Mathematical Geosciences

, Volume 50, Issue 2, pp 147–167 | Cite as

Hybrid Inversion Method to Estimate Hydraulic Transmissivity by Combining Multiple-Point Statistics and a Direct Inversion Method

  • Alessandro ComunianEmail author
  • Mauro Giudici
Special Issue


Inversion methods that rely on measurements of the hydraulic head h cannot capture the fine-scale variability of the hydraulic properties of an aquifer. This is particularly true for direct inversion methods, which have the further limitation of providing only deterministic results. On the other hand, stochastic simulation methods can reproduce the fine-scale heterogeneity but cannot directly incorporate information about the hydraulic gradient. In this work, a hybrid approach is proposed to join a direct inversion method (the comparison model method, CMM) and multiple-point statistics (MPS), for determination of a hydraulic transmissivity field T from a map of a reference hydraulic head \(h^\mathrm {(ref)}\) and a prior model of the heterogeneity (a training image). The hybrid approach was tested and compared with pure MPS and pure CMM approaches in a synthetic case study. Also, sensitivity analysis was performed to test the importance of the acceptance threshold \(\delta \), a simulation parameter that allows one to tune the influence of \(h^\mathrm {(ref)}\) on the final results. The transmissivity fields T obtained using the hybrid approach take into account information coming from the hydraulic gradient while simultaneously reproducing some of the fine-scale features provided by the training image. Furthermore, many realizations of T can be obtained thanks to the stochasticity of MPS. Nevertheless, it is not straightforward to exploit the correlation between the T maps provided by the CMM and the prior model introduced by the training image, because the former depends on the boundary conditions and flow settings. Another drawback is the growing number of simulation parameters introduced when combining two diverse methods. At the same time, this growing complexity opens new possibilities that deserve further investigation.


Inverse problem Multiple-point statistics Direct method Heterogeneity Training image 



The authors thank P. Renard, G. Mariethoz, and G. Pirot for fruitful discussions, two anonymous reviewers and the editor for constructive comments, and J. Straubhaar and the University of Neuchâtel for providing the deesse simulation code.


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Copyright information

© International Association for Mathematical Geosciences 2018

Authors and Affiliations

  1. 1.Dipartimento di Scienze della Terra “A.Desio”Università degli Studi di MilanoMilanItaly

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