Earthquake occurrence, recurrence and faulting

Probabilistic Seismic Hazard Assessment (PSHA) plays a fundamental role in the defence strategy from earthquake damage of most countries. In light of this paramount importance, PSHA should be rooted on solid ground but it is not, since it ignores earthquake Physics starting from its most important phenomenological features. These are scale invariance, which allows to infer the behaviour of large earthquakes from smaller seismicity for which copious data are available, and clustering in time and space, which states that the more earthquakes one sees the more he should ex- pect. The latter is just the opposite of the Characteristic Earthquake, ubiquitously used in Seismology and Geology under the paradigm of elastic rebound. As a consequence, PSHA estimates are essentially speculative and void of scientific significance. In practical terms, while PSHA has the merit of raising attention on an important problem, its faulty physical and statistical premises lead it to untrustworthy results. A first substantial improvement may come from appropriately basing estimates on earthquake physical phenomenology, and realistically evaluating and reporting all uncertainties.