共查询到20条相似文献，搜索用时 281 毫秒
1.
2.
G. Christakos D. T. Hristopulos 《Stochastic Environmental Research and Risk Assessment (SERRA)》1994,8(2):117-138
In earlier publications, certain applications of space transformation operators in subsurface hydrology were considered. These operators reduce the original multi-dimensional problem to the one-dimensional space, and can be used to study stochastic partial differential equations governing groundwater flow and solute transport processes. In the present work we discuss developments in the theoretical formulation of flow models with space-dependent coefficients in terms of space transformations. The formulation is based on stochastic Radon operator representations of generalized functions. A generalized spectral decomposition of the flow parameters is introduced, which leads to analytically tractable expressions of the space transformed flow equation. A Plancherel representation of the space transformation product of the head potential and the log-conductivity is also obtained. A test problem is first considered in detail and the solutions obtained by means of the proposed approach are compared with the exact solutions obtained by standard partial differential equation methods. Then, solutions of three-dimensional groundwater flow are derived starting from solutions of a one-dimensional model along various directions in space. A step-by-step numerical formulation of the approach to the flow problem is also discussed, which is useful for practical applications. Finally, the space transformation solutions are compared with local solutions obtained by means of series expansions of the log-conductivity gradient. 相似文献
3.
The Bayesian inverse approach proposed by Woodbury and Ulrych (2000) is extended to estimate the transmissivity fields of highly heterogeneous aquifers for steady state ground water flow. Boundary conditions are Dirichlet and Neumann type, and sink and source terms are included. A first-order approximation of Taylor's series for the exponential terms introduced by sinks and sources or the Neumann condition in the governing equation is adopted. Such a treatment leads to a linear finite element formulation between hydraulic head and the logarithm of the transmissivity-denoted as ln(T)-perturbations. An updating procedure similar to that of Woodbury and Ulrych (2000) can be performed. This new algorithm is examined against a generic example. It is found that the linearized solution approximates the true solution with an R2 coefficient = 0.96 for an ln(T) variance of 9 for the test case. The addition of hydraulic head data is shown to improve the ln(T) estimates, in comparison to simply interpolating the sparse ln(T) data alone. The new Bayesian code is also employed to calibrate a high-resolution finite difference MODFLOW model of the Edwards Aquifer in southwest Texas. The posterior ln(T) field from this application yields better head fit when compared to the prior ln(T) field determined from upscaling and cokriging. We believe that traditional MODFLOW grids could be imported into the new Bayes code fairly seamlessly and thereby enhance existing calibration of many aquifers. 相似文献
4.
5.
Modeling of flow features that are important in assessing stream habitat conditions has been a long-standing interest of stream biologists. Recently, they have begun examining the usefulness of two-dimensional (2-D) hydrodynamic models in attaining this objective. Current modeling practices consider relatively long channel sections with their bathymetry represented in terms of large, macro-scale, topographic features. Meso-scale topographic features, such as boulders, root-wads and other obstructions are typically not considered in the modeling process. Instead, the overall effects of these flow obstructions are captured through increased values in the channel roughness parameters. Such an approach to 2-D modeling allows one to accurately predict average depth and velocity values; however, it is not capable of providing any information about the flow patterns in the vicinity of these obstructions. Biologists though have known that such meso-scale features and the complex velocity patterns generated by their presence, play an important role in the ecology of streams, and thus cannot be ignored. It is therefore evident that there is a need to develop better tools, capable of modeling flow characteristics at scales of ecological importance. The purpose of this study is to expand the utility of 2-D hydraulic models to capture these flow features that are critical for characterizing stream habitat conditions.
There exists a paucity of research addressing what types of topographic features should be included in 2-D model studies and to what extent a boulder or series of exposed boulders can influence predicted flow conditions and traditional useable habitat computations. Moreover, little research has been performed to evaluate the impact mesh refinement has on model results in natural streams. Numerical simulations, based on a natural river channel containing several large boulders, indicate that explicitly modeling local obstructions/boulders can significantly impact predicted flow parameters. The presence of these obstructions create velocity gradients, velocity shelters, transverse flows and other ecologically important flow features that are not reproduced when their geometry is not incorporated into the hydraulic model. Sensitivity analyses show that reducing element sizes in the vicinity of obstructions and banks is crucial in modeling the spatial flow patterns created by meso-scale topographic features. This information, combined with similar data obtained in future studies, can provide guidelines for the placement of fishrocks and other structures often used in stream restoration projects as well as determining what types of meso-scale topographic features might need to be incorporated into habitat suitability studies. Such information may also ultimately allow new spatial habitat metrics to be developed. 相似文献
6.
