GNGTS 2015 - Atti del 34° Convegno Nazionale

depth of 3.75 m. Model #2 has the same patterns (fig. 1 a), but the prisms are conductive (10 Ωm) and the background is resistive (100 Ωm). Models #3 and #4 show respectively a resistive and a conductive buried vertical dyke. 72 electrodes were considered; with a minimum spacing of 1 m. Forward problem was solved using RES2DMOD software. A fundamental role in the simulation process is the simulation of noise on the predicted data. However, in practice the methods of array optimization to maximize the resolution of tomographic image should also take into account the effect of data errors on the resolution obtained. However, most of the optimization techniques used so far have not sufficiently taken into account the effects of noise on apparent resistivity data. Generally, in the ERT inverse problem the problem due to error on data caused by improper positioning of the electrodes is not sufficiently considered. This error may be higher in steep or heavily vegetated areas and it generates an incorrect estimate of the geometric factor. To reduce the effect of this type of error on the resulting electrical tomography it is possible to select datasets that include arrays with relatively low geometric factors and therefore less sensitive to position errors (Wilkinson et al. , 2008). The study of the influence of errors on the resolution of the inverse model and especially on its ability to retrieve correct information of the subsurface is important to understand how the performance vary from a few simple parameters such as the total number of measurements of the data set and the distribution of the geometric factor values. For this porpoise, noise was added by simulating errors both on electrode spacing and on potential, rather than consider the typical random noise. A standard deviation of 3% was considered to add noise to the electrode positions. The potential errors were generated by simulating the trend showed by Zhou and Dahlin (2003). We used the formula: noisy data = U(1+R*β/100) , where U is the potential reading, R is a random number and β = ( c 1 / U ) c 2 denotes absolute relative errors of the potential observations (Dahlin and Zhou, 2004). From observed data we considered c 1 = 10 4 and c 2 = 0.4 in order to obtain an average error on resistivity data of approximatively 5%. Inversion was performed using the EarthImager 2D Software (Advanced Geosciences, 2009), considering the same optimized parameter settings, in order to compare the results obtained from the different data sets of noise-free data as well as of noisy and field data. The evaluation of the results was performed by a quantitative analysis of some parameters that could define the ability of the inverse model to approach to the real situation. Generally, the main parameter used to evaluate the reliability of an inversion is the RMS error , which quantifies the misfit between the observed and predicted data. However, simulated models gives the possibility to define quantitative parameters that describe the discrepancy between the tomographic model and the original one. The inversion program uses an arrangement of cells according to the pseudo-section and to the sensitivity function. This is obviously different from the arrangement of the original model. For this reason, in order to evaluate the resistivity mismatch between inverted and original models, a refined mesh was designed, obtained from the superposition of the boundaries of all the blocks of the inverted and the original models. Parameters to estimate the reliability of inversion. For the j -th refined mesh the model misfit is defined as where ρ j,inv and ρ j,mod are the resistivity in the inverse model and in the original model. A useful parameter to evaluate the model resolution is the relative model sensitivity, that can be calculated by expressions for the elements of the Jacobian matrix for the direct problem 102 GNGTS 2015 S essione 3.2