共查询到20条相似文献，搜索用时 984 毫秒
1.
A calibration method to solve the groundwater inverse problem under steady- and transient-state conditions is presented. The method compares kriged and numerical head field gradients to modify hydraulic conductivity without the use of non-linear optimization techniques. The process is repeated iteratively until a close match with piezometric data is reached. The approach includes a damping factor to avoid divergence and oscillation of the solution in areas of low hydraulic gradient and a weighting factor to account for temporal head variation in transient simulations. The efficiency of the method in terms of computing time and calibration results is demonstrated with a synthetic field. It is shown that the proposed method provides parameter fields that reproduce both hydraulic conductivity and piezometric data in few forward model solutions. Stochastic numerical experiments are conducted to evaluate the sensitivity of the method to the damping function and to the head field estimation errors. 相似文献
2.
Multi-source seismic technology is an efficient seismic acquisition method that requires a group of blended seismic data to be separated into single-source seismic data for subsequent processing. The separation of blended seismic data is a linear inverse problem. According to the relationship between the shooting number and the simultaneous source number of the acquisition system, this separation of blended seismic data is divided into an easily determined or overdetermined linear inverse problem and an underdetermined linear inverse problem that is difficult to solve. For the latter, this paper presents an optimization method that imposes the sparsity constraint on wavefields to construct the object function of inversion, and the problem is solved by using the iterative thresholding method. For the most extremely underdetermined separation problem with single-shooting and multiple sources, this paper presents a method of pseudo-deblending with random noise filtering. In this method, approximate common shot gathers are received through the pseudo-deblending process, and the random noises that appear when the approximate common shot gathers are sorted into common receiver gathers are eliminated through filtering methods. The separation methods proposed in this paper are applied to three types of numerical simulation data, including pure data without noise, data with random noise, and data with linear regular noise to obtain satisfactory results. The noise suppression effects of these methods are sufficient, particularly with single-shooting blended seismic data, which verifies the effectiveness of the proposed methods. 相似文献
3.
Doherty J 《Ground water》2003,41(2):170-177
Use of nonlinear parameter estimation techniques is now commonplace in ground water model calibration. However, there is still ample room for further development of these techniques in order to enable them to extract more information from calibration datasets, to more thoroughly explore the uncertainty associated with model predictions, and to make them easier to implement in various modeling contexts. This paper describes the use of "pilot points" as a methodology for spatial hydraulic property characterization. When used in conjunction with nonlinear parameter estimation software that incorporates advanced regularization functionality (such as PEST), use of pilot points can add a great deal of flexibility to the calibration process at the same time as it makes this process easier to implement. Pilot points can be used either as a substitute for zones of piecewise parameter uniformity, or in conjunction with such zones. In either case, they allow the disposition of areas of high and low hydraulic property value to be inferred through the calibration process, without the need for the modeler to guess the geometry of such areas prior to estimating the parameters that pertain to them. Pilot points and regularization can also be used as an adjunct to geostatistically based stochastic parameterization methods. Using the techniques described herein, a series of hydraulic property fields can be generated, all of which recognize the stochastic characterization of an area at the same time that they satisfy the constraints imposed on hydraulic property values by the need to ensure that model outputs match field measurements. Model predictions can then be made using all of these fields as a mechanism for exploring predictive uncertainty. 相似文献
4.
The inverse problem of parameter structure identification in a distributed parameter system remains challenging. Identifying a more complex parameter structure requires more data. There is also the problem of over-parameterization. In this study, we propose a modified Tabu search for parameter structure identification. We embed an adjoint state procedure in the search process to improve the efficiency of the Tabu search. We use Voronoi tessellation for automatic parameterization to reduce the dimension of the distributed parameter. Additionally, a coarse-fine grid technique is applied to further improve the effectiveness and efficiency of the proposed methodology. To avoid over-parameterization, at each level of parameter complexity we calculate the residual error for parameter fitting, the parameter uncertainty error and a modified Akaike Information Criterion. To demonstrate the proposed methodology, we conduct numerical experiments with synthetic data that simulate both discrete hydraulic conductivity zones and a continuous hydraulic conductivity distribution. Our results indicate that the Tabu search allied with the adjoint state method significantly improves computational efficiency and effectiveness in solving the inverse problem of parameter structure identification. 相似文献
5.
