An Algorithm for Hydraulic Tomography Based on a Mixture Model

Minutti, Carlos; Illman, Walter A.; Gómez, Susana

doi:10.1007/978-3-030-22744-9_37

Cited by 1 publication

(2 citation statements)

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“…Furthermore, the parameterization also can affect the number of local or global optima in the solution of the inverse problem, and it also has to do with how realistic the solution is. In order to model the spatial distribution of K, a preliminary study was conducted by Minutti et al (2019) to introduce a new algorithm called the Gaussian Mixture (GM) inversion algorithm, to solve the inverse problem for HT applications. This algorithm is based on the statistical concept of a mixture model, specifically a Gaussian Mixture Model (GMM), which is used to parameterize the K field.…”

Section: Introductionmentioning

confidence: 99%

“…This algorithm is based on the statistical concept of a mixture model, specifically a Gaussian Mixture Model (GMM), which is used to parameterize the K field. In Minutti et al (2019), the results of the GM algorithm were compared to those of SSLE using two synthetic experiments as well as data from a laboratory sandbox aquifer (Illman et al, 2010). This initial study showed the higher accuracy and shorter computational time of the GM inversion algorithm compared to SSLE, but the results were limited to a small sample.…”

Section: Introductionmentioning

confidence: 99%

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A New Inverse Modeling Approach for Hydraulic Conductivity Estimation Based on Gaussian Mixtures

Minutti¹,

Illman

Gómez³

2020

Water Resources Research

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This study proposes a new inverse algorithm to estimate the hydraulic conductivity (K) distribution based on a Gaussian Mixture Model that significantly reduces the number of parameters to be estimated during the inversion process. Moreover, a new objective function that increases the sensitivity of parameters using the spatial derivatives of hydraulic heads is introduced, and the algorithm is further improved by including a Bayes estimator that takes advantage of different possible solutions. The developed approach is tested through multiple synthetic experiments consisting of 250 randomly generated K fields resulting in different levels of heterogeneity and the use of different number of pumping tests, with a total of 1,000 cases of two-dimensional configuration. A large number of cases are considered to ensure that our findings and conclusions are not based on a single realization. Results revealed significant improvements to K estimates, computational time, and predictions of independently conducted tests not used in the calibration effort when compared to a geostatistical inverse approach. Overall, our results reveal that the Gaussian Mixture inversion approach is able to achieve similar or higher levels of accuracy using half of the pumping tests and 20% of the computational time compared to a geostatistical inversion approach.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%