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.