Subsurface fluid flow and solute transport take place in a multiscale heterogeneous environment. Neither these phenomena nor their host environment can be observed or described with certainty at all scales and locations of relevance. The resulting ambiguity has led to alternative conceptualizations of flow and transport and multiple ways of addressing their scale and space–time dependencies. We focus our attention on four approaches that give rise to nonlocal representations of advective and dispersive transport of nonreactive tracers in randomly heterogeneous porous or fractured continua. We compare these approaches theoretically on the basis of their underlying premises and the mathematical forms of the corresponding nonlocal advective–dispersive terms. One of the four approaches describes transport at some reference support scale by a classical (Fickian) advection–dispersion equation (ADE) in which velocity is a spatially (and possibly temporally) correlated random field. The randomness of the velocity, which is given by Darcy’s law, stems from random fluctuations in hydraulic conductivity (and advective porosity though this is often disregarded). Averaging the stochastic ADE over an ensemble of velocity fields results in a space–time-nonlocal representation of mean advective–dispersive flux, an approach we designate as stnADE. A closely related space–time-nonlocal representation of ensemble mean transport is obtained upon averaging the motion of solute particles through a random velocity field within a Lagrangian framework, an approach we designate stnL. The concept of continuous time random walk (CTRW) yields a representation of advective–dispersive flux that is nonlocal in time but local in space. Closely related to the latter are forms of ADE entailing fractional derivatives (fADE) which leads to representations of advective–dispersive flux that are nonlocal in space but local in time; nonlocality in time arises in the context of multirate mass transfer models, which we exclude from consideration in this paper. We describe briefly each of these four nonlocal approaches and offer a perspective on their differences, commonalities, and relative merits as analytical and predictive tools. 相似文献
7.
We consider identification of absolute permeability (hydraulic conductivity) based on time series of pressure data in sparsely distributed wells for two-phase porous-media flow. For this problem, it is impossible to recover all details of the parameter function. On the other hand, a coarser, approximate recovery may be sufficient for many applications. We propose a novel solution approach, based on reparametrization, for such approximate identification of the parameter function. We use a nonlinear, composite representation, which is detached from the computational grid, allowing for a flexible representation of the parameter function at many resolution levels. This is utilized in a sequential multi-level estimation of the parameter function, starting at a coarse resolution, which is then gradually refined. The composite representation is designed to allow for smooth as well as sharp transitions between regions of nearly constant parameter value. Moreover, it facilitates the estimation also of the structure and smoothness of the parameter function itself. As a limiting case, the chosen representation is reduced to a zonation with implicit representation of the interior boundaries that is equivalent to a level-set representation. A motivation for the selected representation and the multi-level estimation is presented in terms of an analysis of sensitivity and nonlinearity. Numerical examples demonstrate identification of coarse-scale features of reference permeability distributions with varying degree of smoothness. Comparisons show how the multi-level strategy stabilize the identification and avoid local minima of the objective function compared to a single-level strategy. 相似文献
8.
RAFAEL G. QUIMPO 《水文科学杂志》2013,58(4):111-118
Abstract The need for specifying water availability in terms of its time sequence and distribution, rather than in terms of lumped quantities or flow duration, has given rise to data asquisition programs which use shorter sampling intervals. Shorter time intervals, in turn, has resulted in serially correlated observations. In order to determine the reliability of design variables derived from these observations, it is necessary to reduce these data to an equivalent series of independent observations, or find the effective lenght of the series. A general parametric formula is developed for the effective number of observations for the second order autoregressive process, which has been found to apply to the series of mean daily river flows. Different values of the parameters were programmed in a digital computer to obtain tables for data reduction. 相似文献
9.
