## 5 Discussion  
Previous investigations based on the hydrogeochemistry of the fluids [43; 65] highlighted that the groundwater hydrogeochemistry of the San Vittorino Plain is the result of the addition of deep fluids (i.e., mantle-derived and crustal fluids) to the shallow groundwater circulating in a regional carbonate fractured aquifer. All of the selected springs represent the main discharge points and are not affected by surface runoff. Based on chemical parameters, in the Piper diagram, the groundwater of the 15 selected springs seems to be aligned along a single mixing trend or evolutionary path, whose end-members are Ca-HCO\({}_{3}\) and Ca-SO\({}_{4}\) types (Figure 2). However, a closer look at the bicarbonate corner of the Langleier-Ludwig diagram, which has the same meaning as the central diamond in Piper's plot (Figure S1), reveals at least two possible evolutionary trends: (i) an increase of the sulphate concentration in the Antrodoco area (i.e., S1 and S2) due to dissolution of Upper Triassic gypsum/anhydrite; and (ii) a trend from samples with higher HCO\({}_{3}\) relative concentrations, Peschiera/Paterno areas (S10, S7, S8), towards the S11 and S15 samples. Furthermore, the comparison with the historical data of the selected springs showed that the systematic enrichments of alkali elements Na and K, relative to alkaline earth metals Ca and Mg, occurred in the past (Figure S1) [36; 37; 43; 87; 88; 89; 90]. Regardless, the main chemical constituents alone are not enough to explain the hydrogeochemical processes to quantify deep components and their influence on each spring. With the aim of identifying both chemically and physically the deep fluid end-member, in this paragraph, we will focus on: (i) the reconstruction of thermodynamic balances through the application of different geothermometers; (ii) the study of the possible water-rock interaction processes through the analysis of some conservative elements; (iii) the determination of the origin of free and dissolved gases; and (iv) the connection between deep and shallow aquifer systems through the study of the relationship between the geochemistry of groundwater and neotectonics. Some relevant chemical data are reported in Table 1.  
The evaluation of the deep temperature in low enthalpy carbonate-evaporitic systems (T \(<\) 150 \({}^{\circ}\)C) is frequently a demanding challenge [91]. Regarding central Italy, several approaches using chemical geothermometry have been proposed [91; 92; 93; 94; 95]. Recently, the temperatures inferred by the Na-Li ratio offered results consistent with those obtained from multicomponent geochemical models [33]. In this study, the Na-Li inferred temperatures by the [96] equation gradually increase as the contribution of deep inorganic carbon, traceable by the \(\delta^{13}\)C\({}_{\text{ext}}\) parameter, increases (Figure 4; Figure S2). Taking into account the absolute uncertainties of this kind of geothermometer (\(\pm\) 20 \({}^{\circ}\)C) [96], negative results on waters with shallower circulation in the heterothermic zone of a karst system such as S7 are not as astrushing (Figure 4) [97]. In contrast, most of the spring samples at \(\delta^{13}\)C\({}_{\text{ext}}\)\(>-\)5% seem to have a relevant deep contribution and/or circulation in the deep homothermic zone affected by the local geothermal gradient, with a temperature that can be inferred by the Na-Li geothermometer and clustering around the low-high enthalpy limit [33] (T = 150 \({}^{\circ}\)C, see Supplementary File Table S1). We did not measure the \(\delta^{13}\)C(DIC) parameter in some springs (S6, S8, S10, S12, S13, and S15). However, an analysis of historical data reveals how the S10 spring (Peschiera) falls close to the abovementioned \(\delta^{13}\)C\({}_{\text{ext}}\) divide of \(-\)5% (\(\delta^{13}\)C\({}_{\text{ext}}\) = \(-\)6.6 \(\pm\) 1.2%) (Figure 4; Figure S2), confirming the involvement of both shallow and deep fluids [33; 36; 43; 89].