We present a methodology for identifying highly-localized flow channels embedded in a significantly less permeable medium using steady-state head and geometrical data. This situation is typical of fractured media where flows are often strongly channeled at the scales of interest (10 m–1 km). The objective is to identify both geometrical and hydraulic characteristics of the conducting structures. Channels are identified in decreasing order of importance by successive optimizations of an objective function. The identification strategy takes advantage of the hierarchical flow organization to restrict the dimension of the solution space of each individual optimization step. The characteristics of the secondary channels are strongly determined by the main flow channels. The latter are slightly modified by the secondary channels through the addition of a regularization term to the main channel characteristics in the objective function. As the objective function is strongly non-convex with numerous local minima, inversion is performed using a stochastic algorithm (simulated annealing). We assess the possibilities of the hierarchical identification strategy on simple synthetic steady-state flow configurations where hydraulic data are made up of 25 regularly spaced heads and of the boundary conditions. Those flow structures that are dominated by at most two simple channels can be identified with these head data only. Configurations comprising up to three complex and interconnected channels can still be identified with additional geometrical information including the distances of piezometers to their closest channel. The capabilities of the hierarchical identification strategy are limited to flow structures dominated by at most three equivalent flow channels. We finally discuss the perspectives of application of the method to transient-state data obtained on a more restricted number of piezometers. 相似文献
6.
Baha Y. Mirghani Kumar G. Mahinthakumar Michael E. Tryby Ranji S. Ranjithan Emily M. Zechman 《Advances in water resources》2009
Groundwater characterization involves the resolution of unknown system characteristics from observation data, and is often classified as an inverse problem. Inverse problems are difficult to solve due to natural ill-posedness and computational intractability. Here we adopt the use of a simulation–optimization approach that couples a numerical pollutant-transport simulation model with evolutionary search algorithms for solution of the inverse problem. In this approach, the numerical transport model is solved iteratively during the evolutionary search. This process can be computationally intensive since several hundreds to thousands of forward model evaluations are typically required for solution. Given the potential computational intractability of such a simulation–optimization approach, parallel computation is employed to ease and enable the solution of such problems. In this paper, several variations of a groundwater source identification problem is examined in terms of solution quality and computational performance. The computational experiments were performed on the TeraGrid cluster available at the National Center for Supercomputing Applications. The results demonstrate the performance of the parallel simulation–optimization approach in terms of solution quality and computational performance. 相似文献
7.
Inverse problems involving the characterization of hydraulic properties of groundwater flow systems by conditioning on observations of the state variables are mathematically ill-posed because they have multiple solutions and are sensitive to small changes in the data. In the framework of McMC methods for nonlinear optimization and under an iterative spatial resampling transition kernel, we present an algorithm for narrowing the prior and thus producing improved proposal realizations. To achieve this goal, we cosimulate the facies distribution conditionally to facies observations and normal scores transformed hydrologic response measurements, assuming a linear coregionalization model. The approach works by creating an importance sampling effect that steers the process to selected areas of the prior. The effectiveness of our approach is demonstrated by an example application on a synthetic underdetermined inverse problem in aquifer characterization. 相似文献
8.
