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Bayesian evidential learning: a field validation using push-pull tests

  • Thomas HermansEmail author
  • Nolwenn Lesparre
  • Guillaume De Schepper
  • Tanguy Robert
Paper

Abstract

Recent developments in uncertainty quantification show that a full inversion of model parameters is not always necessary to forecast the range of uncertainty of a specific prediction in Earth sciences. Instead, Bayesian evidential learning (BEL) uses a set of prior models to derive a direct relationship between data and prediction. This recent technique has been mostly demonstrated for synthetic cases. This paper demonstrates the ability of BEL to predict the posterior distribution of temperature in an alluvial aquifer during a cyclic heat tracer push-pull test. The data set corresponds to another push-pull experiment with different characteristics (amplitude, duration, number of cycles). This experiment constitutes the first demonstration of BEL on real data in a hydrogeological context. It should open the range of future applications of the framework for both scientists and practitioners.

Keywords

Bayesian evidential learning Push-pull tests Tracer tests Heterogeneity Uncertainty 

Bayesian evidential learning: validation à partir de tests expérimentaux d’injection-pompage

Résumé

Les développements récents en quantification de l’incertitude montrent que l’inversion complète des paramètres d’un modèle n’est pas toujours nécessaire pour prévoir l’intervalle d’incertitude d’une prédiction spécifique en Sciences de la Terre. Une alternative est l’utilisation de la technique Bayesian evidential learning (BEL) qui utilise une série de réalisations a priori pour générer une relation directe entre données et prédiction. Cette technique récente a été démontrée principalement dans des cas synthétiques. Ce papier démontre la capacité de BEL à prédire la distribution a posteriori de la température dans un aquifère alluvial lors d’un test d’injection-pompage de chaleur cyclique. Les données correspondent à un autre test d’injection-pompage avec des caractéristiques différentes (amplitude, durée, nombre de cycles). Cette expérience constitue la première validation de BEL sur des données réelles dans un contexte hydrogéologique. Cela devrait accroître le spectre d’applications futures de la méthode à la fois pour les scientifiques et les professionnels.

Aprendizaje bayesiano basado en evidencias: una validación de campo mediante pruebas push-pull

Resumen

La evolución reciente de la cuantificación de la incertidumbre muestra que no siempre es necesaria una inversión completa de los parámetros del modelo para prever el margen de incertidumbre de una predicción específica en las Ciencias de la Tierra. En cambio, el aprendizaje bayesiano (BEL) utiliza un conjunto de modelos anteriores para derivar una relación directa entre los datos y la predicción. Esta técnica reciente se ha demostrado principalmente en casos sintéticos. Este trabajo demuestra la capacidad de BEL para predecir la distribución posterior de la temperatura en un acuífero aluvial durante una prueba push-pull del trazador de calor cíclico. El conjunto de datos corresponde a otro experimento push-pull con características diferentes (amplitud, duración, número de ciclos). Este experimento constituye la primera demostración de BEL sobre datos reales en un contexto hidrogeológico. Ello debería abrir un abanico de aplicaciones futuras del marco de trabajo tanto para los científicos como para los profesionales.

贝叶斯证据学习:使用推拉测试进行现场验证

摘要

不确定性量化的最新发展表明,模型参数的全反演并不总需要预测地球科学中具体预测的不确定性范围。相反,贝叶斯证据学习(BEL)使用一组先验模型来推导数据和预测之间的直接关系。这种最新技术主要被用于综合案例。本文证明了BEL在循环热示踪推拉试验中预测冲积含水层中温度后验分布的能力。该数据集对应于具有不同特征(振幅,持续时间,循环次数)的另一类推拉实验。该实验是BEL用于水文地质行业真实数据的首个案例。它为科学家和相关专业人员未来开展相关应用提供了参考。

Aprendizagem evidencial Bayesiana: uma validação de campo usando testes push-pull

Resumo

Desenvolvimentos recentes na quantificação da incerteza mostram que uma inversão completa dos parâmetros do modelo nem sempre é necessária para prever o intervalo de incerteza de uma previsão específica em Ciências da Terra. Em vez disso, a aprendizagem evidencial bayesiana (AEB) usa um conjunto de modelos anteriores para derivar uma relação direta entre dados e previsão. Esta técnica recente tem sido demonstrada principalmente para casos sintéticos. Este artigo demonstra a capacidade da AEB em predizer a distribuição posterior da temperatura em um aquífero aluvial durante um teste push-pull de traçador de calor cíclico. O conjunto de dados corresponde a outro experimento push-pull com características diferentes (amplitude, duração, número de ciclos). Este experimento constitui a primeira demonstração de AEB em dados reais em um contexto hidrogeológico. Deve abrir o leque de aplicações futuras do quadro para cientistas e profissionais.

Notes

Acknowledgements

We thank Thomas Kremer, Maxime Evrard and Solomon Eshioke for their precious help in the field and Frédéric Nguyen and Jef Caers for fruitful discussions. We thank the associated editor and four anonymous reviewers for their constructive comments.

Funding information

Field experiments were possible thanks to the F.R.S.-FNRS research credit 4D Thermography, grant number J.0045.16. N. Lesparre and G. De Schepper were supported by the project SUITE4D from the BEWARE Fellowships Academia Program (contract No. 1510466) and the SMARTMODEL project from the BEWARE Fellowships Industry Program (contract No. 1610056), respectively. Both programs are co-financed by the department of Research Programs of the Wallonia-Brussels Federation and Marie Skłodowska-Curie COFUND program of the European Union.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Thomas Hermans
    • 1
    Email author
  • Nolwenn Lesparre
    • 2
    • 3
  • Guillaume De Schepper
    • 4
  • Tanguy Robert
    • 3
    • 4
    • 5
  1. 1.Department of GeologyGhent UniversityGhentBelgium
  2. 2.Laboratory of Hydrology and GeochemistryStrasbourg UniversityStrasbourgFrance
  3. 3.Department of Urban and Environmental EngineeringLiege UniversityLiegeBelgium
  4. 4.R&D DepartmentAquale SPRLNoville-les-BoisBelgium
  5. 5.F.R.S.-FNRS (Fonds de la Recherche Scientifique)BrusselsBelgium

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