Three‐dimensional interference test interpretation in a fractured aquifer using the Pilot Point Inverse Method

Lavenue, Marsh; Marsily, Ghislain de

doi:10.1029/2000wr000289

Cited by 55 publications

(56 citation statements)

References 31 publications

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“…Among the inverse techniques, the Monte-Carlo approach, in which multiple equally likely realisations of aquifer properties are conditioned to hydraulic head and concentration data, allows estimating uncertainty. Inverse methods have been applied successfully in a wide range of problems [7,27,28,41].…”

Section: Introductionmentioning

confidence: 99%

Issues in characterizing heterogeneity and connectivity in non-multiGaussian media

Kerrou

Renard

Franssen

et al. 2008

Advances in Water Resources

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The performances of kriging, stochastic simulations and sequential self-calibration inversion are assessed when characterizing a nonmultiGaussian synthetic 2D braided channel aquifer. The comparison is based on a series of criteria such as the reproduction of the original reference transmissivity or head fields, but also in terms of accuracy of flow and transport (capture zone) forecasts when the flow conditions are modified. We observe that the errors remain large even for a dense data network. In addition some unexpected behaviours are observed when large transmissivity datasets are used. In particular, we observe an increase of the bias with the number of transmissivity data and an increasing uncertainty with the number of head data. This is interpreted as a consequence of the use of an inadequate multiGaussian stochastic model that is not able to reproduce the connectivity of the original field.

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Section: Introductionmentioning

confidence: 99%

Issues in characterizing heterogeneity and connectivity in non-multiGaussian media

Kerrou

Renard

Franssen

et al. 2008

Advances in Water Resources

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“…Gomez-Hernandez et al (2001) applied this method in conductivity simulation of a fractured rock block and Franssen et al (2003) extended it to a coupled groundwater flow and mass transport problem. Ramarao et al (1995) developed the pilot point method for conditional simulation of transmissivity field and it was later applied in a fractured aquifer by Lavenue and de Marsily (2001). Kentel and Aral (2005).…”

Section: Introductionmentioning

confidence: 99%

Parameter estimation in nonlinear environmental problems

Liu

Cardiff

Kitanidis

2010

Stoch Environ Res Risk Assess

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Popular parameter estimation methods, including least squares, maximum likelihood, and maximum a posteriori (MAP), solve an optimization problem to obtain a central value (or best estimate) followed by an approximate evaluation of the spread (or covariance matrix). A different approach is the Monte Carlo (MC) method, and particularly Markov chain Monte Carlo (MCMC) methods, which allow sampling from the posterior distribution of the parameters. Though available for years, MC methods have only recently drawn wide attention as practical ways for solving challenging highdimensional parameter estimation problems. They have a broader scope of applications than conventional methods and can be used to derive the full posterior pdf but can be computationally very intensive. This paper compares a number of different methods and presents improvements using as case study a nonlinear DNAPL source dissolution and solute transport model. This depth-integrated semianalytical model approximates dissolution from the DNAPL source zone using nonlinear empirical equations with partially known parameters. It then calculates the DNAPL plume concentration in the aquifer by solving the advection-dispersion equation with a flux boundary. The comparison is among the classical MAP and some versions of computer-intensive Monte Carlo methods, including the Metropolis-Hastings (MH) method and the adaptive direction sampling (ADS) method.

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“…Another approach is the pilot point method, which is applied as a parameterization technique for reducing the number of unknown parameters to estimate by evaluating the model parameters only at few key-locations in the aquifer (called pilot points) where the values of the transmissivity can be assessed to fit the hydraulic head measurements via deterministic or stochastic optimization processes [16,36,37,55]. The full spatial field is obtained by geostatistical interpolation (kriging) of the values of the transmissivity at the pilot points by assuming a cross-covariance function.…”

Section: Introductionmentioning

confidence: 99%

Image-guided inversion in steady-state hydraulic tomography

Ahmed

Zhou

Jardani

et al. 2015

Advances in Water Resources

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a b s t r a c tIn 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.

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Three‐dimensional interference test interpretation in a fractured aquifer using the Pilot Point Inverse Method

Cited by 55 publications

References 31 publications

Issues in characterizing heterogeneity and connectivity in non-multiGaussian media

Issues in characterizing heterogeneity and connectivity in non-multiGaussian media

Parameter estimation in nonlinear environmental problems

Image-guided inversion in steady-state hydraulic tomography

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