D. G. Zeitoun C. Braester 《Stochastic Environmental Research and Risk Assessment (SERRA)》1991,5(3):207-226
A stochastic approach is used for the study of flow through highly heterogeneous aquifers. The mathematical model is represented by a random partial differential equation in which the permeability and the porosity are considered to be random functions of position, defined by the average value, constant standard deviation and autocorrelation function characterized by the integral scale. The Laplace transform of the solution of the random partial differential equation is first written as a solution of a stochastic integral equation. This integral equation is solved using a Neumann series expansion. Conditions of convergence of this series are investigated and compared with the convergence of the perturbation series. For mean square convergence, the Neumann expansion method may converge for a larger range of variability in permeability and porosity than the classic perturbation method. Formal expressions for the average and for the correlation moments of the pressure are obtained. The influence of the variability of the permeability and porosity on pressure is analyzed for radial flow. The solutions presented for the pressure at the well, as function of the permeability coefficient of variation, may be of practical interest for evaluating the efficiency of well stimulation operations, such as hydraulic fracturing or acidizing methods, aimed at increasing the permeability around the well. 相似文献
10.
Paul Francis Worthington 《Surveys in Geophysics》1975,2(3):313-366
Groundwater flow and storage in granular aquifers are much more amenable to analysis than in fissured reservoirs. The hydrological parameters used to describe the behaviour of a granular aquifer have been seen to be related to geophysical parameters in diverse water-bearing formations. This means that certain geophysical survey techniques are potentially useful as quantitative hydrogeological tools. Yet the study of these basic relationships and their subsequent field application have been disjointed and lacking in overal co-ordination. Consequently these quantitative hydrogeophysical procedures have not been applied to maximum advantage. The role of geophysics in quantitative studies of granular aquifers is reviewed in terms of the prediction of effective porosity and intergranular permeability from geophysical measurement. The potential usefulness of these methods manifests itself through the degree of correlation between hydrological and geophysical parameters observed from laboratory studies, borehole logging investigations or field survey data. Their application is exemplified through an ordered series of hydrogeophysical case histories. It is contended that the potential of geophysical methods in quantitative studies of this kind has by no means been fully exploited. 相似文献
11.
We introduce a new method for prestack depth migration of seismic common-shot gathers. The computational procedure follows
standard steps of the reverse-time migration, i.e., downward continuation of the source and the receiver wavefields, followed
by application of an imaging condition (e.g. zero-lag cross-correlation of these fields). In our method we first find a sparse
data representation with a small number of Gaussian wave packets. We then approximate the downward wavefield propagation (for
the source and the receiver fields) by a rigid flow of these wave packets along seismic rays. In this case, the wave packets
are simply translated and rotated according to the ray geometry. One advantage of using Gaussian wave packets is that analytic
formulas can be used for translation, rotation, and the application of the cross-correlation imaging condition. Moreover,
they allow more sparse representations than competing methods. Finally we formulate a computationally and memory efficient
migration procedure, as only few rays have to be traced, and since it is cheap to compute the cross-correlation for the intersecting
rays. 相似文献
12.
AbstractThis paper aims at revisiting the use of non-dimensional representations for catchment change and model robustness analysis. As well as being helpful for catchment classification according to hydroclimatic conditions, the Turc-Budyko representation enables visualization of temporal changes in these conditions and/or modification of the hydrological behaviour of the catchment. This brings a new perspective to hydrological analysis, different from the classical time series plots, which helps when interpreting catchment functioning with respect to hydroclimatic constraints. These tools do not require statistical analyses of observed series and are therefore very simple to implement. Four case studies are considered here to illustrate the use of the Q/P = f(P/Ep) graph. When combined with the inter-annual Turc-Mezentsev formula, this visual framework enables anticipation of potential difficulties for models based on the same hypotheses, solely using the analysis of observed data. 相似文献
13.
