A technical-disclosure guide to the EqForecast model.
Autore: Stefano Calandra, ORCID: https://orcid.org/0000-0001-5324-2298
1. Introduction: a new key to understanding earthquake risk
What triggers an earthquake? It is not enough to know where an active fault is located, or how much stress is building up underground.
It also needs to understand when this energy can be released. The EqForecast model proposes an original key supported by astronomical and geophysical data: the timing of seismic triggering may be related to external gravitational forces, generated not only by the Moon and Sun, but also by the seven planets of the Solar System. These forces act on a large scale, but with localized effects when the Earth’s crust is in critical condition. These forces do not directly cause an earthquake, but they can act as the final trigger in an already critical geological system. In particular, the EqForecast model distinguishes between the horizontal components of tidal forces, linked to the load state of the system, and the vertical components, which can modulate the lithostatic load and promote triggering only when specific dynamic conditions are met.
2. Planetary forces involved and when they become dangerous
The core of the EqForecast model is based on the analysis of the resulting gravitational force generated by Mercury, Venus, Mars, Jupiter, Saturn, Uranus, and Neptune.
The most effective configuration (termed “line 3”) temporarily excludes Sun and Moon to improve statistical consistency with an observed polynomial theoretical curve (Calandra & Teti, 2024)¹. This does not mean that Sun and Moon are unimportant, but that the modeling is cleaner and smoother when excluding these two celestial bodies, whose influence is more unstable on a local scale.
In this first study, we calculate the gravitational force that each pair of planets exerts on a point in the Earth’s crust and then analyze its variation σ (sigma) in the 24- and 48-hour time windows (Parameters B and A, in the study). It is essential to clarify that EqForecast does not take into account the absolute intensity of gravitational forces, since these alone are physically insignificant in terms of moving a fault. In fact, an earthquake releases energies vastly greater than those exerted by any single celestial body: for example, a magnitude 6 event releases about 10¹⁵ joules, while the mechanical work directly associated with the local variation in lunar gravitational pull is on the order of 3 × 10⁻⁵ joules, enough to lift just 1 milligram of mass one meter. The EqForecast model therefore exclusively analyzes the relative temporal variation of the resulting gravitational force, which represents a dynamic indicator of the stress state of the system. This variation integrates both the horizontal and vertical components of the tidal forces. In this scheme, stress accumulation is mainly associated with horizontal components, while the physical mechanism of seismic triggering is generally linked to the vertical component, which modulates the lithostatic load once the horizontal stress threshold has been reached. Strong correlations were observed between seismic triggers and moments when the gravitational force is:
- extremely stable (very low σ variation, where σ is the symbol for standard deviation, i.e., the indicator of force stability over time), or
- highly unstable (very high σ variation). In either case, the crust may be subjected to anomalous stress that alters the equilibrium state of already stressed faults.
3. How the energy of an earthquake builds up and how it can be triggered
According to Doglioni et al. (2020)², horizontal tidal forces, exerted mainly by the Sun and Moon, contribute in the long run to the accumulation of tectonic stress in faults. This stress corresponds to elastic potential energy, gradually accumulated by the deformation of rocks. The clods move, collide and drag, but the faults remain locked due to friction, accumulating energy over time.
The EqForecast model complements this view with the role of the vertical component of the tidal forces themselves, acting as a trigger. This vertical component would intervene at the moment of maximum stability or instability, calculated over time windows of 24-48 hours, of the resultant gravitational force exerted by the seven planets of the Solar System. Vertical forces do not slowly accumulate energy but operate as a triggering element (trigger), changing the normal pressure along the fault and thus promoting seismic initiation. When a fault is close to the critical rupture threshold, even a small change in the normal pressure across the fault plane can break the static equilibrium, transforming the stored potential energy into kinetic energy. Importantly, we do not know exactly the energy state of a fault, that is, the sufficient condition to predict with certainty the time and place of an earthquake. In this regard, the Previsio model developed by geologist Giulio Riga attempts precisely to calculate this critical energy threshold for numerous faults in Italy (Riga, 2015)³.
Since we cannot directly measure the energy state of faults, we rely on indirect data, such as astronomical data analyzed by the EqForecast model. This approach identifies necessary, but not sufficient, conditions for seismic triggering. This paper discusses only one part of the EqForecast model, related to the stability and instability of planetary gravitational forces; further aspects will be explored in subsequent publications. However, even integrating all this information, the EqForecast model can never provide an absolute deterministic prediction of the seismic event. It will always provide a range of assumptions regarding possible locations, timing, and magnitude, with alert time windows that, experimentally for earthquakes with magnitude greater than 4.7 Richter in Italy, cover about 3% of the year (approximately nine days) during which the event could occur. Therefore, the model will inevitably generate some false alerts, but the earthquake event will likely occur within the assumed range.
4. From theory to probabilistic prediction
The EqForecast model, by combining astronomical dynamics and fault physics, makes it possible to identify critical time windows for seismic triggering. Using calculations based on planetary orbits and the relative variation of the resulting gravitational force, EqForecast identifies the exact moments when this force, being particularly stable or unstable, can result in seismic triggering.
Thus, it is not simply a probabilistic prediction, but a deterministic approach based on the Galilean experimental method: through long cycles of repeated observations, The model identified a stable statistical relationship linking specific astronomical configurations with past seismic events, thus enabling it to predict, with high reliability, the time windows in which the seismic risk is concretely greater than the historical average. The system can be integrated with traditional seismological tools to strengthen monitoring and prevention in high-risk areas.
See also:
Bibliographical notes
¹ Calandra, S., & Teti, D. (2024). Correlation Study: Triggering and Magnitude of Earthquakes in Italy (≥ M4.3) in Relation to the Positions and Gravitational Forces of the Sun, Moon, and Planets Relative to Earth. NCGT – New Concepts in Global Tectonics Journal, 12(1), 26–52.
https://users.neo.registeredsite.com/6/9/1/18560196/assets/NCGTJournalV12N1Pub24435.pdf#page=28; DOI: https://dx.doi.org/10.13140/RG.2.2.15806.29762
² Zaccagnino, D., Vespe, F., & Doglioni, C. (2020). Tidal modulation of plate motions. Earth-Science Reviews, 205, 103179. https://doi.org/10.1016/j.earscirev.2020.103179
³ Riga, G. (2015). Il terremoto de L’Aquila di M 6.1 e i suoi precursori sismici. Disponibile su Academia.edu: https://www.academia.edu/14544250/Il_terremoto_de_LAquila_di_M_6_1_e_i_suoi_precursori_sismici
For further study
Those who wish to learn more can read the popular book by the author of this model, available at the link:
https://www.gruppoalbatros.com/prodotti/prevedere-i-terremoti-osservando-il-cielo-unincredibile-avventura-stefano-calandra/
The author’s full list of publications is available through his ORCID profile:
https://orcid.org/0000-0001-5324-2298