Cross‐correlated random field generation with the direct Fourier Transform Method

Robin, Michel; Gutjahr, Allan L.; Sudicky, E. A.; Wilson, John L.

doi:10.1029/93wr00386

Cited by 209 publications

(127 citation statements)

References 28 publications

(10 reference statements)

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“…A heterogeneous distribution of hydraulic conductivity was achieved by including stochastically generated fields of hydraulic conductivity in the simulations. With the code FGEN (Robin et al, 1993), the K-fields were generated from the mean and variance of ln(K) and the correlation lengths in each direction (Table 1). These data were obtained from field observations of K, except the variance which was calibrated with the observed temperature distribution by Kalbus et al (2008a,b).…”

Section: Model Set-upmentioning

confidence: 99%

Influence of aquifer and streambed heterogeneity on the distribution of groundwater discharge

Kalbus

Schmidt

Molson

et al. 2009

Hydrol. Earth Syst. Sci.

120

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Abstract. The spatial distribution of groundwater fluxes through a streambed can be highly variable, most often resulting from a heterogeneous distribution of aquifer and streambed permeabilities along the flow pathways. Using a groundwater flow and heat transport model, we defined four scenarios of aquifer and streambed permeability distributions to simulate and assess the impact of subsurface heterogeneity on the distribution of groundwater fluxes through the streambed: (a) a homogeneous low-K streambed within a heterogeneous aquifer; (b) a heterogeneous streambed within a homogeneous aquifer; (c) a well connected heterogeneous low-K streambed within a heterogeneous aquifer; and (d) a poorly connected heterogeneous low-K streambed within a heterogeneous aquifer. The simulation results were compared with a base case scenario, in which the streambed had the same properties as the aquifer, and with observed data. The results indicated that the aquifer has a stronger influence on the distribution of groundwater fluxes through the streambed than the streambed itself. However, a homogeneous low-K streambed, a case often implemented in regional-scale groundwater flow models, resulted in a strong homogenization of fluxes, which may have important implications for the estimation of peak mass flows. The flux distributions simulated with heterogeneous low-K streambeds were similar to the flux distributions of the base case sceCorrespondence to: E. Kalbus (edda.kalbus@web.de) nario, despite the lower permeability. The representation of heterogeneous distributions of aquifer and streambed properties in the model has been proven to be beneficial for the accuracy of flow simulations.

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Section: Model Set-upmentioning

confidence: 99%

Influence of aquifer and streambed heterogeneity on the distribution of groundwater discharge

Kalbus

Schmidt

Molson

et al. 2009

Hydrol. Earth Syst. Sci.

120

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“…The 2-D Goff-Jordan power law spectrum [66) is also extensively used to simulate the seafloor [7,68). Nevertheless, the literature on 3-D random field generation can hardly be found in underwater acoustics, in contrast to the large number of papers in water resource research literature [69,70,71). The reason may rest on the fact that the computational requirement is too big for the scale of the random field that we are dealing with in underwater acoustics.…”

Section: Statement Of the Problemmentioning

confidence: 68%

Modeling of monostatic bottom backscattering from three-dimensional volume inhomogeneities and comparisons with experimental data

Li¹

1997

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Acoustic propagation in the ocean inevitably encounters inhomogeneities of various types, which give rise to scattering. Acoustic scattering from rough water /bottom interfaces comprised of exposed rocks and sea mountains gives way to volumetric scattering in areas with fiat interfaces and thick sediment cover. The data analysis of the ARSRP backscattering experiment revealed that random inhomogeneities in two irregular layers beneath the seafloor were the primary contributors to oblique backscattering in a sediment pond on the western flank of the Mid-Atlantic Ridge. In this thesis, an attempt has been made to model monostatic backscattering from 3-D volume inhomogeneities in the sediment and to compare the results with the ARSRP backscattering data.A scattering process cannot be modeled correctly without a proper account of the incident field . Several approximate propagation models have been evaluated against the exact solution, while the appropriateness of using the equivalent surface scattering strength in volume scattering characterizations is studied. This study concludes that precautions need to be taken in modeling both the propagation effects and the scattering mechanisms associated with the bottom volume scattering process.A volume scattering model based on perturbation theory and the Born approximation is developed incorporating contributions from both sound speed and density fluctuations. With the propagation part handled accurately by OASES and random fluctuations generated effectively by a new scheme modified from the spectral method, the model is capable of simulating the monostatic backscattered field and time series due to 3-D volumetric sediment inhomogeneities. Both the characteristic length scale and power spectrum descriptions of the random inhomogeneities are shown to have great impact on the backscattered field by parameter studies in a free-space scenario. The important roles played by horizontal anisotropy and the vertical correlation of the random field have been demonstrated. Density fluctuations are further confirmed to be the dominant force in backscattering. The model matches the ARSRP backscattering data very well , with the fluctuations of sound speed and density in the two irregular layers described by a power law type of power spectrum. To my fellow-students in 5-007 and 5-435, thank you for t he wonderful atmosphere that you have created and t he team-work spirit t hat I have enjoyed. Believe me, you are t he best.Life would not have been so fun without all my friends. Qing, Henry, and Chenyang, how about playing some Tetris the next t ime we get together? And t hank you for introducing me t o the "real world" . Wenjie and Co. , guess no card game is scheduled for now. Thank you, Elaine, for many "Sloanish" advice, Lia ng-wu, for the ride to chase t he sunset, Richard , for the parties, and Feng, for making me a part-time Ashdowner. Helen, Lan and Xiaoou, I will surely not forget t he summer at Cape Cod.My most grateful thanks goes to my parents and my sister. You are ...