Monica Riva Alberto Guadagnini Shlomo P. Neuman Emanuela Bianchi Janetti Bwalya Malama 《Advances in water resources》2009
We present a nonlinear stochastic inverse algorithm that allows conditioning estimates of transient hydraulic heads, fluxes and their associated uncertainty on information about hydraulic conductivity (K) and hydraulic head (h ) data collected in a randomly heterogeneous confined aquifer. Our algorithm is based on Laplace-transformed recursive finite-element approximations of exact nonlocal first and second conditional stochastic moment equations of transient flow. It makes it possible to estimate jointly spatial variations in natural log-conductivity (Y=lnK), the parameters of its underlying variogram, and the variance–covariance of these estimates. Log-conductivity is parameterized geostatistically based on measured values at discrete locations and unknown values at discrete “pilot points”. Whereas prior values of Y at pilot point are obtained by generalized kriging, posterior estimates at pilot points are obtained through a maximum likelihood fit of computed and measured transient heads. These posterior estimates are then projected onto the computational grid by kriging. Optionally, the maximum likelihood function may include a regularization term reflecting prior information about Y. The relative weight assigned to this term is evaluated separately from other model parameters to avoid bias and instability. We illustrate and explore our algorithm by means of a synthetic example involving a pumping well. We find that whereas Y and h can be reproduced quite well with parameters estimated on the basis of zero-order mean flow equations, all model quality criteria identify the second-order results as being superior to zero-order results. Identifying the weight of the regularization term and variogram parameters can be done with much lesser ambiguity based on second- than on zero-order results. A second-order model is required to compute predictive error variances of hydraulic head (and flux) a posteriori. Conditioning the inversion jointly on conductivity and hydraulic head data results in lesser predictive uncertainty than conditioning on conductivity or head data alone. 相似文献
9.
Dylan R. Harp Velimir V. Vesselinov 《Stochastic Environmental Research and Risk Assessment (SERRA)》2010,24(7):1023-1042
An approach is presented for identifying statistical characteristics of stratigraphies from borehole and hydraulic data. The
approach employs a Markov-chain based geostatistical framework in a stochastic inversion. Borehole data provide information
on the stratigraphy while pressure and flux data provide information on the hydraulic performance of the medium. The use of
Markov-chain geostatistics as opposed to covariance-based geostatistics can provide a more easily interpreted model geologically
and geometrically. The approach hinges on the use of mean facies lengths (negative inverse auto-transition rates) and mean
transition lengths (inverse cross-transition rates) as adjustable parameters in the stochastic inversion. Along with an unconstrained
Markov-chain model, simplifying constraints to the Markov-chain model, including (1) proportionally-random and (2) symmetric
spatial correlations, are evaluated in the stochastic inversion. Sensitivity analyses indicate that the simplifying constraints
can facilitate the inversion at the cost of spatial correlation model generality. Inverse analyses demonstrate the feasibility
of this approach, indicating that despite some low parameter sensitivities, all adjustable parameters do converge for a sufficient
number of ensemble realizations towards their “true” values. This paper extends the approach presented in Harp et al. (doi:, 2008) to (1) statistically characterize the hydraulic response of a geostatistical model, thereby incorporating an uncertainty
analysis directly in the inverse method, (2) demonstrate that a gradient-based optimization strategy is sufficient, thereby
providing relative computational efficiency compared to global optimization strategies, (3) demonstrate that the approach
can be extended to a 3-D analysis, and (4) introduce the use of mean facies lengths and mean transition lengths as adjustable
parameters in a geostatistical inversion, thereby allowing the approach to be extended to greater than two category Markov-chain
models. 相似文献
10.
This work proposes a complete method for automatic inversion of data from hydraulic interference pumping tests based on both homogeneous and fractal dual-medium approaches. The aim is to seek a new alternative concept able to interpret field data, identify macroscopic hydraulic parameters and therefore enhance the understanding of flow in porous fractured reservoirs. Because of its much contrasted sensitivities to parameters, the dual-medium approach yields an ill-posed inverse problem that requires a specific optimization procedure including the calculation of analytical sensitivities and their possible re-scaling. Once these constraints are fulfilled, the inversion proves accurate, provides unambiguous and reliable results. In the fractal context inverting several drawdown curves from different locations at the same time reveals more accurate. Finally, hydraulic parameters drawn from inversion should be taken into account to improve in various situations the conditioning of up-scaled flow in fractured rocks. 相似文献
11.