The method of temporal moments is an efficient approach for analyzing breakthrough curves (BTCs). By matching the moments of the BTCs computed through parametric transfer-function models or one-dimensional transport models to those of the data, one can estimate the parameters characterizing the transfer function or apparent transport parameters. The classical method of moments presumes infinite duration. However, the measurement of BTCs is usually terminated prematurely, before the concentration has reached zero. Unless this truncation of the BTCs has been taken into account, the estimates of the parameters may be in error. Truncated measured BTCs are sometimes extrapolated assuming exponential decay. In this study, we use the concept of moments of the truncated impulse–response function [Jawitz JW. Moments of truncated continuous univariate distributions. Adv Water Res 2004;27:269–81] in the analysis of truncated BTCs corresponding to the commonly encountered step and step-pulse injection modes. The method is straightforward, based on the relation, which we derive, between truncated moments of the impulse–response function and the measured BTC. It is practical to apply and does not require the extrapolation of the measured BTC. The method is also accurate. In a numerical study we discuss how short a step-pulse injection may be so that we can approximate it as instantaneous. Finally, we apply the method to the analysis of a field-scale tracer test. 相似文献
14.
Accurate representation of groundwater flow and solute transport requires a sound representation of the underlying geometry of aquifers. Faults can have a significant influence on the structure and connectivity of aquifers, which may allow permeable units to connect, and aquifers to seal when juxtaposed against lower permeability units. Robust representation of groundwater flow around faults remains challenging despite the significance of faults for flow and transport. We present a methodology for the inclusion of faults utilizing the unstructured grid features of MODFLOW-USG and MODFLOW 6. The method focuses on the representation of fault geometries using non-neighbor connections between juxtaposed layers. We present an illustration of the method for a synthetic fluvial aquifer. The combined impact of the heterogeneous aquifer and fault offset is clearly visible where channel features at different depths in the aquifer were connected at the fault. These results highlight the importance of representing fault features in groundwater flow models. 相似文献
15.
The convolution-type and correlation-type representation theorems are building blocks of wave-scattering theory whose usefulness expands in many seismological applications. For example, the Kirchhoff scattering series currently used for attenuating free-surface multiples has been derived from the convolution-type representation theorem. The recently introduced concept of virtual events, which allows us to put virtual sources and virtual receivers inside the subsurface based on the data collected at the sea surface, has been derived by a combined use of the convolution-type and correlation-type representation theorems. The formulation of inverse Kirchhoff scattering series and virtual events has been limited so far to the cases in which sources or receivers, or both, are located in the water. Unfortunately, this assumption is not valid, especially in the context of virtual events, in which both sources and receivers will often be located in a solid. We here redescribe the Kirchhoff scattering series and reformulate the concept of virtual events for the cases in which sources and receivers are in a solid. Moreover, we describe a new form of Kirchhoff series based on the correlation-type representation theorem and new formulae for computing virtual events which do not include the complex renormalization operation of the previous formulation. 相似文献
16.
K. HELBIG 《Geophysical Prospecting》1981,29(4):550-577
Waves propagating through a sequence of layers that are thin compared with the wavelength show effects of anisotropy: velocity and displacement direction depend on the angle between the plane of layering and the wave normal, and shear waves split up into two distinct types of different velocity. The layered medium can thus be replaced by a transversely isotrophic medium the parameters of which depend on the parameters of the individual constituent layers. A survey of the anisotropy effects possible in such a medium is generally done by varying the layer parameters in order to obtain different replacement media. This approach guarantees that the replacement medium is realistic, but it does not guarantee adequate sampling of the set of replacement media. To this end one has to begin by selecting the replacement media and then check whether the chosen media possess stable (and eventually realistic) representations by layer sequences. In general, there is an infinite number of layer representations for any transversely isotropic medium that can at all be represented. However, if one restricts the solutions to those requiring the minimal number of layers and the minimum number of different layer parameters, the set of solutions has only one free parameter (i.e., it is a one-dimensional manifold), and an important subset even has a unique solution. A simple algorithm exists for the determination of these “simplest representations”. Aside from sampling the set of representable transversely isotropic media for survey purposes, the method can be applied to the problem of determining the cause of observed anisotropy effects (or lateral changes in such effects). If this method can be applied to real data, it would for instance allow to determine changes in relative thickness or lithology on a scale smaller than the limit of resolution of the seismic method. 相似文献
17.
