Identification of transmissivity fields using a Bayesian strategy and perturbative approach

Zanini, A.; Tanda, Maria Giovanna; Woodbury, Allan D.

doi:10.1016/j.advwatres.2017.07.022

Cited by 7 publications

(6 citation statements)

References 42 publications

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“…Based on the assumption that S j is only related to the collocated H i = α ( j ) (Doyen et al., 1996), the secondary attribute data S j are assumed to be the summation of the vector of the model output

f (H_{i = α (j)}) = {[f^{k} (H_{i = α (j)}), k = 1, \dots, M]}^{normalT}

and the noise vector

{boldε}_{j} = {[ε_{j}^{k}, k = 1, \dots, M]}^{normalT}

{boldS}_{j} = f (H_{i = α (j)}) + {boldε}_{j},

where f k is the mathematical model that relates the k th kind of secondary attribute to H i = α ( j ) , α is an operator used to transform j into the corresponding i at a given location, and

ε_{j}^{k}

is the misfit of the k th kind of secondary attribute data with its model output

f^{k} (H_{i = α (j)})

. Note that f k can be either a regression (J. Chen et al., 2001), geostatistical (Ruggeri et al., 2013), or physical inversion model (Zanini & Woodbury, 2016; Zanini et al., 2017). A regression model is utilized in this study.…”

Section: Bayesian Integration Methodsmentioning

confidence: 99%

“…. Note that f k can be either a regression (J. Chen et al, 2001), geostatistical (Ruggeri et al, 2013), or physical inversion model (Zanini & Woodbury, 2016;Zanini et al, 2017). A regression model is utilized in this study.…”

Section: Likelihood Functionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Studies have demonstrated the successful application of the Bayesian statistical method integrating continuous secondary data with the primary data for practical use (J. Chen et al, 2001;Dubreuil-Boisclair et al, 2011;Jiang et al, 2013;Ruggeri et al, 2013;Zanini et al, 2017). Ruggeri et al (2013) used a two-step Bayesian approach to estimate K by integrating spatially exhaustive but poorly resolved airborne electrical resistivity data and two highly resolved but spatially sparse continuous secondary data sets.…”

mentioning

confidence: 99%

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Bayesian Integration Using Resistivity and Lithology for Improving Estimation of Hydraulic Conductivity

Cheng

Hsu

2021

Water Resources Research

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The characterization of spatially heterogeneous hydraulic conductivity (K) is important in groundwater resources management. We propose a Bayesian statistical method that integrates multiple secondary data (continuous and category data) with primary data (K) to improve regional K field characterization. Considering the disparity of the data scale, spatial scarcity of primary and secondary data, and need for regional-scale site characterization, the aquifer thickness is used as the scale for data integration. We transform the high-resolution secondary data to the scale of K and perform linear/ nonlinear regression analyses for the transformed secondary data and primary data. A Bayesian approach using Metropolis-within-Gibbs sampling is developed for jointly integrating the primary and transformed secondary data without a limitation on the type of data attribute and the number of data set. A synthetic example is first presented to demonstrate the capability of the proposed method. Results show that the correlation strength, not the relation type, is the primary factor for improving the estimates. The Bayesian method is applied to Choushui River alluvial fan in Taiwan. Resistivity logs and a lithological description are first upscaled and then simultaneously integrated in the K estimation. Results indicate that the improvement of the K estimate obtained using resistivity data is higher in the proximal and mid fans but lower in the distal fan compared to that obtained using lithofacies data. Jointly integrating two-attribute data outperforms using one or no secondary data set for K estimates. The proposed Bayesian integration method is thus versatile and suitable for large-scale aquifer characterization.

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f (H_{i = α (j)}) = {[f^{k} (H_{i = α (j)}), k = 1, \dots, M]}^{normalT}

and the noise vector

{boldε}_{j} = {[ε_{j}^{k}, k = 1, \dots, M]}^{normalT}

{boldS}_{j} = f (H_{i = α (j)}) + {boldε}_{j},

where f k is the mathematical model that relates the k th kind of secondary attribute to H i = α ( j ) , α is an operator used to transform j into the corresponding i at a given location, and

ε_{j}^{k}

is the misfit of the k th kind of secondary attribute data with its model output

f^{k} (H_{i = α (j)})

Section: Bayesian Integration Methodsmentioning

confidence: 99%

Section: Likelihood Functionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Bayesian Integration Using Resistivity and Lithology for Improving Estimation of Hydraulic Conductivity

Cheng

Hsu

2021

Water Resources Research

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show abstract

“…At this point, the knowledge of the aquifer hydraulic conductivity (HK) becomes essential. In the last two decades, the challenge of determining the aquifer hydraulic parameters starting from field data (transmissivity measurements and/or hydraulic heads) is still motivating the development of new approaches; see, for instance, references [4][5][6][7][8][9][10][11][12]. These references are by no means exhaustive and serve only to highlight the importance of the overall problem of parameter estimation.…”

Section: Introductionmentioning

confidence: 99%

Characterization of Hydraulic Heterogeneity of Alluvial Aquifer Using Natural Stimuli: A Field Experience of Northern Italy

D’Oria

Zanini

2019

Water

Self Cite

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This study investigates the hydraulic heterogeneity of the alluvial aquifer underneath the dam and the stilling basin of a flood protection structure in Northern Italy. The knowledge of the interactions between the water in the reservoir upstream of the dam and the groundwater levels is relevant for the stability of the structure. A Bayesian Geostatistical Approach (BGA) combined with a groundwater flow model developed in MODFLOW 2005 has been used to estimate the hydraulic conductivity (HK) field in a context of a highly parameterized inversion. The transient hydraulic heads collected in 14 monitoring points represent the calibration dataset; these observations are the results of the hydraulic stresses induced by the variations of the lake stage upstream of the dam (natural stimuli). The geostatistical inversion was performed by means of a computer code, bgaPEST, developed according to the free PEST software concept. The results of the inversion show a moderate degree of heterogeneity of the estimated HK field, consistent with the alluvial nature of the aquifer and the other information available. The calibrated groundwater model is useful for simulating the interactions between the reservoir and the studied aquifer under different flood scenarios and for forecasting the hydraulic head levels due to strong flood events. The use of natural stimuli is useful for obtaining information for aquifer heterogeneity characterization.

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Groundwater contamination source-sink analysis based on random statistical method for a practical case

Wang

2022

Stoch Environ Res Risk Assess

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Identification of transmissivity fields using a Bayesian strategy and perturbative approach

Cited by 7 publications

References 42 publications

Bayesian Integration Using Resistivity and Lithology for Improving Estimation of Hydraulic Conductivity

Bayesian Integration Using Resistivity and Lithology for Improving Estimation of Hydraulic Conductivity

Characterization of Hydraulic Heterogeneity of Alluvial Aquifer Using Natural Stimuli: A Field Experience of Northern Italy

Groundwater contamination source-sink analysis based on random statistical method for a practical case

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