**4. Discussion**

Tidal triggering of earthquakes is still a debated theme in Solid Earth Geophysics. In particular, there are three sources of discussion among geophysicists:

•From a statistical viewpoint, earthquake catalogs are often insufficient to detect significant modulations of seismic activity over time.

Tides are tiny perturbations of the gravitational field (0.1–100 kPa) with respect to typical earthquake stress drops (1–50 MPa), but nonetheless they are able to generate significant stress variation rates ( ∼100 mbar/day compared with 1–10 mbar/day due to tectonic stress, [39]). However, the actual impact on the stability of rock volumes largely depends on the tectonic setting, the spatial orientation of the fault, the depth, and the hypocentral latitude; finally, also the magnitude of the impending event modifies the response of the system to the tidal perturbation. Therefore, a wide range of results were found in several geographical regions.

•It is sometimes difficult to distinguish between the effects of Solid Earth tides from those of ocean tides. Even though the stress amplitude of liquid tides (up to 100 kPa) often exceeds that of the Solid Earth tide (usually ∼0.1–1 kPa), the mechanism of action is quite different. In the first case, tides are concentrated on limited surfaces, at most of the order 10<sup>5</sup> km2, and act mainly through the *σrr* vertical component, which is transmitted to the horizontal components (almost symmetrically) thanks to the elastic properties of the lithosphere. However, the incremental stress decreases exponentially as depth increases, therefore it can strongly modulate shallow oceanic small magnitude seismicity, for example, at ocean ridges or submarine volcanoes, but it is unlikely that intermediate and deep earthquakes might be triggered by liquid tides.

Solid tides, on the other hand, deform the outer layers of the planet mainly in the horizontal components, acting on very large surfaces. For this reason, solid tides have a dominant role in triggering earthquakes except for the just cited peculiar cases. For these reasons, liquid tides are neglected in this work.

• Seismic response to tidal loading strongly depends on the duration of earthquake nucleation.

Beyond the aforementioned issues, well-established scientific evidence exists about tidal synchronization in seismic catalogs, as already discussed in the introduction. Both global and regional seismic series show semiannual, annual, biennial, with approximately 9-, 19-, 37-, and 56-years-long periods activity modulations. While the first three frequencies are generally associated with seasonal patterns, the others have no explanation other than lunisolar tidal loading. The FFT of European magnitudes (SHEEC 2020 catalogue) in Figure 6 clearly attests this phenomenon. Since M*c* ≈ 6 for the SHEEC catalogue, the nonuniform FFT is applied to include at least <sup>M</sup>*wdef* > 5.0. Instrumental recordings are rarely available before the 1950s also for violent earthquakes, and therefore, macroseismic intensity data are widely used combined with epicentral macroseismic intensities and other parametric data sources. Therefore, parametric catalogs must be used with caution and results must be interpreted according to their reliability. Even if an accurate analysis cannot be performed for the aforementioned reasons, the power spectrum of the European seismicity shows typical tidal frequencies such as 8–10- or 18–19-years-long periodicities and some multiples. Moreover, local seismic rates are noticed to be directly correlated with the phase of tidal shear stress or the Coulomb failure stress change in submarine volcanic seismicity [31] and seismic tremors [6]. Finally, it is reasonable to expect that the triggering power of tides is affected by the following variables:


assume 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.

**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.

To perform a reliable statistical analysis

$$N \approx \left(\frac{k\sigma\_{\rm n}}{\Delta\sigma\_{\rm s}}\right)^2 \approx 10^3\tag{33}$$

events are required if we assume *σn* ∼ 1–10 MPa, Δ*σs* ∼ 0.1–1 kPa and *k* ∼ 10−<sup>3</sup> (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, coseismic 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]

$$R(t) = \frac{R\_0}{1 + e^{-\frac{t}{\tau\_A}} \left(e^{-\frac{\Lambda CFS}{\mathcal{A}v\_n}} - 1\right)}\tag{34}$$

where *R*0 is initial seismic rate, A is a constitutive parameter, and *tA* is the duration of the loading.

In brief, observations sugges<sup>t</sup> 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 sugges<sup>t</sup> that clustered shallow seismicity tends to occur in correspondence with positive values of the correlation *ρ* between nucleated seismic energy and ΔCFS. The correlation values show progressive growth before major seismic sequences, while they fall while seismicity is ongoing. Preslip, in agreemen<sup>t</sup> with [44], and aftershock activity are also both associated with the lowering of correlation values. On the contrary, *ρ* seems to increase during quiescent periods, which is compatible with [45]. We think that locked faults become more and more sensitive to stress perturbation as they reach the breaking point, which can provide a simple explanation to the observed trends of *ρ*.

In summary, we develop a method to highlight the different phases of the seismic cycle in fault systems by studying their response to a well-known stress perturbation, i.e., tidal stress. Even though seismic prediction was considered impossible [46], no theoretical reason prevents it. Since the physics of fracture at seismological spatio-temporal scale is still poorly understood and no unique mechanism for nucleation was proven to exist, then seismic precursors cannot be effective in predicting impending earthquakes. By the same token, it is unlikely that the probability of occurrence of single earthquakes may ever be reliably assessed. However, it was proven, also in this article, that fault systems change their mechanical response during the different phases of seismic activity, which is certainly not sufficient for forecasting, but it can be used to understand whether fault systems are evolving towards instability. Our analysis shows that a preseismic phase is observed before large and intermediate (M*w* 5) shallow (depth ≤ 50 km) earthquakes. Therefore, our advances achieved in this research are significant, with a potential impact on seismic hazards. In addition, they provide new insights for the comprehension of the relationship between stress perturbations, earthquake nucleation, and seismic sequences, which are still to be fully investigated.

**Author Contributions:** Conceptualization, D.Z. and C.D.; methodology, D.Z. and L.T.; data analysis, D.Z.; writing—original draft preparation, D.Z.; writing—review and editing, C.D. and L.T.; supervision, C.D. and L.T. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by ESA through the TILDE Project.

**Data Availability Statement:** We used free data available at several seismological catalogs, as written inside the text.

**Acknowledgments:** Discussions with G. Nico, F. G. Panza, F. Ricci, and F. Vespe were precious.

**Conflicts of Interest:** The authors declare no conflict of interest. This work was developed as part of the TILDE project, ESA. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.
