GNGTS 2024 - Atti del 42° Convegno Nazionale

Session 3.3 GNGTS 2024 In (1) and (2), σ is the data standard deviaton, p 1 and p 2 control the shape of the norm before and afer x/σ=1 and α determines the total weight of the penalty. With this choice of values for the norm setngs the AGMS norm gives misft 1 for x/σ=1 (i.e. the same value of the L2 norm), with similar penalty for low misft (because of p_1=1) and a slow growth of the penalty when x/σ>1 (because of p 2 =0.5). This slow growth allows for applying the AGMS norm in an iteratve minimizaton process, because a decrease in x/σ gives a measurable penalty reducton. This data norm is applied in a IRLS inversion composed of three inversion cycles (Fiandaca et al., 2024) with 1D forward/Jacobian computatons: 1. a preliminary cycle which fnds the best startng model without vertcal variability of the parameters, through the use of a single-layer forward mesh; 2. a cycle where the AGMS norm is applied 3. the data norm is switched to the L2 norm, to reject the data with misft above the set thresholds, and the inversion is carried out untl the reach of the minimum misft. In all cycles, borehole logs are treated as data, with the forward response of the logs consistng in the interpolaton of the model resistvity at the log locatons (Fiandaca et al., 2024). Fig. 1 presents a synthetc model of a fresh aquifer enclosed between an unsaturated sand dune and a brackish aquifer, and confned by clay layers. AEM data (Xcite system, New Resoluton Geophysics) and three borehole logs are simulated and inverted with a classic L2 data norm and the AGMS norm, with three data scenarios: 1. only AEM data are available (Fig. 1D and 1G); 2. AEM data are complemented with the logs that bear correct informaton (Fig. 1E and 1H); 3. one log contains wrong resistvity values (Fig. 1F and 1I) . Figure 1. Conceptual model (A), boreholes informaton (all correct in B, one incorrect in C); model recovered by Xcite AEM data without drilling informaton using L2 norm (D) and AGMS norm (G); model recovered by Xcite with all correct drilling informaton using L2 norm (E) and AGMS norm (H); model recovered by Xcite with partally incorrect drilling informaton using L2 norm (F) and AGMS norm (I).