This paper presents a method for inverting ground penetrating radargrams in terms of one-dimensional profiles. We resort to a special type of linearization of the damped E-field wave equation to solve the inverse problem. The numerical algorithm for the inversion is iterative and requires the solution of several forward problems, which we evaluate using the matrix propagation approach. Analytical expressions for the derivatives with respect to physical properties are obtained using the self-adjoint Green's function method. We consider three physical properties of materials; namely dielectrical permittivity, magnetic permeability and electrical conductivity. The inverse problem is solved minimizing the quadratic norm of the residuals using quadratic programming optimization. In the iterative process to speed up convergence we use the Levenberg–Mardquardt method. The special type of linearization is based on an integral equation that involves derivatives of the electric field with respect to magnetic permeability, electrical conductivity and dielectric permittivity; this equation is the result of analyzing the implication of the scaling properties of the electromagnetic field. The ground is modeled using thin horizontal layers to approximate general variations of the physical properties. We show that standard synthetic radargrams due to dielectric permittivity contrasts can be matched using electrical conductivity or magnetic permeability variations. The results indicate that it is impossible to differentiate one property from the other using GPR data. 相似文献
12.
Conditioning mean steady state flow on hydraulic head and conductivity through geostatistical inversion 总被引：5，自引：2，他引：3
Nonlocal moment equations allow one to render deterministically optimum predictions of flow in randomly heterogeneous media and to assess predictive uncertainty conditional on measured values of medium properties. We present a geostatistical inverse algorithm for steady-state flow that makes it possible to further condition such predictions and assessments on measured values of hydraulic head (and/or flux). Our algorithm is based on recursive finite-element approximations of exact first and second conditional moment equations. Hydraulic conductivity is parameterized via universal kriging based on unknown values at pilot points and (optionally) measured values at other discrete locations. Optimum unbiased inverse estimates of natural log hydraulic conductivity, head and flux are obtained by minimizing a residual criterion using the Levenberg-Marquardt algorithm. We illustrate the method for superimposed mean uniform and convergent flows in a bounded two-dimensional domain. Our examples illustrate how conductivity and head data act separately or jointly to reduce parameter estimation errors and model predictive uncertainty.This work is supported in part by NSF/ITR Grant EAR-0110289. The first author was additionally supported by scholarships from CONACYT and Instituto de Investigaciones Electricas of Mexico. Additional support was provided by the European Commission under Contract EVK1-CT-1999-00041 (W-SAHaRA-Stochastic Analysis of Well Head Protection and Risk Assessment). 相似文献
13.
Combination of FEM and CMA‐ES algorithm for transmissivity identification in aquifer systems 
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下载免费PDF全文 In this paper, we propose a coupling of a finite element model with a metaheuristic optimization algorithm for solving the inverse problem in groundwater flow (Darcy's equations). This coupling performed in 2 phases is based on the combination of 2 codes: This is the HySubF‐FEM code (hydrodynamic of subsurface flow by finite element method) used for the first phase allowing the calculation of the flow and the CMA‐ES code (covariance matrix adaptation evolution strategy) adopted in the second phase for the optimization process. The combination of these 2 codes was implemented to identify the transmissivity field of groundwater by knowing the hydraulic head in some point of the studied domain. The integrated optimization algorithm HySubF‐FEM/CMA‐ES has been validated successfully on a schematic case offering an analytical solution. As realistic application, the integrated optimization algorithm HySubF‐FEM/CMA‐ES was applied to a complex groundwater in the north of France to identify the transmissivity field. This application does not use zonation techniques but solves an optimization problem at each internal node of the mesh. The obtained results are considered excellent with high accuracy and fully consistent with the hydrogeological characteristics of the studied aquifer.However, the various numerical simulations performed in this paper have shown that the CMA‐ES algorithm is time‐consuming. Finally, the paper concludes that the proposed algorithm can be considered as an efficient tool for solving inverse problems in groundwater flow. 相似文献
14.
