocean, hydraulic engineering, and atmospheric modeling. These equations have still water steady state solutions in which the flux gradients are balanced by the source term. It is desirable to develop numerical methods which preserve exactly these steady state solutions. Another main difficulty usually arising from the simulation of dam breaks and flood waves flows is the appearance of dry areas where no water is present. If no special attention is paid, standard numerical methods may fail near dry/wet front and produce non-physical negative water height. A high-order accurate finite volume weighted essentially non-oscillatory (WENO) scheme is proposed in this paper to address these difficulties and to provide an efficient and robust method for solving the shallow water equations. A simple, easy-to-implement positivity-preserving limiter is introduced. One- and two-dimensional numerical examples are provided to verify the positivity-preserving property, well-balanced property, high-order accuracy, and good resolution for smooth and discontinuous solutions. 相似文献
17.
Existing analytical solutions to 2D and 3D contaminant transport problems are limited by the mathematically convenient assumption of uniform flow. An approximate method is developed herein for coordinate mapping of 2D (vertically-averaged) transport solutions to non-uniform steady-state irrotational and divergence-free flow fields in single-layer aquifers. The method enables existing analytical transport solutions to be applied to aquifer systems with wells, non-uniform saturated thickness, surface water features, and (to a limited degree) heterogeneous hydraulic conductivity and recharge. This mass-conservative coordinate mapping approach is inexact in its approximation of the dispersion process but is still sufficiently accurate for many simple flow systems. The degree of model error is directly proportional to the variation of velocity magnitude within the domain. These mapped analytical solutions are compared to numerical simulation results and the coordinate mapping errors are investigated. The methods described herein may be used in the traditional capacity of analytical transport models, i.e., screening and preliminary site assessment, without sacrificing accuracy by assuming locally uniform flow conditions or applying an ad-hoc coordinate transformation. The solutions benefit from the traditional advantages of analytical methods, particularly the removal of artifacts due to spatial and temporal discretization: no time-stepping or numerical discretization is required. 相似文献
18.
电磁法的三维数值模拟是一个对数值算法和计算机硬件要求都非常高的问题.对常用的微分类方法如有限单元法和有限差分法而言,求解最后所得的大型线性方程组是至关重要的一步,直接影响到正演算法的实用性.如何高效、稳定且准确地解线性方程长期以来一直是被探讨的问题.本文实现了基于线性系统直接求解技术的频率域可控源电磁(CSEM)三维正演.使用交错网格有限体积法(FV)来离散化关于二次电场的Helmholtz方程;使用直接解法取代传统的迭代解法来求解离散线性系统,即对系统矩阵进行完全LU分解,具体通过调用大规模并行矩阵直接求解器(MUMPS)来实现.基于理论模型做了一系列数值实验,首先证明了直接解法的高精度和稳定性,并考察了其内存需求、计算时间和并行可伸缩性等主要计算性能,最后检验了所开发的算法快速模拟多场源CSEM问题的能力以及对常规海洋和陆地CSEM模拟的有效性. 相似文献
19.
Soil erosion by water is the root cause of ecological degradation in the Shiwalik foothills of Northern India. Simulation of runoff and its component processes is a pre‐requisite to develop the management strategies to tackle the problem, successfully. A two‐dimensional physically based distributed numerical model, ROMO2D has been developed to simulate runoff from small agricultural watersheds on an event basis. The model employs the 2‐D Richards equation with sink term to simulate infiltration and soil moisture dynamics in the vadoze zone under variable rainfall conditions, and 2‐D Saint‐Venant equations under the kinematic wave approximation along with Manning's equation as the stage‐discharge equation for runoff routing. The various flow‐governing equations have been solved numerically by employing a Galerkin finite element method for spatial discretization using quadrilateral elements and finite difference techniques for temporal solutions. The ROMO2D computer program has been developed as a class‐based program, coded in C + + in such a way that with minor modifications, the model can be used to simulate runoff on a continuous basis. The model writes output for a runoff hydrograph of each storm. Model development is described in this paper and the results of model testing and field application are to be presented in a subsequent paper. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
20.
Estimation of vertical water fluxes from temperature time series by the inverse numerical computer program FLUX‐BOT 下载免费PDF全文
下载免费PDF全文 The application of heat as a hydrological tracer has become a standard method for quantifying water fluxes between groundwater and surface water. The typical application is to estimate vertical water fluxes in the shallow subsurface beneath streams or lakes. For this purpose, time series of temperatures in the surface water and in the sediment are measured and evaluated by a vertical 1D representation of heat transport by advection and conduction. Several analytical solutions exist to calculate the vertical water flux from the measured temperatures. Although analytical solutions can be easily implemented, they are restricted to specific boundary conditions such as a sinusoidal upper temperature boundary. Numerical solutions offer higher flexibility in the selection of the boundary conditions. This, in turn, reduces the effort of data preprocessing, such as the extraction of the diurnal temperature variation from the raw data. Here, we present software to estimate water fluxes based on temperatures—FLUX‐BOT. FLUX‐BOT is a numerical code written in MATLAB that calculates vertical water fluxes in saturated sediments based on the inversion of measured temperature time series observed at multiple depths. FLUX‐BOT applies a centred Crank–Nicolson implicit finite difference scheme to solve the one‐dimensional heat advection–conduction equation. FLUX‐BOT includes functions for the inverse numerical routines, functions for visualizing the results, and a function for performing uncertainty analysis. We present applications of FLUX‐BOT to synthetic and to real temperature data to demonstrate its performance. 相似文献