Ebook: Mechanics of Earthquake Faulting

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

In this paper we will review the fundamental aspects of the supershear earthquake ruptures, i.e., events which propagate with speeds greater than the shear wave speed of the medium surrounding the fault. The rupture starts from an imposed hypocenter and then it spreads spontaneously (i.e., without imposed rupture speed) over the entire fault plane. The latter is characterized by a rheology described by the linear slip-weakening model, which analytically prescribe the evolution of the fault frictional as a function of the cumulated fault slip. The problem is solved numerically, by using two different finite-difference schemes, because it is not possible, even in homogeneous conditions, to solve the elastodynamic problem in an analytical, closed form. We will discuss the main differences exsisting between sub- and supershear synthetic earthquakes, by considering both the on-fault and the off-fault solutions. The results presented here summarizes the most prominent and recent researches in this field, as well as the seismological implications.

According to the classical theory of plate tectonics, oceanic transform faults do not usually have “large” or “great” earthquakes. In this paper, we discuss several transform fault earthquakes, some now moved into unusual tectonic settings due to plate motion, which did have earthquakes lying in the magnitude range 7.8 ≤ M_w ≤ 8.1. The 2004 M_w8.1 earthquake occurred on a fossil fracture zone in the Tasman Sea. The 2000 M_w7.8 earthquake occurred in the Wharton Basin and ruptured two conjugate faults simultaneously. The largest known strike-slip earthquake in 2012 (M_w8.6) occurred off the coast of Sumatra and ruptured cross-cutting faults. An oceanic strike-slip earthquake in 1998 with M_w8.0 occurred on the Antarctic plate, but on a fault parallel to the ridge and nearly normal to the transform faults that is, it occurred on the ridge fabric! All these earthquakes together with the 2012 twin earthquakes (M_w8.6 and 8.2) in the Wharton Basin, the 1987–1992 (6.8 ≤ M_w ≤ 7.8) Gulf of Alaska sequence and the M_w7.9 2018 Gulf of Alaska earthquakes, show that the oceanic lithosphere is breaking up along the ridge-transform conjugate fault systems under tectonic stresses.

The earthquake nucleation process is inherently complex, due to an involvement of several deformation mechanisms with multiple spatial and time scales. Natural fault hosts a wide spectrum of slip rate from fast- to slow-slip. Before large earthquakes, the number of smaller magnitude events often increases, retrospectively named foreshocks. Foreshock can be interpreted to be a physical process implying unlocking of fault by fast-slip mode. Recent seismic and geodetic studies of foreshock sequences suggest that partial unlocking of fault took place episodically through interplay between fast- and slow-slip modes before some large earthquakes such as the 2011 Tohoku-Oki, the 2014 Iquique and the 2016 Kumamoto earthquakes. The partial unlocking causes stress loading onto the nearby critically loaded fault segments, resulting to triggering of subsequent dynamic and unstable slip. Alternatively, the partial unlocking of fault enhances the strength weakening of the earthquake nucleation area through slip invasion or fluid migration, that ultimately initiates the subsequent dynamic rupture. However, the manner of the unlocking is “episodic”, not “smooth acceleration” which has been typically observed as nucleation phase in laboratory experiment and numerical simulation model having simple fault zone structure. This episodic manner precludes a possibility of forecasting the subsequent large earthquake with a high degree of accuracy. The triggering of a subsequent large earthquake on nearby fault segments depends on the areal extent of the critically loaded seismic patches and how close these areas are to failure, even though the partial unlocking by both fast- and slow-slip processes is observed. An important research area is the development of methods for assessing the degree of criticality within fault segments adjacent to already ruptured portions. In addition, earthquake triggering probability by slow-slip transient shall be incorporated into operational earthquake forecasting scheme as future challenge, especially during the latter phase of the inter-seismic periods.

Earthquake science is in the midst of a revolution. Our understanding of tectonic faulting has been shaken to the core by the discovery of seismic tremor, low frequency earthquakes, slow slip events, and other modes of fault slip. These phenomena represent modes of failure that were thought to be non-existent and theoretically impossible only a few years ago. Despite the growing number of observations of slow earthquakes and the fact that they can trigger catastrophic large earthquakes their origin remains unresolved. Basic questions remain regarding how slow ruptures can propagate quasi-dynamically, at speeds far below the Rayleigh wave speed, and how tectonic faults can host both slow slip and dynamic earthquake rupture. Here, I summarize results from laboratory experiments showing repetitive slow slip, describe friction laws for slow earthquakes, and discuss implications of the work for earthquake scaling laws. The lab results suggest that slow earthquakes occur for conditions near the stability boundary defined by the critical fault rheologic weakening rate Kc and that the spectrum of fault slip behaviors can be described with a single frictional mechanism. Other processes may contribute to the origin of slow earthquakes but the work summarized here shows that slow and quasi-dynamic fault slip can occur entirely as a result of frictional processes and fault zone heterogeneity.

