# New Insights on the Seismic Activity of Ostuni (Apulia Region, Southern Italy) Offshore
## 6 Stress Regime  
As we discussed in the Introduction, information on stress field orientation and seismogenic sources for Southern Apulia is lacking in the Italian catalogs, and an effort is needed to fill in this gap. A crucial parameter that provides information about regional tectonics and deformation mechanisms is the stress axis orientation, which can be retrieved using different techniques based on focal mechanisms. To obtain an estimate of the orientation of the stress tensor, we performed the inversion of stress field orientation by applying the FMSI (Focal Mechanism Stress Inversion) code developed by [PERSON] [52; 53]. This inversion method can retrieve four of the six independent components of the stress tensor, commonly represented by the directions of the three principal stress axes (\(\sigma\)1, \(\sigma\)2 and \(\sigma\)3) and a dimensionless parameter R = \((\sigma 2-\sigma 1)/(\sigma 3-\sigma 1)\), which constrains the shape of the stress ellipsoid and ranges between 0 and 1. The angular difference between the shear stress on the fault plane, computed by the stress tensor inversion, and the observed slip direction on the same fault plane, obtained by focal mechanisms, measures the discrepancy (or misfit) between the data and the model. The dataset consists of the trend and plunge angles of the T and P axes, as obtained by FPFIT inversion. To better constrain the stress values obtained by the inversion, we adopted a weighting scheme given by the weight, W, which takes into account the quality of the focal mechanism solution, described by Qf and Op, and the event magnitude (taken as reported in Table 1). The Qf and Op of each focal mechanism solution (Table 4) are converted from letters to numbers, according to Table 6. Earthquake magnitude is included in the value of W on the hypothesis that the regional stress should be better represented by main earthquakes since small earthquakes may represent stress accommodation near the seismogenic source of the main event. We assigned W values that decrease with the quality factors of the focal mechanism inversion and increase with the earthquake magnitude. We then assigned a weight, W, to each fault plane solution in Table 4 as a function of the total quality factor, Qt = Qf + Qp + M, according to Table 7.  
The acceptability and homogeneity of the stress inversion solution was evaluated following the procedure of [PERSON] et al. [54], based on the simultaneous satisfaction of two criteria. The first requires that the 95% confidence intervals of \(\sigma\)1 and \(\sigma\)3 do not overlap for the solution to be acceptable. The second accounts for the degree of heterogeneity of the investigated medium, requiring that the misfit angle be under a certain threshold (misfit \(<6^{\circ}\)) to consider a solution to be homogeneous. The result is shown in Figure 9. The 95% confidence interval of the solution is very narrow, and the misfit = 2.4\({}^{\circ}\) indicates homogeneity of the medium. The stress ratio of R = 0.5 indicates that \(\sigma\)2 has a value exactly intermediate, and the misfit = 2.4\({}^{\circ}\) indicates a \begin{table}
\begin{tabular}{c c} \hline
**Qf = A, Qp = A** & **Qf = B, Qp = B** & **Qf = C, Qp = C** \\ \hline
3 & 2 & 1 \\ \hline \end{tabular}
\end{table} 
Table 6: Weighting criteria assigned to the fault plane solution in the FMSI inversion. \begin{table}
\begin{tabular}{c c} \hline
**Qt** & **Weight W** \\ \hline Qt \(<\) 4.5 & 3.0 \\ Qt \(\geq\) 4.5 & 4.0 \\ Qt \(\geq\) 5.5 & 5.0 \\ Qt \(\geq\) 6.5 & 6.0 \\ \hline \end{tabular}
\end{table} 
Table 7: Relative weight as a function of the total quality factor (Qt). high degree of homogeneity of the solution.