GNGTS 2023 - Atti del 41° Convegno Nazionale

Session 3.3 ______ ___ GNGTS 2023 boundary conditions, and the computational resources. The other settings were specific for each algorithm and were chosen following the most recent findings for GA (Pace et al. 2022), PSO (Pace et al. 2019) and GWO (Mirjalili et al., 2014) applied to geophysical data. A field case study The methods were first validated on a synthetic example of noise-corrupted data and then applied to two field surveys located in Italy. One field case study is a TDEM sounding located in Stupinigi (Torino district area) acquired for groundwater prospection over a known stratigraphy (coming from a close borehole). The TDEM acquisition was a coincident loop of 50 m length for the loop size. The time range of acquisition was 10 -5 –10 -3 s. The 1D model was discretized into 19 layers, whose thickness logarithmically increased with depth. The number of iterations was 500 for PSO and GWO, and 800 for GA since we observed insufficient convergence and minimization. The number of individuals (GA), particles (PSO) and wolves (GWO) were 170, for a proper solution exploration. The boundary conditions of the search space were 1 and 500 Ω m. Each algorithm was independently run 10 times or trials to inspect the variability of the equivalent final solutions and then highlight the solution with the minimum nRMSE. The outcomes of GA, PSO and GWO are shown in in Figs. 1b, 2b and 3b, respectively. The final data misfit (nRMSE) was 0.0764 for GA, 0.0618 for PSO, and 0.0619 for GWO. The lowest runtime and nRMSE were achieved by PSO, while GA had the worst performance. The data fitting is satisfactory for the three methods. There is similarity among the solutions of the PSO and GWO trials, while they significantly differ for GA. Figure 3c plots the minimization of the objective function along the iterations for GA (black dots), PSO (blue dots) and GWO (pink dots). The trend of the PSO curve is gradual from the highest to the lowest value, meaning good balance between exploration and exploitation of the search space. GA and GWO show a stepped trend that decreases rapidly and becomes flat earlier than PSO, meaning a possible premature exploitation phase. Conclusions The performance of three different and widely adopted metaheuristic algorithms were analyzed for the optimization of TDEM data. The comparative analysis reveals that PSO and GWO perform better than GA. GA yields the highest data misfit and an ineffective minimization of the objective function. PSO and GWO provide similar outcomes in terms of both resistivity distribution and data misfits, possibly because they are based on the same computational principle known as Swarm Intelligence. The results prove compelling evidence that both the emerging GWO and the established PSO are highly valid tools for stochastic inverse modeling in geophysics, while GA appears to be less competitive than them.