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Falsification and corroboration of conceptual hydrological models using geophysical data

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Geophysical data may provide crucial information about hydrological properties, states, and processes that are difficult to obtain by other means. Large data sets can be acquired over widely different scales in a minimally invasive manner and at comparatively low costs, but their effective use in hydrology makes it necessary to understand the fidelity of geophysical models, the assumptions made in their construction, and the links between geophysical and hydrological properties. Geophysics has been applied for groundwater prospecting for almost a century, but it is only in the last 20 years that it is regularly used together with classical hydrological data to build predictive hydrological models. A largely unexplored venue for future work is to use geophysical data to falsify or rank competing conceptual hydrological models. A promising cornerstone for such a model selection strategy is the Bayes factor, but it can only be calculated reliably when considering the main sources of uncertainty throughout the hydrogeophysical parameter estimation process. Most classical geophysical imaging tools tend to favor models with smoothly varying property fields that are at odds with most conceptual hydrological models of interest. It is thus necessary to account for this bias or use alternative approaches in which proposed conceptual models are honored at all steps in the model building process. This article is categorized under: Science of Water > Hydrological Processes
(a) Test case representing a gravel aquifer with embedded clay lenses overlying bedrock. (b) The result of a standard smoothness‐constrained inversion of electrical resistivity tomography (ERT) data acquired on the ground surface clearly indicates the presence of bedrock, but is unable to resolve detailed variations in the bedrock topography or its actual resistivity.
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(a–b) Different views of a crosshole 3D ERT (electrical resistivity tomography) inversion model for which borehole effects were explicitly included in the modeling. The high resistive central region (low porosity) is in agreement with models obtained by other geophysical models. (c–d) Corresponding views for an inversion model obtained without considering borehole effects. These latter results are of limited value in building a predictive aquifer model. (Reprinted with permission from Ref , Figure 6. Copyright 2010 Society of Exploration Geophysicists)
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One realization of a discrete fracture network model that is conditioned to a large set of geophysical and hydrological data acquired at the Ploemeur research site in France. (a) Graph representation of the network and (b) the simulated hydraulic head distribution for an injection‐withdrawal experiment.
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Conditioning of multiple‐point statistics facies simulations to geophysical tomograms. Many sections of a (a) training image (TI) that is representative of the expected depositional setting is generated and transformed using a petrophysical relation into (b) geophysical fields on which realistic geophysical data are generated and inverted to obtain a (c) tomogram. The real (d) underlying facies distribution is related to the underlying (e) geophysical property field from which a geophysicist can derive a lower‐resolution (f) tomogram. Using direct sampling, it is possible to generate (g) multiple realizations of subsurface models that are coherent with both the geophysical tomogram and the training image.
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(a) Chair plot of a ground penetrating radar (GPR) data volume acquired across a gravel bar in the vicinity of the Thur River in Switzerland. (b) Electrical resistivity tomography (ERT) inversion results using standard smoothness‐constrained model regularization and (c) for the case, in which no model regularization is imposed across GPR‐defined boundaries outlined in (a) and across the water table. The regularization decoupling enforces similarity between the GPR and ERT results, thus facilitating interpretation. Furthermore, the constraints from high‐resolution GPR (very sensitive to lithological boundaries) improve the estimates of bulk electrical properties. (Reprinted with permission from Ref , Figures 5 and 8. Copyright 2011 Elsevier B.V.)
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Example illustrating errors associated with the model parameterization, uncertain petrophysical relationships, geometrical, and observational errors. The (a) actual porosity field cannot be fully described by (b) the model parameterization used, which leads to (c) upscaling errors. The actual porosity field is related to a (d) geophysical field (radar wave speed) through a petrophysical relationship. This relationship is never perfectly known, so additional uncertainty and bias occur when using a petrophysical model to represent the (e) expected wave speed as shown in the (f) model residuals. The (g) observed geophysical data are contaminated with observational errors, while the (h) calculated model response of (e) is affected by errors in the forward model or in the geometry, which contribute to (i) data residuals that are biased. These types of errors can be minimized by careful investigations, but not fully removed. Their expected distributions should be carefully considered when inverting (h) in order to retrieve a representative model similar to (b).
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(a) The actual porosity field used to generate noise‐contaminated data. From 20,000 random draws, panels (b–e) show for different conceptual models the realizations that best explain the noise‐contaminated crosshole ground penetrating radar (GPR) data generated by (a). The true geostatistical model is known in case (b), isotropy is assumed in (c), vertical anisotropy is assumed in (d) and uniform porosity is assumed in (e).
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A hypothetical set of 100 noisy data describing the observed relationships between porosity and bulk resistivity. Three models obtained by regularized smoothness‐constrained inversion display not only the decreasing data misfits (underfitted, fitted, and overfitted), but also the increasing model complexity (i.e., more oscillations). The most likely model based on the Schwartz criterion is the fitted model, but it is far from being as satisfactory as the two‐parameter model used to generate the data. A careful choice of model parameterization is thus most important in hydrogeophysical studies.
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