## 4 Discussion
Then normal-fault quakes and oblique flat or low-angle thrust earthquakes are the most sensible to tidal stress changes [40];
* Lithostatic loading increases with a vertical gradient equal to \(\sim\)27 MPa/km, so that confinement stress requires higher and higher energy activation for fracturing (weassume to investigate only crustal volumes above the BDT). If pore pressure is neglected, as a first approximation, earthquakes become less and less susceptible both to ocean and to solid tidal loading with increasing depth;
* Tesseral, sectoral, and zonal components of solid tides reach different amplitudes depending on the latitude, and therefore the intensity of the phenomenon is more or less evident depending on the location. To perform a reliable statistical analysis  
\[N\approx\left(\frac{k\sigma_{n}}{\Delta\sigma_{s}}\right)^{2}\approx 10^{3} \tag{33}\]  
events are required if we assume \(\sigma_{n}\sim 1\)-10 MPa, \(\Delta\sigma_{s}\sim 0.1\)-1 kPa and \(k\sim 10^{-3}\) (compare with [10], p. 12). This means that only high-quality and extended seismological networks can provide an adequate amount of information for our research. Microseismicity strongly correlate with the phase of tidal loading (e.g., [41]), but we neglected this phenomenon in the present work to focus on tectonic earthquakes. Several studies proved a strong sensitivity of seismicity to stress changes of both endogenous and exogenous origins (e.g., [42]). For this reason, Coulomb failure stress was applied to correlate its variations with changes in aftershocks productivity. A difference between static and dynamic Coulomb stress is conventionally done: when loading is slow, so that its increasing/decreasing rate is negligible with respect to the compared time interval, then the static Coulomb stress is at work, on the contrary, if loading occurs suddenly (i.e., fluid injection,oseismic slip), then the dynamic Coulomb failure stress plays a relevant role. In general, the strain produced by earthquakes induces dynamic Coulomb stress swings that, at long distances, can be even an order of magnitude larger than the static stress changes. There is a nonlinear dependence of the time to instability on stress variations [14]; this not only means that seismic rate is a direct effect of loading, but also implies that small additional stress can result in highly unpredictable states of crustal instability. From a mathematical viewpoint, these properties can be summarized in the seismicity rate \(R(t)\) equation, which, in the simplest form, reads [43]  
\[R(t)=\frac{R_{0}}{1+e^{-\frac{t}{t_{A}}}\left(e^{-\frac{\Delta CFS}{\Delta \sigma_{n}}}-1\right)} \tag{34}\]  
Figure 6: Power spectrum of European seismicity (M \(>\) 5.0, 1106–2006, SHEEC catalogue). Tidal periodicities are detected in the recurrence times of intense seismicity in Europe. nuFFT is used for the calculation to take into account progressive decrease of completeness magnitude. where \(R_{0}\) is initial seismic rate, \(\mathcal{A}\) is a constitutive parameter, and \(t_{A}\) is the duration of the loading. In brief, observations suggest that seismicity rate can be influenced by both static and dynamic perturbations. If static stress changes act on crustal stability modulating earthquake occurrence, then seismicity rates might be influenced by the Solid Earth tides, caused by the pull of both the Sun and Moon, even though rather weak with respect to tectonic stress. This is the reason why a research looking for tidal static stress loading signatures along the seismic cycle is meaningful and the results showed in this work can be reliable. The case studies we consider suggest that clustered shallow seismicity tends to occur in correspondence with positive values of the correlation \(\rho\) between nucleated seismic energy and \(\Delta\)CFS. The correlation values show progressive growth before major seismic sequences, while they fall while seismicity is ongoing. Preslip, in agreement with [44], and aftershock activity are also both associated with the lowering of correlation values.