GNGTS 2022 - Atti del 40° Convegno Nazionale

530 GNGTS 2022 Sessione 3.3 ensembles of 2000 prior realisations drawn from a log-gaussian prior distribution associated with ρ 0 and Δρ . The total computational time of 7 iterations is 109 minutes on an Intel Core i7- 8700 CPU @ 3.20GHz. The predicted data computed on the posterior mean models are shown in Figure 1c-d. We observe that the observed data d 0 and d 1 are well matched by the predicted pseudo sections, with satisfying rms errors of 3.1% and 3.4% respectively. The mean posterior model ρ 0 (Figure 2a) shows a high resistivity layer with a decreasing thickness moving from left to right. This layer might be interpreted as the shallow layer of dry sand and fill. Underneath this first layer it appears a sub-horizontal low resistivity anomaly which could be associated the sandy aquifer; the resistivity values of about 50 Ω . m indicates an unsaturated aquifer. Below this zone, the model shows high and low resistivity anomalies that could correspond to the moraine clay. The mean posterior variation, Δρ (Figure 2b), exhibits an evident high ratio value between 16 and 19 meters of elevation that indicates an increase of resistivity from t 0 to t 1 . This variation could be explained as a decrease of the saturation of the aquifer in time. At the moraine clay depth, a negative variation seems to indicate a decrease in resistivity. To better understand the features of the subsurface at the time t 1 the resistivity model ρ 1 is calculated using Equation 1 (Figure 2c). To compare the results of our approach, we invert the same datasets using a deterministic least-square Occam’s algorithm in which the inverted model at the time t 0 is used as starting model of the inversion of at time t 1 (cascaded inversion, Figure 2d-e-f). The estimated ρ 0 shows the same features of the Time-Lapse EB result with minor differences only in the deeper part of the model where the low data illumination decreases the accuracy of the results . Furthermore, the variation computed by the ratio between ρ 1 and ρ 0 shows the same anomalies previously observed on the posterior mean Δρ model , especially between 19 and 16 meters of elevation. In this field data inversion, the posterior mean models as estimated by the EB inversion and the predictions of the cascaded approach Fig. 2 - a) Posterior mean model ρ 0 . b) Posterior mean resistivity variation Δρ . c) ρ 1 computed from ρ 0 and Δρ . d) Estimated ρ 0 with the deterministic Occam’s algorithm. e) Variation obtained from Equation 1. f) Estimated model using the Cascaded Inversion approach. produce comparable data predictions, with similar rms errors. However, differently from the cascaded inversion, the EB approach also provides information on the uncertainties affecting the solution. As illustrated in Figure 3a-b the coefficient of variations allows to assess the reliability of the recovered subsurface resistivity: we observe high uncertainties at the lateral edge and at the bottomof the study area where the cv percentage is almost 50% (Figure 3a) and 25% (Figure 3b). As expected, the largest uncertainties are associated with parameters poorly informed by the observations, thus meaning that in this part of the subsurface model multiple combinations of resistivity values equally reproduce the measured apparent resistivities.