15.
Hydraulic Gradient Comparison Method to Estimate Aquifer Hydraulic Parameters Under Steady-State Conditions 总被引：1，自引：0，他引：1
The hydraulic gradient comparison method is an inverse method for estimation of aquifer hydraulic conductivity (or trans-missivity) and boundary conductance for a ground water flow model under steady-state conditions. This method, following formal optimization techniques, defines its objective function to minimize differences between interpreted (observed) and simulated hydraulic gradients, which results in minimization of differences between observed and simulated hydraulic heads. The key features of this method are that (1) the derived optimality conditions have an explicit form with a clear hydrology concept that is con-sistent with Darcy's law, and (2) the derived optimality conditions are spatially independent as they are a function of only local hydraulic conductivity and local hydraulic gradient. This second feature allows a multidimensional optimization problem to be solved by many one-dimensional optimization procedures simultaneously, which results in a substantial reduction in computation time. The results of the numerical performance testing on a heterogeneous hypothetical case confirm that minimizing gradient residuals in the entire model domain leads to minimizing head residuals. Application of the method in real-world projects requires rigorous conceptual model development, use of a global calibration target, and an iterative calibration proess. The conceptual model development includes interpretation of a potentiometric surface and estimation of other hydrologic parameters. This method has been applied to a wide range of real-world modeling projects, including the Rocky Mountain Arsenal and Rocky Flats sites in Colorado, which demonstrates that the method is efficient and practical. 相似文献
16.
In steady-state hydraulic tomography, the head data recorded during a series of pumping or/and injection tests can be inverted to determine the transmissivity distributions of an aquifer. This inverse problem is usually under-determined and ill-posed. We propose to use structural information inferred from a guiding image to constrain the inversion process. The guiding image can be drawn from soft data sets such as seismic and ground penetrating radar sections or from geological cross-sections inferred from the wells and some geological expertise. The structural information is extracted from the guiding image through some digital image analysis techniques. Then, it is introduced into the inversion process of the head data as a weighted four direction smoothing matrix used in the regularizer. Such smoothing matrix allows applying the smoothing along the structural features. This helps preserving eventual drops in the hydraulic properties. In addition, we apply a procedure called image-guided interpolation. This technique starts with the tomogram obtained from the image-guided inversion and focus this tomogram. These new approaches are applied on four synthetic toy problems. The hydraulic distributions estimated from the image-guided inversion are closer to the true transmissivity model and have higher resolution than those computed from a classical Gauss–Newton method with uniform isotropic smoothing. 相似文献
17.
Modelling the impacts of spatial heterogeneity in soil hydraulic properties on hydrological process in the upper reach of the Heihe River in the Qilian Mountains,Northwest China 总被引：1，自引：0，他引：1 下载免费PDF全文
下载免费PDF全文 Spatial heterogeneity of soil has great impacts on dynamic processes of the hydrological systems. However, it is challenging and expensive to obtain spatial distribution of soil hydraulic properties, which often requires extensive soil sampling and observations and intensive laboratory analyses, especially in high elevation, hard to access mountainous areas. This study evaluates the impacts of soil heterogeneity on hydrological process in a high elevation, topographically complex watershed in Northwest China. Two approaches were used to derive the spatial heterogeneity of soil properties in the study watershed: (1) the spatial clustering method, Full‐Order‐CLK was used to determine five soil heterogeneous clusters (configurations 97, 80, 60, 40 and 20) through large number of soil sampling and in situ observations, and (2) the average values of soil hydraulic properties for each soil type were derived from the coarse provincial soil data sets (Gansu Soil Handbook at 1 : 1 000 000 scale). Subsequently, Soil and Water Assessment Tool model was used to quantify the impact of the spatial heterogeneity of soil hydraulic properties on hydrological process in the study watershed. Results show the simulations by Soil and Water Assessment Tool with the spatially clustered soil hydraulic information from the field sampling data had much better representation of the soil heterogeneity and had more accurate performance than the model using the average soil property values for each soil type derived from the coarse soil data sets. Thus, incorporating detailed field sampling, soil heterogeneity data greatly improve performance in hydrological modelling. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
18.
