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Applicability of the most frequent value method in groundwater modeling

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Abstract

The Most Frequent Value Method (MFV) is applied to groundwater modeling as a robust and effective geostatistical method. The Most Frequent Value method is theoretically derived from the minimization of the information loss called the I-divergence. The MFV algorithm is then coupled with global optimization (Very Fast Simulated Annealing) to provide a powerful method for solving the inverse problems in groundwater modeling. The advantages and applicability of this new approach are illustrated by means of theoretical investigations and case studies. It is demonstrated that the MFV method has certain advantages over the conventional statistical methods derived from the maximum likelihood principle.

Résumé

On a appliqué la méthode de la valeur la plus fréquente (VPF) comme une méthode géostatistique robuste et efficace pour modéliser les eaux souterraines. Du point de vue théorique, la méthode de VPF part de la minimisation de l’information perdue, dénommée I-divergence. On couple après l’algorithme de la méthode de VPF avec la méthode d’optimisation globale affin de réaliser une méthode performante pour résoudre le problème inverse dans le domaine des eaux souterraine. Les avantages et les possibilités d’application de cette nouvelle approche sont illustrées par des investigations théoriques, ainsi que par des études de cas. On montre que la méthode de VPF présente certains avantages par rapport des méthodes statistiques conventionnelles basées sur le principe de la probabilité maximale.

Resumen

El Método del Valor Mas Frecuente (VMF), es aplicado al modelamiento de agua subterránea, como un método geoestadístico simple y efectivo. Este método es derivado teóricamente de la acción de reducir al mínimo la pérdida de información, llamada así divergencia – I. El algoritmo del VMF es entonces acoplado con optimización global(Very Fast Simulated Annealing), para obtener así un método efectivo que resuelva los problemas inversos en el modelamiento de aguas subterráneas. Las ventajas y aplicabilidad de esta aproximación nueva son ilustradas a través de investigaciones teóricas y estudios de caso. Se demuestra que el método VMF tiene ciertas ventajas sobre los métodos estadísticos convencionales derivados del principio de la probabilidad máxima.

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Acknowledgements

The authors gratefully acknowledge the Fulbright Scholarship Program, the Bolyai Janos Research Scholarship of the Hungarian Academy of Sciences, and the Mewbourne School of Petroleum and Geological Engineering at the University of Oklahoma for support of this work

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Authors and Affiliations

  1. Department of Hydrogeology and Engineering Geology, University of Miskolc, 3515, Miskolc-Egyetemvaros, Hungary

    Peter Szucs

  2. Mewbourne School of Petroleum and Geological Engineering, the University of Oklahoma, Norman, OK, 73019, USA

    Faruk Civan

  3. VIZITERV Consult Plc., 4400, Nyiregyhaza, Josa u. 5, Hungary

    Margit Virag

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  1. Peter Szucs
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  2. Faruk Civan
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  3. Margit Virag
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Correspondence to Peter Szucs.

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Szucs, P., Civan, F. & Virag, M. Applicability of the most frequent value method in groundwater modeling. Hydrogeol J 14, 31–43 (2006). https://doi.org/10.1007/s10040-004-0426-1

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