Modern investigations of the subject of mechanics of earthquake faulting and its resulting consequences can be said to have begun with the seminal papers in 1964 and 1966 by B. V. Kostrov. We are therefore very pleased to introduce this volume to commemorate the ∼55th anniversary of the start of our subject. In 2017, the Societ‘a Italiana di Fisica (SIF) invited us to organize a school on the Mechanics of Earthquake Faulting under the umbrella of the International School of Physics “Enrico Fermi”, with support of the Istituto Nazionale di Geofisica e Vulcanologia (INGV). Course 202 was held at the Villa Monastero, Varenna, Lake Como, Italy, from July 2 to July 7, 2018, and was attended by speakers and participants from the four of the five inhabited continents of the world.

One of the most important goals of the school was to present the state of the art of the physics of earthquakes. It is obvious that it is not possible to perform laboratory experiments at the same spatio-temporal scale and with the same boundary conditions as real faults. Therefore, a multi-disciplinary scientific approach which combines laboratory inferences and mathematical models, together with analysis of recorded data from earthquakes, is essential to making progress in our understanding of this very destructive phenomenon. With the very rapid technological advances in computational power, technical facilities for laboratory experiments and high-quality broad-band data from seismological networks, the future of this subject looks very optimistic. We therefore welcome the opportunity to present the proceedings of the lectures presented at the school by some of the most distinguished scholars of this topic today.

The school was arranged into twelve main lectures, which cover widely the most challenging aspects of the mechanics of faulting. These were offered by the three directors (A. Bizzarri (INGV, Bologna), S. Das (University of Oxford) and A. Petri (CNR, Roma)) and by nine scientists of outstanding international fame (R. J. Archuleta (U.C. Santa Barbara), M.Bouchon (Université Grenoble Alpes), Y.-T. Chen (China Earthquake Administration, Beijing), W. L. Ellsworth (Stanford University), A. Kato (University of Tokyo), R. Madariaga (ENS, Paris), C. J. Marone (PennState University), F. Mulargia (Università di Bologna), and A. Schubnel (ENS, Paris). We also organized four short talks given by respected scientists from Israel and France (I. Lior and A. Ziv (Tel-Aviv University), B. Gardonio and H. S. Bhat (ENS, Paris)). A 21-poster session was included to offer advanced doctoral students and junior researchers the possibility to present and discuss their work with these distinguished scientists, as well as with each other. Overall, 50 students, young researchers and observers attended the school, coming from 15 Countries and of 18 different nations.

Bizzarri presented a comprehensive view of earthquakes that propagate spontaneously with rupture speed greater than the shear wave speed characterizing the medium in which the fault is embedded. He discussed the main differences, from theoretical and numerical points of view, existing between sub- and supershear theoretical earthquakes, by considering both the on-fault and the off-fault solutions, and their practical implications.

In her lectures, Das posed the fundamental basis of the inverse problem of earthquake rupture mechanics and then applied them to great subduction zone earthquakes as well as to large earthquakes on transform faults. The former included a detailed study of the rupture speed of the 2001 M_w 7.8 Tibet earthquake, which not only surpassed shear wave speeds, but almost reached the compressional wave speed of the medium. The latter elucidated that the occurrence of large and great earthquakes taking place in oceans implies that the oceanic crust is crumbling by fracture along pre-existing nearly normal conjugate faults, even in regions where the transform fault is no longer active.

In his lecture entitled “The evolution of fault slip rate prior to earthquake: The role of slow- and fast-slip modes”, Kato discussed the complexity of the nucleation stage of seismic ruptures. He showed that recent seismic and geodetic studies of foreshock sequences suggest that partial unlocking of the fault took place episodically through interplay between fast- and slow-slip modes before large earthquakes. He also stressed the importance of assessing the degree of criticality within fault segments adjacent to already ruptured portions.

The world of laboratory experiments was highlighted by Marone, who summarized results from laboratory experiments showing repetitive slow slip, described different friction laws for slow earthquakes and finally discussed the implications of the earthquake scaling laws.

Ellsworth thoroughly scrutinized the differences between the two hypotheses proposed to describe earthquake nucleation, namely, the preslip and the cascade models and highlighted how they take opposing views on the role of aseismic deformation in the nucleation process, as well as the prospects for prediction.

Petri focused on the dynamics of a laboratory spring-plate system, sliding upon a granular bed. Although distant from a seismic fault, this system presents all the hallmarks of critical systems, which are shared by several different physical phenomena including earthquakes. The idea that the dynamics of such systems spring from the presence of a (non-equilibrium) critical transition leads to seek their common features and stimulates to identify the essential mechanisms from which similar statistical properties emerge.

Chen shared with us his experience of the inversion of complex kinematic earthquake rupture processes, by summarizing the most prominent studies made in the past two decades in the analysis of the teleseismic and geodetic data for retrieval of the earthquake rupture process. Such information, released soon after the occurrence of destructive earthquakes, is now routinely being used by local authorities in the task of earthquake emergency response for such catastrophes.

Bouchon illustrated the behaviour of 65 large earthquakes and showed that most of those occurring along the plate interfaces are preceded by foreshocks, while intraplate earthquakes are less prone to foreshocks. He concluded that this difference supports the idea that slow slip of the plate interface precedes many large interplate earthquakes.

Near-field seismic radiation and dynamic inversion of large subduction (or megathrust) earthquakes was the subject of MadariagaâĂŹs lectures. It focused on two great Chilean earthquakes and showed that at low frequencies the ground spectra differ quite significantly from the usual Aki-Brune spectrum used in studies of the far-field spectral properties of earthquakes.

Finally, Mulargia gave a stimulating view of the problem of earthquake occurrence, recurrence and hazard. In particular, he suggested that the Probabilistic Seismic Hazard Assessment (PSHA) —which plays a fundamental role in the defence strategy from earthquake damage of most countries— ignores the physics of the earthquake faulting system and, as a result, PSHA estimates are essentially void of scientific significance and merely speculative.

The stunning location of Villa Monastero with its exceptional historical and cultural heritage, its superb gardens, as well as the charming and breathtaking atmosphere of the Como Lake, with its Manzoniana melancholy, provided a very pleasant backdrop for numerous informal discussions between the entire group of participants, and contributed to the extraordinary success of the school. The topics covered during the school gave a very clear picture of the actual state of the art of the physics of earthquake ruptures and, at the same time, provided a list of open issues and questions that are still under debate, thus providing young researchers with new scientific challenges for the years to come.

Finally, we wish to put on records our thanks to the SIF President, Prof. L. Cifarelli, for promoting this school, the only one to follow earlier schools on similar subjects in 1979 and 1982 —both of them co-directed by Prof. E. Boschi, who passed away while we were writing this preface— and to Dr. T. Pepe (INGV, Rome) for supporting the whole initiative and for his enthusiasm. We also want to acknowledge Dr. S. Topazio (INGV, Rome) for her preliminary help in the very early stages of the organization of the school, our Secretary, Dr. A. M. Loguercio (CNR, Rome) for her precious work, and the whole staff of the SIF (with a special emphasis to B. Alzani) for their invaluable and continuous support in the organization and management of the school.

A. Bizzarri, S. Das and A. Petri