## 2 Materials and Methods
### Seismological Methods: Focal Mechanism, Source Spectra and Static Displacement  
To determine the seismic source geometry, we used the program FPFIT [28] which performs a grid-search of double-couple focal mechanism solutions. The search algorithm uses the P- and S-wave polarities (up or down) and takeoff angles, azimuths, and source-station distances obtained from a location procedure. The earthquakes' location has been obtained with a probabilistic 3D method developed by [PERSON] et al. [29] and based on nonlinear optimization. FPFIT provides the strike, dip and rake of the most reliable focal mechanism and the uncertainties associated with each parameter. In the caption of Table 1 the convention on the geometrical parameters is reported. To estimate the source dimensions and the net slip on the fault, we used a classical approach [30]. The amplitude spectra of the direct S-waves, estimated through Fast Fourier Transform of the ground displacement possibly corrected for propagation and site effects, were used to estimate the scalar seismic moment, M0, and the corner frequency, f0. Considered a pulse-like source shape, at the limit of the low-frequency asymptote and for a constant moment time rate, M0 can be estimated as [31]:  
\[\text{M0}=\frac{4\pi\rho_{0}^{1/2}\rho_{\text{x}}^{1/2}\rho_{0}\beta_{0}^{5/2 }\beta_{\text{x}}^{1/2}\text{R}\Omega_{0}}{2\text{Y}_{\Theta\phi}} \tag{1}\]  
where \(\rho_{0}\) and \(\rho_{\text{x}}\) are the medium densities of the source and receiver regions, respectively, \(\beta_{0}\) and \(\beta_{\text{x}}\) are the shear-wave velocity at the source (Haskell model) and receiver, respectively, R is the hypocentral distance, \(\Omega_{0}\) is the S-wave radiated energy at the limit of low-frequency asymptote, the factor 2 takes into account the free surface contribution and \(\text{Y}_{\Theta\phi}\) is the radiation pattern (0.55, the average over the focal sphere). The corner frequency, fc, can be calculated as the intersection of the low- and high-frequency asymptotes in a loglog plot of the source spectra [30]. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Origin Time** & **Latitude N** & **Longitude E** & **Depth 1** & & & & \\ (yyyyymmdd hh:MM s) & (deg min) & (deg min) & (km) & **MD** & **Strike 2** & **Dip 3** & **Rake 4** \\ \hline  
(-\)0.45 & 2.1 & 20 & 35 & 0 \\ \hline \hline \end{tabular} 1
[FOOTNOTE:1]Footnote 1: Depth is negative above sea level and positive downwards. 2  
Strike is measured clockwise from North. 3  
Dip is measured down from horizontal. 4  
Rake of 0 = left lateral, 90 = reverse, \(\pm\)180 = right lateral, \(-\)90 = normal.  
\end{table} 
Table 1: Earthqu’ origin time, epicenter location, focal depth and source kinematic parameters. Assuming a constant fault rupture velocity \(\beta\)r and no directivity effects, the linear dimension of the source can be estimated as L = (0.37 * \(\beta\)r/fc) (Brune radius). To estimate the net slip on the fault we used the relation [30]:  
\[\overline{u}=\frac{M0}{\mu L^{2}} \tag{2}\]  
\(\mu\) is the rigidity, that we calculated as \(\mu\) = E/(2 * (1 + \(\sigma\))), where E is Young's modulus. Displacements and strains due to shear and tensile faults, in a half-space for both point and finite rectangular sources in a homogeneous elastic and Poissonian half-space, can be estimated following the approach of Okada [32]. Taking into account the body force equivalent relations, the internal displacement field, due to a dislocation across a surface in an isotropic medium, can be expressed by a combination of the displacement fields (u) due to the strain nuclei (\(\partial\dot{u}/\partial\dot{k}_{\lambda}\)). Internal deformation field formulas are then derived for strike, dip, tensile and inflation sources, as functions of fault length along the fault strike direction (L), width along the perpendicular direction to the strike (W), and elastic moduli (E and \(\sigma\)). To estimate the static displacement generated by the VTs, we used Coulomb [23; 24], a software developed in Matlab environment [33].