Jean Beaujean

Calibration of seawater intrusion models: Inverse parameter estimation using surface electrical resistivity tomography and borehole data

Electrical resistivity tomography (ERT) can be used to constrain seawater intrusion models because of its high sensitivity to total dissolved solid contents (TDS) in groundwater and its relatively high lateral coverage. However, the spatial variability of resolution in electrical imaging may prevent the correct recovery of the desired hydrochemical properties such as salt mass fraction. This paper presents a sequential approach to evaluate the feasibility of identifying hydraulic conductivity and dispersivity in density-dependent flow and transport models from surface ERT-derived mass fraction. In the course of this study, geophysical inversion was performed by using a smoothness constraint Tikhonov approach, whereas the hydrological inversion was performed using a gradient-based Levenberg-Marquardt algorithm. Two synthetic benchmarks were tested. They represent a pumping experiment in a homogeneous and heterogeneous coastal aquifer, respectively. These simulations demonstrated that only the lower salt mass fraction of the seawater-freshwater transition zone can be recovered for different times. This ability has here been quantified in terms of cumulative sensitivity and our study has further demonstrated that the mismatch between the targeted and the recovered salt mass fraction occurs from a certain threshold. We were additionally able to explore the capability of sensitivity-filtered ERT images using ground surface data only to recover (in both synthetic cases) the hydraulic conductivity while the dispersivity is more difficult to estimate. We attribute the latter mainly to the lack of ERT-derived data at depth (where resolution is poorer) as well as to the smoothing effect of the ERT inversion.

A comparison study of different image appraisal tools for electrical resistivity tomography

To date, few studies offer a quantitative comparison of the performance of image appraisal tools. Moreover, there is no commonly accepted methodology to handle them even though it is a crucial aspect for reliable interpretation of geophysical images. In this study, we compare quantitatively different image appraisal indicators to detect artefacts, estimate depth of investigation, address parameters resolution and appraise ERT-derived geometry. Among existing image appraisal tools, we focus on the model resolution matrix (R), the cumulative sensitivity matrix (S) and the depth of investigation index (DOI) that are regularly used in the literature. They are first compared with numerical models representing different geological situations in terms of heterogeneity and scale and then used on field data sets. The numerical benchmark shows that indicators based on R and S are the most appropriate to appraise ERT images in terms of the exactitude of inverted parameters, DOI providing mainly qualitative information. In parallel, we test two different edge detection algorithms – Watershed’s and Canny’s algorithms – on the numerical models to identify the geometry of electrical structures in ERT images. From the results obtained, Canny’s algorithm seems to be the most reliable to help practitioners in the interpretation of buried structures. On this basis, we propose a methodology to appraise field ERT images. First, numerical benchmark models representing simplified cases of field ERT images are built using available a priori information. Then, ERT images are produced for these benchmark models (all simulated acquisition and inversion parameters being the same). The comparison between the numerical benchmark models and their corresponding ERT images gives the errors on inverted parameters. These discrepancies are then evaluated against the appraisal indicators (R and S) allowing the definition of threshold values. The final step consists in applying the threshold values on the field ERT images and to validate the results with a posteriori knowledge. The developed approach is tested successfully on two field data sets providing important information on the reliability of the location of a contamination source and on the geometry of a fractured zone. However, quantitative use of these indicators remains a difficult task depending mainly on the confidence level desired by the user. Further research is thus needed to develop new appraisal indicators more suited for a quantitative use and to improve the quality of inversion itself.

Physically Based Groundwater Vulnerability Assessment Using Sensitivity Analysis Methods

A general physically based method is presented to assess the vulnerability of groundwater to external pressures by numerical simulation of groundwater flow. The concept of groundwater vulnerability assessment considered here is based on the calculation of sensitivity coefficients for a user-defined groundwater state for which we propose several physically based indicators. Two sensitivity analysis methods are presented: the sensitivity equation method and the adjoint operator method. We show how careful selection of a method can significantly minimize the computational effort. An illustration of the general methodology is presented for the Herten aquifer analog (Germany). This application to a simple, yet insightful, case demonstrates the potential use of this general and physically based vulnerability assessment method to complex aquifers.

Image Appraisal Tools for Electrical Resistivity Tomography

Image appraisal is a problem frequently encountered in electrical resistivity Tomography (ERT), and more generally in non-linear geophysical Inversion. It may include several aspects such as the identification of the geometry of buried structures, the detection of numerical artefacts, the estimation of the depth of Investigation or the exactitude of inverted parameters. Geophysicists can rely on several Tools published in the literature to address these issues. However, few studies offer a quantitative comparison on the performance of these Tools concerning the different mentioned aspects. Moreover, to our knowledge, there is no commonly accepted methodology to handle image appraisal. in this contribution, we compared quantitatively the ability of different image appraisal indicators to reach different objectives (geometry, artefacts, depth of Investigation, parameter resolution). Among possible image appraisal Tools, the model resolution matrix (MRM), the cumulative sensitivity matrix (CSM) and the depth of Investigation index (DOI) are the most cited ones and were studied here. We compared them first on numerical models representing different geological situations. This numerical benchmark showed that indicators based on the MRM and CSM were the more appropriate to appraise ERT images in terms of the geometry of structures and the exactitude of inverted parameters, DOI providing mainly qualitative Information. On this basis, we propose a methodology to appraise field ERT images focusing on the resolution and geometric aspects (others being implicitly studied). First, True Synthetic Models (TSM), representing simplified cases of field ERT images, are built using available Information. then, through forward modelling, synthetic ERT data are computed and inverted to provide the inverted Synthetic Models (ISM). Afterwards, a comparison between TSM and ISM (or their gradients for geometry) is made in order to define the errors on inverted parameters. This discrepancy is then plotted with respect to resolution indicator values and points out in every tested cases a resolution range over which the errors abruptly increase allowing the definition of threshold values. the final step consists in applying the threshold values on the field ERT images and to validate the results with a posteriori knowledge.