Earthquakes begin without any obvious sign of their coming. Two hypotheses have been advanced to describe the underlying physical processes that lead to their nucleation. These are the preslip and cascade models which take opposing views on the role of aseismic deformation in the nucleation process as well as the prospects for prediction. In this paper, foreshocks, the small earthquakes that sometimes precede larger ones, and the initial seismic wave radiation of the earthquake itself are used to examine how earthquakes nucleate and grow. Earthquake are found to begin abruptly and grow irregularly, consistent with laboratory-derived predictions for limited aseismic slip and in agreement with the predictions of the cascade model.

These lectures illustrate laboratory experiments investigating a spring-slider system shearing a granular bed. When the shear rate is low enough, the dynamics is intermittent, displaying a chaotic stick-slip motion which can only be described statistically. This is an instance, among many others, of systems exhibiting intermittent and erratic activity, in the form of avalanches characterized by self-similar fluctuations of physical quantities in a wide range of values. In analogy with equilibrium systems, it is thought that such properties originate from the vicinity of some critical transition, and therefore that systems microscopically very different could display similar and universal statistical properties. Investigation of such systems is thence not only interesting in itself, but can be of help in understanding the dynamics of a wider class of phenomena and in devising effective models.

We present the theory and methods of earthquake rupture process inversion by using seismic and geodetic data, and their applications to scientific researches and earthquake emergency responses. It is shown that the knowledge obtained from these studies has much improved our understanding of the complexities of the earthquake source and causative mechanism of the earthquake disaster, and is of important reference value in earthquake disaster mitigation such as rapid earthquake emergency response. Especially since the 2008 M_w7.9 (M_S8.0) Wenchuan, Sichuan, earthquake, fast and routine determination of the earthquake rupture process has been performed for significant earthquakes (M_S ≥ 6.5 in China and M_S ≥ 7.5 worldwide), and the results obtained are timely reported to the au- thorities and released to the public on the web site. The time consumed by the inversion has been reduced from more than 5 hours in 2009 to approximately 1–3 hours at present. The timely released rupture model was routinely used by the China Earthquake Administration and other authorities during the earthquake emergency responses period for destructive earthquakes, such as the 2010 M_w6.9 Yushu earthquake, the 2013 M_w6.6 Lushan earthquake, the 2014 M_w6.1 Ludian earthquake, and the 2015 M_w7.8 Gorkha, Nepal, earthquake, among the others.

Many earthquakes are preceded by foreshocks. However, the mechanisms that generate foreshocks and the reason why they occur before some earthquakes and not others are still poorly understood. We investigate here the evolution of seismic activity before 65 large earthquakes which have occurred in well instrumented areas. We show that most of the earthquakes occurring along the plate interfaces are preceded by foreshocks. Intraplate earthquakes which result from the internal deformation of the plates are less prone to foreshocks. This difference supports that slow slip of the plate interface precedes many large interplate earthquakes. Within this group a large difference exists in the spatial distribution of foreshocks: While foreshocks to transform fault earthquakes tend to localize close to the future hypocenter, those preceding subduction earthquakes are often spread over a broad area of the plate interface, suggesting that these earthquakes are preceded by the slow slip of a large patch of the subduction interface.

We have studied the spectra of several large earthquakes in the Chilean subduction zone using both accelerograms and CNSS instruments. For the two events studied here, the Iquique M_w 8.1 earthquake of 24 April 2014 and the M_w 6.9 Valparaiso earthquake of 24 April 2017 we observe similar features. For these earthquakes the velocity records at low frequencies obtained by integrating accelerograms agree quite well with the ground velocity derived from GNSS records at the same sites. These observations show 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. The most important difference is that at short distances the near-field term of the source dominates the spectra at low frequencies. The near-field term in seismic radiation is proportional to the moment time function of the source which is very different from the moment rate function that controls farfield. The ground velocity spectrum is flat at low frequencies and proportional to the static displacement produced by the earthquke at the observation site. The displacement spectrum on the other hand has a low-frequency asympote proportional to omega – 1 instead of the usual flat spectrum predicted by the Aki-Brune model. More theoretical work is needed to identify the region where the near-field spectrum dominates.

Probabilistic Seismic Hazard Assessment (PSHA) plays a fundamental role in the defence strategy from earthquake destruction of most countries. In light of this paramount importancePSHA 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 expect. 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 substantial improvement comes from appropriately basing estimates on earthquake physical phenomenology, and realistically evaluating and reporting all uncertainties.