**4.2 Background on inversion artefacts**

In case of ill-posed problem, the inversion process can become unstable and generate artefacts. Moreover, it is well known that the potential of inversion methods depends on the amount of information contained in the data (Tarantola, 1982). Therefore, the concepts of model resolution matrix or Region Of Investigation (Oldenburg & Li, 1999; Marescot et al., 2006) were introduced to assess the robustness of geophysical imaging methods. Neglecting 3D effects decreases the model resolution matrix or values of the region of investigation. This matrix represents a direct link between measurements and robustness of the result. Thus, this information can be used to enhance the method by:


#### **4.3 Normalisation technique**

The **normalisation technique** makes use of the original definition of apparent resistivity (Kunetz, 1966; Marescot et al., 2006). It indicates that the topography effects can be normalized and partly accounted during the inversion. This first technique is based on the definition of a general geometrical factor which is a generalisation of the conventional geometrical factor. This method requires an approximate knowledge of the topography (digital terrain model) as well as the resistivity of the media. As a result, this normalisation partly decreases 3D effects. However, in theory, the diffusion of an electrical field is a highly non-linear problem and the normalisation technique cannot completely take into account this non-linearity. This limitation can cause the formation of artefacts and can lead to misinterpretation.

#### **4.4 2D<sup>+</sup> inversion strategy**

Contrary to relevant works of Fox et al. (1980), Tong & Yang (1990) showed that previous normalisation techniques cannot completely take into account all non-linear effects. They showed also that the best way to remove non linear effects is to integrate explicitly the topography in the model. This principle is not only dedicated to the topography but can be extended to all finite media inside the observed domain.

Therefore, it is necessary to develop inversion methods capable of taking this non-linearity into account. To limit the financial cost of the acquisition and the computational cost of inversion, new inversion codes specifically dedicated to the dike and dam context have been developed (Fargier et al., 2011). The code InGEOTH-2D+ proposes a 2D inversion that integrates part of the full 3D geo-electrical behaviour of a dam (topography and water reservoir are included). The purpose of this code is twofold. The first purpose is to provide new discretization capabilities to better state the problem. The second purpose is to allow the inclusion of any explicit prior information that the geophysicist provides.

#### **4.5 Results**

276 Novel Approaches and Their Applications in Risk Assessment

*Geological study* substratum depth material variation *Hydrogeological study* water table depth roughness *visual inspection* focused measurement - *Historical research* internal composition smoothness

In case of ill-posed problem, the inversion process can become unstable and generate artefacts. Moreover, it is well known that the potential of inversion methods depends on the amount of information contained in the data (Tarantola, 1982). Therefore, the concepts of model resolution matrix or Region Of Investigation (Oldenburg & Li, 1999; Marescot et al., 2006) were introduced to assess the robustness of geophysical imaging methods. Neglecting 3D effects decreases the model resolution matrix or values of the region of investigation. This matrix represents a direct link between measurements and robustness of the result.

 Allowing **image appraisal** (Stummer et al., 2004; Oldenburg & Li, 1999) by compensating the loss of spatial resolution and the topographic effects. This technique

Finding an optimized design of electrode location to focus the survey and increase the

The **normalisation technique** makes use of the original definition of apparent resistivity (Kunetz, 1966; Marescot et al., 2006). It indicates that the topography effects can be normalized and partly accounted during the inversion. This first technique is based on the definition of a general geometrical factor which is a generalisation of the conventional geometrical factor. This method requires an approximate knowledge of the topography (digital terrain model) as well as the resistivity of the media. As a result, this normalisation partly decreases 3D effects. However, in theory, the diffusion of an electrical field is a highly non-linear problem and the normalisation technique cannot completely take into account this non-linearity. This limitation

Contrary to relevant works of Fox et al. (1980), Tong & Yang (1990) showed that previous normalisation techniques cannot completely take into account all non-linear effects. They showed also that the best way to remove non linear effects is to integrate explicitly the topography in the model. This principle is not only dedicated to the topography but can be

allows a quality control of the image and a better interpretation of the result; Creating optimized sequences of measurements to increase the quality of the information contained in the data (Tsourlos et al., 1999; Stummer et al., 2004; Sjödahl et

*Topography* geometry -

Table 1. External information gathered form preliminary studies.

Thus, this information can be used to enhance the method by:

reliability of the inversion result (Fargier et al., 2010*).*

can cause the formation of artefacts and can lead to misinterpretation.

extended to all finite media inside the observed domain.

**4.2 Background on inversion artefacts** 

al., 2006; Hennig et al., 2005);

**4.3 Normalisation technique** 

 **inversion strategy** 

**4.4 2D<sup>+</sup>**

**Explicit constrain on the model** 

**Explicit constrain during the inversion** 

> To test the relevance of the presented techniques a measurement campaign has been carried out at the crest of a dam. An historical research, a topographic survey, a geological study, and a visual inspection were realized before the geo-electrical survey.

> A dense Wenner-Schlumberger protocol was used because of its spatial resolution and robustness. Fig. 10 a) shows one electrical resistivity section obtained after inversion of the raw data without any external information. Fig. 10 b) represents the same section after normalization of the water reservoir effect and the topography. Fig. 10 c) shows the final result of the inversion obtained with InGEOHT - 2D+. Fig. 10 d) illustrates the inverse model used for the inversion shown in Fig 10 c). For all three results, and after four iterations, the convergence data criterion is less than 1%.

Fig. 10. Results of the the inversion process obtained a) without any correction procedure (Res2dinv®), b) with normalization of water reservoir effect and topography effect (Res2dinv®), c) with the InGEOHT - 2D+ inversion code. d) presents a view of the measurement campaign and The 2D+ inversion model used to inverse the result.

A first interpretation of the inverted section in Fig. 10 a) indicates that the medium is quite regular in the longitudinal direction and composed by two layers. The upper layer whose wall varies between 9 m and 12 m has a resistivity oscillating between 500 .m and 2500 .m. The resistivity of the lower layer decreases to 40 .m. In Fig. 10 b) the electrical resistivity of the water reservoir was integrated in the inversion process (81 .m). The effect

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of the normalization indicates that the influence of the lower layer decreases. This result suggests that the lower layer is in fact an artefact due to the presence of the water reservoir.

Figure 10.c), after applying InGEOHT - 2D+, shows that the effects of the water reservoir has been entirely removed (the lower conductive layer disappeared). The resistivity section is smoother than the two previous calculations except for three resistive anomalies between 9m and 12m depth. In conclusion, we think that this last result provide a better insight of the true behaviour of the dike and the detection of some suspicious zones will be further investigated by high resolution geophysical and geotechnical methods to validate this result.