《Advances in water resources》1998,21(7):581-590
Advances in computer power and in reservoir characterization allow simulation of pressure transients in complex reservoirs generated stochastically. Generally, interpretation of these transient gives useful information about the reservoir hydraulic properties: a major goal is to interpret these transients in the stochastic context. First we ensemble average the pressure over all the random permeability field realizations to derive an equation which drives the ensemble averaged pressure. We use the Fourier transform in space and the Laplace transform in time, in conjuction with a perturbation series expansion in successive powers of the permeability fluctuations to obtain an explicit solution. The Nth order term of this series involves the hydrodynamic interaction between N permeability heterogeneities and after averaging we obtain an expansion containing correlation functions of permeability fluctuations of increasing order.Next, Feynman graphs are introduced allowing a more attractive graphical interpretation of the perturbation series. Then series summation techniques are employed to reduce the graph number to be summed at each order of the fluctuation expansion. This in turn gives useful physical insights on the homogenization processes involved. In particular, it is shown that the sum of the so-called ‘one-particle irreducible graphs’ gives the kernel of a linear integro-differential equation obeyed by the ensemble average pressure. All the information about the heterogeneity structure is contained in this renormalized kernel, which is a limited range function.This equation on its own is the starting point of useful asymptotic results and approximations. In particular it is shown that interpretation of pumping tests yields the steady-state equivalent permeability after a sufficiently long time for an infinite reservoir, as expected. 相似文献
18.
—?A 2-D and a 3-D finite element representation using Drucker-Prager cap model is employed in the study to determine the seismic response of a volcanic hill located in one of the islands in the Azores Archipelago. In order to test the applicability of these models we used the motion recorded at the base of the hill during an aftershock of the July 9, 1998 earthquake and compared the numerical response with the record obtained at the top of the hill. Several comparisons and sensitivity analyses were made to identify the most important dynamic parameters influencing the response. Even though the match is not yet adequate for any one of the representations, especially in time domain, the 3-D model showed a good fitting in terms of Fourier Spectrum. Up to a PGA of 0.24?g the behavior of the hill is approximately linear, with higher amplifications going upwards along a vertical interior column; beyond this limit, there is a clear nonlinear behavior. 相似文献
19.
Technological advances, by facilitating extensive data collection, better data sharing, formulation of sophisticated methods, and development of complex models, have brought hydrologic research to a whole new level. Despite these obvious advances, there are also concerns about their general use in practice. On the one hand, it is natural to develop more complex models than perhaps needed (i.e. representations having too many parameters and requiring too much data); on the other hand, it is often difficult to ‘translate’ results from one specific situation to another. Recent studies have addressed these concerns, albeit in different forms, such as dominant processes, thresholds, model integration, and model simplification. A common aspect in some of these studies is that they recognize the need for a globally agreed upon ‘classification system’ in hydrology. The present study explores this classification issue further from a simple phase‐space data reconstruction perspective. The reconstruction involves representation of the given multidimensional hydrologic system using only an available single‐variable series through a delay coordinate procedure. The ‘extent of complexity’ of the system (defined especially in the context of variability of relevant data) is identified by the ‘region of attraction of trajectories’ in the phase space, which is then used to classify the system as potentially low‐, medium‐ or high‐dimensional. A host of river‐related data, representing different geographic and climatic regions, temporal scales, and processes, are studied. Yielding ‘attractors’ that range from ‘very clear’ ones to ‘very blurred’ ones, depending on data, the results indicate the usefulness of this simple reconstruction concept for studying hydrologic system complexity and classification. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
20.
A flow pattern is characterized by aquifer features and the number, type, and distribution of stagnation points (locations where the discharge is zero). This article identifies a condition for transition of flow patterns in two-dimensional groundwater flow obeying Darcy’s law by examining changes in stagnation points, using the Taylor series expansion of the discharge vector. It is found that the three standard types of stagnation points (minimums, maximums, and saddle points) are completely characterized by the first-order term containing the discharge gradient tensor. However, when the determinant of the tensor becomes zero, stagnation points of other types characterized by higher-order terms come into existence. In this article, we call these zero-determinant stagnation points as critical stagnation points; they may emerge suddenly, split to a set of new stagnation points, or disappear from the flow, resulting in transitions of flow patterns. Examples of both transient and steady flows are used to illustrate the usefulness and significance of critical stagnation points. 相似文献