In most real-world hydrogeologic situations, natural heterogeneity and measurement errors introduce major sources of uncertainty in the solution of the inverse problem. The Bayesian Maximum Entropy (BME) method of modern geostatistics offers an efficient solution to the inverse problem by first assimilating various physical knowledge bases (hydrologic laws, water table elevation data, uncertain hydraulic resistivity measurements, etc.) and then producing robust estimates of the subsurface variables across space. We present specific methods for implementing the BME conceptual framework to solve an inverse problem involving Darcys law for subsurface flow. We illustrate one of these methods in the case of a synthetic one-dimensional case study concerned with the estimation of hydraulic resistivity conditioned on soft data and hydraulic head measurements. The BME framework processes the physical knowledge contained in Darcys law and generates accurate estimates of hydraulic resistivity across space. The optimal distribution of hard and soft data needed to minimize the associated estimation error at a specified sampling cost is determined.
This work was supported by grants from the National Institute of Environmental Health Sciences (Grant no. 5 P42 ES05948 and P30ES10126), the National Aeronautics and Space Administration (Grant no. 60-00RFQ041), the Army Research Office (Grant no. DAAG55-98-1-0289), and the National Science Foundation under Agreement No. DMS-0112069. 相似文献
19.
Yong Jung G. Mahinthakumar Ranji Ranjithan 《Stochastic Environmental Research and Risk Assessment (SERRA)》2013,27(8):2003-2013
Strategically applied geo-environmental clean-up methods require a better groundwater flow and transport model. Hydraulic conductivity of the subsurface is one of great sources of uncertainty of this model. In order to search hydraulic conductivities, the simultaneous search-based pilot point method (SSBM) was developed to reduce computational procedure of pilot point method and increase characterization accuracy using a global optimization tool (genetic algorithm). SSBM searches pilot point locations and hydraulic conductivities at selected pilot points simultaneously. In the four different scenarios, the comparison between random pilot point locations and SSBM showed that SSBM produced less than two orders magnitude differences in terms of average of minimum fitness for thirty trials (e.g. 4.05E?02 for scenario 2). With respect to average minimum fitness and average hydraulic conductivity difference, SSBM was comparable to D-optimality based pilot point method (DBM). SSBM produced lower average minimum fitness values and similar average hydraulic conductivity difference but it had more variance. Through these results, SSBM showed the potential to replace the DBM through reduced computational procedures in sensitivity calculation with consideration of variance minimization. 相似文献
20.
Hakan Sirin 《Stochastic Environmental Research and Risk Assessment (SERRA)》2006,20(6):381-390
Solute plume subjected to field scale hydraulic conductivity heterogeneity shows a large dispersion/macrodispersion, which is the manifestation of existing fields scale heterogeneity on the solute plume. On the other hand, due to the scarcity of hydraulic conductivity measurements at field scale, hydraulic conductivity heterogeneity can only be defined statistically, which makes the hydraulic conductivity a random variable/function. Random hydraulic conductivity as a parameter in flow equation makes the pore flow velocity also random and the ground water solute transport equation is a stochastic differential equation now. In this study, the ensemble average of stochastic ground water solute transport equation is taken by the cumulant expansion method in order to upscale the laboratory scale transport equation to field scale by assuming pore flow velocity is a non stationary, non divergence-free and unsteady random function of space and time. Besides the stochastic explanation of macrodispersion and the velocity correction term obtained by Kavvas and Karakas (J Hydrol 179:321–351, 1996) before a new velocity correction term, which is a function of mean pore flow velocity divergence, is obtained in this study due to strict second order cumulant expansion (without omitting any term after the expansion) performed. The significance of the new velocity correction term is investigated on a one dimensional transport problem driven by a density dependent flow field. 相似文献