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See detailImaging artificial salt water infiltration using electrical resistivity tomography constrained by geostatistical data
Hermans, Thomas ULg; Vandenbohede, Alexander; Lebbe, Luc et al

in Journal of Hydrology (2012), 438-439

Electrical resistivity tomography is a well-known technique to monitor fresh-salt water transitions. In such environments, boreholes are often used to validate geophysical results but rarely used to ... [more ▼]

Electrical resistivity tomography is a well-known technique to monitor fresh-salt water transitions. In such environments, boreholes are often used to validate geophysical results but rarely used to constrain the geoelectrical inversion. To estimate the extent of salt water infiltration in the dune area of a Natural Reserve (Westhoek, Belgium), electrical resistivity tomography profiles were carried out together with borehole electromagnetic measurements. The latter were used to calculate a vertical variogram, representative of the study site. Then, a geostatistical constraint, in the form of an a priori model covariance matrix based on the variogram, was imposed as regularization to solve the electrical inverse problem. Inversion results enabled to determine the extension of the salt water plume laterally and at depth, but also to estimate the total dissolved solid content within the plume. These results are in agreement with the hydrogeological data of the site. A comparison with borehole data showed that the inversion results with geostatistical constraints are much more representative of the seawater body (in terms of total dissolved solids, extension and height) than results using standard smoothness-constrained inversion. The field results obtained for the Westhoek site emphasize the need to go beyond standard smoothness-constrained images and to use available borehole data as prior information to constrain the inversion. [less ▲]

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See detailIncorporation of prior information in the regularized inversion of ERT data with CRTomo
Hermans, Thomas ULg; Caterina, David ULg; Martin, Roland et al

Conference (2012, February 03)

The electrical resistivity tomography (ERT) inverse problem is ill-posed leading to non-uniqueness of its solution. A possible way to reduce the amount of mathematical solutions to more geologically ... [more ▼]

The electrical resistivity tomography (ERT) inverse problem is ill-posed leading to non-uniqueness of its solution. A possible way to reduce the amount of mathematical solutions to more geologically plausible models is to incorporate priori information in the inversion process. In this presentation, we describe the implementation of three different techniques ways to go beyond standard Occam’s inversion for ERT with the code CRTomo : a simple reference model weighted by a user-defined parameter, a structural constraint defined by modifying the construction of the roughness matrix compared to standard Occam’s inversion and a geostatistical constraint based on a vertical correlation length deduced from borehole data to build the model covariance matrix and use it to regularize the inversion. With several examples, we show that the traditional smoothness constraint yield small contrasts of resistivity, far from the reality revealed by borehole measurements. Incorporating prior information from boreholes clearly or from another geophysical technique (like GPR or seismic refraction) improves the misfit with logging data. The choice of the prior information incorporation technique highly depends on which king of information is available and further developments are needed to extend the techniques to more complex cases. [less ▲]

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See detailHow to incorporate prior information in geophysical inverse problems: deterministic and geostatistical approaches.
Hermans, Thomas ULg; Caterina, David ULg; Martin, Roland et al

in EarthDoc - Near Surface 2011 - 17th European Meeting of Environmental and Engineering Geophysics (2011, September 13)

Many geophysical inverse problems are ill-posed leading to non-uniqueness of the solution. It is thus important to reduce the amount of mathematical solutions to more geologically plausible models by ... [more ▼]

Many geophysical inverse problems are ill-posed leading to non-uniqueness of the solution. It is thus important to reduce the amount of mathematical solutions to more geologically plausible models by regularizing the inverse problem and incorporating all available prior information in the inversion process. We compare three different ways to go beyond standard Occam’s inversion for electrical resistivity tomography (ERT) using electromagnetic logging data in the context of salt water infiltration: a simple reference model, a structural constraint and a geostatistical constraint based on a vertical correlation length. Results with the traditional smoothness constraint yield small contrasts of resistivity, far from the reality revealed by borehole measurements. Incorporating prior information from boreholes clearly improves the misfit with logging data. If a good reference model can always be used, it can lead to misinterpretation if its weight is too strong. When the computation of the correlation length is possible, the geostatistical inversion gives satisfactory results everywhere in the section. In this specific case, the geostatistical approach seems to be a more robust way to incorporate prior information. The structural constraint seems to be more indicated when integrating information from other geophysical methods such as GPR or seismic. [less ▲]

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See detailUsing geostatistical constraints in electrical imaging for improved reservoir characterization
Martin, Roland; Kemna, Andreas; Hermans, Thomas ULg et al

Conference (2010, December 14)

Developing predictive models of reservoirs is often complicated by the spatial heterogeneities and the different scales which control flow and transport processes. In numerous studies over the past two ... [more ▼]

Developing predictive models of reservoirs is often complicated by the spatial heterogeneities and the different scales which control flow and transport processes. In numerous studies over the past two decades, geophysical imaging techniques have proved very useful for reservoir characterization. However, the loss of resolution and the non-uniqueness of standard solutions to inverse problems strongly limit the use of such deterministic imaging approaches. On the other hand, the use of common geostatistical approaches for reservoir characterization, for instance from logging information, may be a difficult task, since accurate variogram information is difficult to obtain (dense sampling in the vertical and lateral directions), and also because a high number of conditioned simulations is needed to remove statistical bias. Combining the high spatial sampling of deterministic geophysical imaging methods with geostatistical constraints, valid in the whole image plane, appears as a very promising approach to enhance reservoir characterization. To do so, we use a parameterized model covariance matrix based on standard variogram functions and a prior model as regularization operator in the inversion of electrical resistance data. This way of including additional data is not restricted to electrical data but the variogram parameters may be also inferred from for example available textural or lithological information. The benefit of the presented approach is twofold: (i) It honors the spatial statistics of the reservoir and (ii) it alters the posterior model by further reducing model ambiguity inherent to the inversion compared to classical (smooth model) regularization. The proof of concept is given by synthetic studies carried out on random fields from Gauss simulations with varying (an)isotropic scale lengths using different model (co)variogram functions. We also demonstrate the approach on electrical field data combined with borehole electromagnetic data from two artificial sea inlets in the nature reserve "The Westhoek" near the French-Belgian border. The electromagnetic logs were used to calculate an experimental vertical variogram characteristic of the study site. The results enabled to determine the extension of the salt water plume laterally, and significantly enhance its extension in depth, but also in terms of total dissolved solid content. These observations are in agreement with the hydrogeological situation at the site. A comparison with borehole data shows that the results are much more plausible than results obtained with a traditional smoothness constraint used as regularization operator. In conclusion, the incorporation of geostatistical information, vertical variograms in our case, in the inverse process improves imaging capabilities for reservoir characterization significantly. [less ▲]

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