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“…Our approach is straightforward ( Figure 1). Using standard stochastic mcthods (e.g., Robin et al,, 1993), wc synthetically gencrate and sample a series of artificjal spatial realities (sets of parameter fields). At each sampled location, observation and inversion-model crrors are propagated through numerical simulations of parameter rneasurcments.…”

Section: Methods and Resultsmentioning

confidence: 99%

New Permeameters for In Situ Characterization of Unsaturated Heterogeneous Permeability: Development, Design, Testing, and Application

Wilson¹,

Glass²

2001

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EXECUTIVE SUMMARYThe original objective of our EMSP research was to design, develop, and test new in situ ficld pcrmeameters for use in spatial variability studies of unsaturated hydraulic properties. We initially focused on activities rclated to development and testing of techniques for inverting perrneameter data, devclopment of numerical tools for data inversion, error evaluation for permeametcr dcsign, and penneameter component design. However, the rcsults of error evaluations for pcrmeametet design caused us to redirect our tesearch, and reformulate our research objectives. We discovered that small, simple measurement errors lead to significant bias in the estimated hydraulic properties and thcir spatial statistics. Our rerormulated research objective became the cvaluation of the origin, impact and relevance oF spatial bias in field-and laboratory-estimated unsaturated hydraulic propertics, with an emphasis on spatial statistics and h e resulting predictions of stochastic models of flow and contaminant transport.Spatial statistics of hydraulic properties can be accurately estimatcd when measurement errors arc unbiased. Unfortunately, measurements become spatially biased &e., their spatial pattern is systematically distorted) when random observation errors are propagated through nonlinear invcrsion models or inversion models that incorrectly describe experimental physics. This type of bias rcsults in a distortion of the spatial distribution and statistics of the hydmulic property and in crroneous predictions of flow and transport.We developed a Monte Carlo approach to determine the spatial bias in field-and laboratory-estimated unsaturated hydraulic propcrties subject to simple measurcrnent errors I For thcse analyses, we simulatcd measurements in a series of idealized realities and considered only simple measurenient errors that can be easily modclcd. We found that hydraulic properties are strongly biased by small observation and inversion-model crrors. T h i s bias leads to order-ofrnagnitudc crrors in spatial statistics and artificial cross-correlation between measurcd properties. We also found that measurement crrors amplifj. uncertainty in estimated (experimental) variograms and can preclude identification of variogram-modcl parameters. Using biascd spatial statistics in stochastic flow and transport models yields order-of-magnitude errors in critical transport predictions. Thc effects of observation and inversion-model mors are insidious, as hydraulic property estimates may appear reasonablc and generate realistic looking spatial statistics that are, however. inaccurate and misleading. LO 'd -3 - 'ON XWdWd EO:PO nHI POOZ-OI-Nnr RESEARCH OBJECTIVESThick unsaturated zones underlie many Department of Encrgy (DOE) landfills, industrial areas, and waste storage sites in the western United Statcs and are the primary pathway for contaminants to migrate into underlying aquifcrs. The spatial variability of unsaturated hydraulic properties in these heterogeneous gcologic materials directly influences tlie moveme...

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Cross‐correlated random field generation with the direct Fourier Transform Method

Cited by 209 publications

References 28 publications

Influence of aquifer and streambed heterogeneity on the distribution of groundwater discharge

Influence of aquifer and streambed heterogeneity on the distribution of groundwater discharge

Modeling of monostatic bottom backscattering from three-dimensional volume inhomogeneities and comparisons with experimental data

New Permeameters for In Situ Characterization of Unsaturated Heterogeneous Permeability: Development, Design, Testing, and Application

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